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Hooks are issued to and returned by employes, between the hours
of 11 a. m. and 2 p. m. on all days except Sundays.
The Library is open to employes, for reference, from 9 a. rn. till
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borrow books from toe Library.
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or of the Bureau or < office in which employed.
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borrower shall have been registered by the Librarian.
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to suspend or refuse the issue of books to the culpable persons.
By order of the Secretary:
GEO. A. HOWARD.
14520b—i m Ohief Clerk.




SMITHSONIAN
MISCELLANEOUS COLLECTIONS.
«
VOL. XXXIII.
EVERY MAN IS A VALUABLE MEIUEER OF SOCIETY WHO BY HIS OBSERVATIONS, RESEARCHES,
AND EXPERIMENTS PROCURES KNOWLEDGE FOR MEN."—SMITHSON.
WASHINGTON:
PUBLISHED BY THE SMITHSONIAN INSTITUTION.
1888.
PRINTED AND STEREOTYPED BY
JTJDD & DETWEILER.
AT WASHINGTON. D 0.
ADVERTISEMENT.
The present series, entitled "Smithsonian Miscellaneous Collec-
tions," is intended to embrace all the publications issued directly
by the Smithsonian Institution in octavo form ; those in quarto
constituting the "Smithsonian Contributions to Knowledge." The
quarto series includes memoirs, embracing the records of extended
original investigations and researches, resulting in what are be-
lieved to be new truths, and constituting positive additions to the
"um of human knowledge. The octavo series is designed to contain
reports on the present state of our knowledge of particular branches
of science ; instructions for collecting and digesting facts and mate-
rials for research ; lists and synopses of species of the organic and
inorganic world ; museum catalogues ; reports of explorations ; aids
to bibliographical investigations, etc., generally prepared at the ex-
press request of the Institution, and at its expense.
The assignment of a work to one or the other of the two series
will sometimes depend upon whether the required illustrations can
be presented more conveniently in the quarto or the octavo form.
In the Smithsonian Contributions to Knowledge, as well as in
the present series, each article is separately paged and indexed, and
the actual date of its publication is that given on its special title
page, and not that of the volume in which it is placed. In many
cases works have been published and largely distributed, years
before their combination into volumes.
S. P. LANGLEY,
Secretary S. I.
m

TABLE OF CONTENTS.
Article I. (543.) Bulletin of the Philosophical Society
of Washington. Vol. VI. For the year 1883.
Pp. 220.
Article II. (592.) Bulletin of the Philosophical Society
of Washington. Vol. VII. For the year 1884.
Pp. 194.
Article III. (636.) Bulletin of the Philosophical Society
of Washington. Vol. VIII. For the year 1885.
Pp. 115.
Article IV. (661.) Bulletin of the Philosophical Society
of Washington. Vol. IX. For the year 1886.
Pp. 113. And Vol. X. For the year 1887. Pp.
263.
NOTE.
With this volume
—
(containing the last five volumes of the " Bul-
letins of the Philosophical Society of Washington ")—is terminated
the reissue of these proceedings in the series of Miscellaneous
Collections. It may be stated that volumes 1, 2, and 3 of these
"Bulletins" formed Vol. XX of the Miscellaneous Collections.
Volumes 4 and 5 were included in Vol. XXV of the Miscellaneous
Collections. And, lastly, volumes 6, 7, 8, 9, and 10—together
with the Memorial Proceedings in honor of Prof. Baird, and a
full Index of the whole ten volumes—constitute the present Vol.
XXXIII of the Miscellaneous Collections.
(5j

BULLETIN
PHILOSOPHICAL SOCIETY
OF
WASHINGTON.
VOL. VI.
Containing the Minutes of the Society for the year 1883, and the
Minutes of the Mathematical Section from its organiza-
tion, March 29th, to the close of the year.
PUBLISHED BY THE COOPERATION OF THE SMITHSONIAN INSTITUTION.
WASHINGTON:
1884.

CONTENTS.
Page.
Constitution VII
Standing Rules of the Society ix
Standing Rules of the General Committee XII
Rules for the Publication of the Bulletin XIII
Officers elected December, 1882 xiv
Officers elected December, 1883 xv
List of Members, corrected to December 31, 1883- xvi
Annual Report of the Treasurer xxn
Annual Address of the President, J. W. Powell XXV
Bulletin of the General Meeting I
Experiments in binary arithmetic, H. Farquhar 3
Refraction in a triaxial ellipsoid, [Title only,) S. M. Burnett 4
Monochromatic aberration in aphakia, ( Title only,) W. Harkness 5
The nature of matter, {Title only,) H. H. Bates 5
Prevention of malarial diseases, A. F. A. King 5
Response of climate to variations of solar radiation, G. K. Gilbert- 10
Thermal belts of North Carolina, J. W. Chickering II
Geology of the Hawaiian Islands, C. E. Dutton 13
Substance, matter, motion, and force, ( Title only,) M. H. Doolittle_ 14
Formulas for the computation of Easter, E. B. Elliott 15
Florida expedition for observing transit of Venus, J. R. Eastman 21
Determining the temperature of the air, C. Abbe 24
Determination of specific gravity of solids, C. E. Munroe 26
Geology of Hatteras, W. C. Kerr 28
Topographical indications of a fault, H. F. Walling 30
Ore deposition by replacement, S. F. Emmons 32
Glaciation in Alaska, W. H. Dall 33
The Eucalyptus on the Roman Campagna, ( Title only,) F. B. Hough 36
Hygrometric observations, H. A. Hazen 36
Dreams in their relation with psychology, E. Farquhar 37
Recent experiments on serpent venom, [Title only,) R. Fletcher 38
Further experiments in binary arithmetic, H. Farquhar 38
Medallic medical history, W. Lee 39
III
IV CONTENTS.
Page.
Bulletin of Ihe General Meeting—Continued.
Note on the rings of Saturn, W. B. Taylor 41
Focal lines in astigmatism, (Title only,) S. M. Burnett 45
Thermometer exposure, H. A. Hazen 46
Ichthyological results of the Albatross, ( Title only,) T. N. Gill 48
Fallacies concerning the deaf, A. G. Bell 48
Seismographic record from Japan, (Title only,) E. Smith 87
The volcanic problem stated, C. E. Dutton 87
Drainage system and loess of eastern Iowa, W J McGee 93
Cambrian system in the United States and Canada, C. D. Walcott _ 98
Distribution of surplus money of the United States, J. J. Knox 103
An initial meridian and universal time, R. D. Cutts 106
Bulletin of the Mathematical Section 113
Rules of the Section 115
Members of the Section 116
Inaugural Address of the Chairman, A. Hall 117
A quasi general differentiation, (Title only,) A. S. Christie 122
Alignment curves on any surface, C. H. Kummell 123
Determination of the mass of a planet, A. Hall 132
Infinite and infinitesimal quantities, M. H. Doolittle 133
Graphic tables for computing heights, (Title only,) G. K. Gilbert 136
Computation of lunar perturbations, G. W. Hill 136
Units of force and energy, (Title only,) E. B. Elliott 137
Theory of errors tested by target shooting, C. H. Kummell 138
A special case in maxima and minima, B. Alvord 149
A financial problem, E. B. Elliott 149
A form of least-square computation, H. Farquhar 150
Note on problem discussed by Mr. Alvord, H. Farquhar 152
The rejection of doubtful observations, M. H. Doolittle 152
Special treatment of observation-equations, R. S. Woodward 156
Contact of plane curves, A. S. Christie 157
Committees on papers 161
Corrigenda to Vol. V. 162
Index 163
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
CONSTITUTION, RULES,
OFFICERS AND MEMBERS,
TREASURER'S REPORT.

CONSTITUTION
THE PHILOSOPHICAL SO0IETY OF WASHINGTON.
Article I. The name of this Society shall be The Philosophi-
cal Society of Washington.
Article II. The officers of the Society shall be a President,
four Vice-Presidents, a Treasurer, and two Secretaries.
Article III. There shall be a General Committee, consisting of
the officers of the Society and nine other members.
Article IV. The officers of the Society and the other members
of the General Committee shall be elected annually by ballot ; they
shall hold office until their successors are elected, and shall have
power to fill vacancies.
Article V. It shall be the duty of the General Committee to
make rules for the government of the Society, and to transact all
its business.
Article VI. This constitution shall not be amended except by
a three-fourths vote of those present at an annual meeting for the
election of officers, and after notice of the proposed change shall
have been given in writing at a stated meeting of the Society at
least four weeks previously.
vn

STANDING RULES
FOR THE GOVERNMENT OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The Stated Meetings of the Society shall be held at 8 .o'clock
p. m. on every alternate Saturday ; the place of meeting to be
designated by the General Committee.
2. Notice of the time and plaee of meeting shall be sent to each
member by one of the Secretaries.
When necessary, Special Meetings may be called by the President.
3. The Annual Meeting for the election of officers shall be the
last stated meeting in the month of December.
The order of proceedings (which shall be announced by the
Chair) shall be as follows
:
First, the reading of the minutes of the last Annual Meeting.
Second, the presentation of the annual reports of the Secretaries,
including the announcement of the names of members elected since
the last annual meeting.
Third, the presentation of the aunual report of the Treasurer.
Fourth, the announcement of the names of members who, having
complied with Section 13 of the Standing Rules, are entitled to vote
on the election of officers.
Fifth, the election of President.
Sixth, the election of four Vice-Presidents.
Seventh, the election of Treasurer.
Eighth, the election of two Secretaries.
Ninth, the election of nine members of the General Committee.
Tenth, the consideration of Amendments to the Constitution of
the Society, if any^ such shall have been proposed in accordance
with Article VI of the Constitution.
Eleventh, the reading of the rough minutes of the meeting.
ix
X PHILOSOPHICAL SOCIETY OF WASHINGTON.
4. Elections of officers are to be held as follows
:
Iu each case nominations shall be made by means of an informal
ballot, the result of which shall be announced by the Secretary
;
after which the first formal ballot shall be taken.
In the ballot for Vice-Presidents, Secretaries, and Members of the
General Committee, each voter shall write on one ballot as many
names as there are officers to be elected, viz., four on the first ballot
for Vice-Presidents, two on the first for Secretaries, and nine on the
first for Members of the General Committee ; and on each subse-
quent ballot as many names as there are persons yet to be elected
;
and those persons who receive a majority of the votes cast shall be
declared elected.
If in any case the informal ballot result in giving a majority for
any one, it may be declared formal by a majority vote.
5. The Stated Meetings, with the exception of the annual meet-
ing, shall be devoted to the consideration and discussion of scientific
subjects.
The Stated Meeting next preceding the Annual Meeting shall
be set apart for the delivery of the President's Annual Address.
6. Sections representing special branches of science may be
formed by the General Committee upon the written recommenda-
tion of twenty members of the Society.*
7. Persons interested in science, who are not residents of the Dis-
trict of Columbia, may be present at any meeting of the Society,
except the annual meeting, upon invitation of a member.
8. Similar invitations to residents of the District of Columbia,
not members of the Society, must be submitted through one of the
Secretaries to the General Committee for approval.
9. Invitations to attend during three months the meetings of the
Society and participate in the discussion of papers, may, by a vote
of nine members of the General Committee, be issued to persons
nominated by two members.
10. Communications intended for publication under the auspices
* Under this rule the Mathematical Section was organized March 29, 1883.
Its rules and proceedings follow the Bulletin of the General Meeting.
STANDING RULES. XI
of the Society shall be submitted in writing to the General Com-
mittee for approval.
11.* Any paper read before a Section may be repeated, either
entire or by abstract, before a general meeting of the Society, if
such repetition is recommended by the General Committee of the
Society.
12. New members may be proposed in writing by three members
of the Society for election by the General Committee ; but no per-
son shall be admitted to the privileges of membership unless he
signifies his acceptance thereof in writing within two months after
notification of his election.
13. Each member shall pay annually to the Treasurer the sum
of five dollars, and no member whose dues are unpaid shall vote at
the annual meeting for the election of officers, or be entitled to a
copy of the Bulletin.
In the absence of the Treasurer, the Secretary is authorized to
receive the dues of members.
The names of those two years in arrears shall be dropped from
the list of members.
Notice of resignation of membership shall be given in writing to
the General Committee through the President or one of the Secre-
taries.
14. The fiscal year shall terminate with the Annual Meeting.
15. f Members who are absent from the District of Columbia for
more than twelve months may be excused from payment of the
annual assessments. They can, however, resume their membership
by giving notice to the President of their wish to do so.
16. Any member not in arrears may, by the payment of one
hundred dollars at any one time, become a life member, and be
relieved from all further annual dues and other assessments.
All moneys received in payment of life membership shall be
invested as portions of a permanent fund, which shall be directed
solely to the furtherance of such special scientific work as may be
ordered by the General Committee.
Adopted, May 19, 18S3. f Amended, Nov. 10, 1883.
STANDING RULES
OP THE
GENERAL COMMITTEE OF THE PHILOSOPHICAL
SOCIETY OF WASHINGTON.
1. The President, Vice-Presidents, and Secretaries of the Society
shall hold like offices in the General Committee.
2. The President shall have power to call special meetings of the
Committee, and to appoint Sub-Committees.
3. The Sub-Committees shall prepare business for the General
Committee, and perform such other duties as may be entrusted to
them.
4. There shall be two Standing Sub-Committees ; one on Com-
munications for the Stated Meetings of the Society, and another on
Publications.
5. The General Committee shall meet at half-past seven o'clock
on the evening of each Stated Meeting, and by adjournment at
other times.
6. For all purposes except for the amendment of the Standing
Pules of the Committee or of the Society, and the election of mem-
bers, six members of the Committee shall constitute a quorum.
7. The names of proposed new members recommended in con-
formity with Section 11 of the Standing Rules of the Society, may
be presented at any meeting of the General Committee, but shall
lie over for at least four weeks before final action, and the concur-
rence of twelve members of the Committee shall be necessary to
election.
The Secretary of the General Committee shall keep a chronologi-
cal register of the elections and acceptances of members.
8. These Standing Rules, and those for the government of the
Society, shall be modified only with the consent of a majority of
the members of the General Committee.
xii
BTJLES
FOR THE
PUBLICATION OF THE BULLETIN
OP THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The President's annual address shall be published in full.
2. The annual reports of the Secretaries and of the Treasurer
shall be published in full.
3. When directed by the General Committee, any communication
may be published in full.
4. Abstracts of papers and remarks on the same will be pub-
lished, when presented to the Secretary by the author in writing
within two weeks of the evening of their delivery, and approved by
the Committee on Publications. Brief abstracts prepared by one
of the Secretaries and approved by the Committee on Publications
may also be published.
5.* If the author of any paper read before a Section of the
Society desires its publication, either in full or by abstract, it shall
be referred to a committee to be appointed as the Section may
determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the Secretary of the Section, together with any
action of the section taken thereon.
6. Communications which have been published elsewhere, so as
to be generally accessible, will appear in the Bulletin by title only,
but with a reference to the place of publication, if made known in
season to the Committee on Publications.
* Adopted May 19, 1883.
2 a xiii
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 16, 1882.
President J. W. Powell.
Vice-Presidents J. C. Welling, J. E. Hilgard,
C. H. Crane, J. S. Billings.
Treasurer « Cleveland Abbe.
Secretaries G. K. Gilbert, Henry Farquhar.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
W. H. Dall, C. E. Dutton,
J. R. Eastman, E. B. Elliott,
R. Fletcher, Wm. Harkness,
D. L. Huntington, Garrick Mallery,*
C. A. Schott.
STANDING COMMITTEES.
On Communications :
J. S. Billings, Chairman, G. K. Gilbert, Henry Farquhar.
On Publications :
G. K. Gilbert, Chairman, Henry Farquhar, Cleveland Abbe,
S. F. BAIRD.f
* Mr. Mallery was elected Vice-President October 13 to fill the vacancy occasioned by
the death of Mr. Crane. Mr. C. V. Riley was at the same time added to the General
Committee to fill its number.
f As Secretary of the Smithsonian Institution.
xiv
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 22, 1883.
President J. C. Welling.
Vice-Presidents J. S. Billings. Garrick Mallery.
J. E. Hilgard. Asaph Hall.
Treasurer Cleveland Abbe.
Secretaries Henry Farquhar. G. K. Gilbert.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates. E. B. Elliott.
W. H. Dall. Robert Fletcher.
C. E. Dutton. William Harkness.
J. R. Eastman. J. J. Knox.
C. V. Riley.
STANDING COMMITTEES.
On Commtinications :
J. S. Billings, Chairman. Henry Farquhar. G. K. Gilbert.
On Publications :
G. K. Gilbert, Chairman. Cleveland Abbe. Henry Farquhar.
S. F. Baird.*
*As Secretary of the Smithsonian Institution.
LIST OF MEMBERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON,
Cdrrected to December 31, 1883.
The Dames of founders are printed in Small Capitals.
(d) indicates deceased.
(a) indicates absent from the District of Columbia and excused from payment of dues
until announcing his return,
(r) indicates resigned.
NAME. P. O. Address and Residence. Date ofAdmission.
Abbe, Cleveland
Abert, Sylvanus Thayer.
Adams, llenry
Aldis, Asa Owen
Allen, James
Alvord, Benjamin
Antisell, Thomas
Avery, Robert Stanton..
Babcock, Orville Elias
Bailey, Theodoras (d)
B.\ir.D, Spencer Fulleeton.
Baker, Frank
Baker, Marcus ,
Bancroft, George
Barnes, Joseph K. (d)
Bates, Henry Hobart
Beardslee, Lester Anthony (a).,
Bell, Alexander Graham
Bell, Chichester Alexander
Benet, Stephen Vincent ,
Bessels, Emil
Billings, John Shaw..
Birney, William
Birnie, Rogers (a)..
•HBodfish, Sumner omer..
Browne, John Mills
Burchard, Horatio Chapin.
Burgess, Edward Sanford.
Burnett, Swan Moses
Army Signal Office. 2017 I St. N. W..
Engineer's Office, War Department.
1724 Penn. Ave. N. W.
1607 H St
1518 H St. N. W
Army Signal Office. 1707 G St. N. W,
1207 Q St. N. W
Patent Office. 1311 Q St. N. W
Coast and Geodetic Survey Office.
320 A St. S. E.
2024 G St. N. W.
Smithsonian Institution. 1445 Mass.
Ave. N. W.
32G C St. N. W
347 Hill St., Los Angeles, Cal
1G23 H St. N. W
Patent Office. The Portland
Navy Department
Scott Circle, 1500 R. I. Ave
1221 Conn. Ave. N. W
Ordnance Office, War Department.
1717 I St. N. W
Smithsonian Institution. 1444 N St.
N. W.
Surg. Genl's Office, U. S. A. 3026 N
St. N. W.
456 Louisiana Ave. 1901 Harewood
Ave., Le Droit Park.
Cold Spring, Putnam Co., N. Y
Geological Survey. 605 F St. N. W....
Medical Director, U.S. N. The Port-
land.
Director of the Mint. Riggs House.
High School. 1214 K St. N. W
1215 I St. N. W
1871, Oct. 29
1875. Jan. 30
1881, Feb. 5
1873, Mar. I
1882, Feb. 25
1872, Mar. 23
1871, Mar. 13
1879, Oct. 11
1871, June 9
1873, Mar. 1
1871, Mar. 13
1881, May 14
1876, Mar. 11
1875, Jan. 16
1871, Mar. 13
1871. Nov. 4
1875. Feb. 27
1879, Mar. 29
1881, Oct. 8
1871, Mar. 13
Jan. 16
Mar. 13
Mar. 29
Mar. 11
Mar. 24
Nov. 24
May 10
Mar. 24
Mar. 29
1875,
1871,
1879,
1876,
1883,
1883,
1879,
1883,
1879,
XVI
LIST OF MEMBERS. XVII
NAME. P. O. Address and Residence. Date of
Admission.
Busey, Samuel Clagett.
Capron, Horace
Case, Augustus Ludlow (a)..
Casey, Thomas Lincoln
1525 I St. N. W.
Caziarc, Louis Vasmer
Chase, Salmon Portland (d)
Chamberlin, Thomas Crowder..
Chickering, John White, Jr
Christie, Alexander Smyth
Clapp, William Henry (a)
Clark, Edward
The Portland
Navy Department. Bristol, R. I
Lieut. Col., Corps of Engineers. 1419
K St. N. W
Army Signal Office. 1415 G St. N.W..
Clark, Ezra Westcotc.
Clarke, Frank Wigglesworth
Coffin, John Huntington Crane.
Collins, Frederick (d)
Comstock, John Henry (a) ,
Coues, Elliott ,
Craig, Benjamin Faneuil (d)
Craig, Robert
Craig, Thomas (a)
Crane, Charles Henry (i)
Curtis, Josiah (d)
Cutts, Richard Dominicus (d) ,
Dall, William Healey....
Davis, Charles Henry (d).,
Davis, Charles Henry
Geological Survey
Deaf Mute College, Kendall Green..
Coast and Geodetic Survey Office.
513 Gth St. N. W.
1416 Corcoran St
Architect's Office, Capitol. 417 4th St.
N. W.
Revenue Marine Bureau, Treasury
Department. Woodley Road.
Geological Survey. 1425 Q St. N.W..
1901 I St. N. W
Cornell University, Ithaca, N. Y
Smithsonian Inst. 1726 N. St. N. W..
Army Signal Office. 1008 I St. N. W..
Johns Hopkins Univ., Baltimore, Md.
P. O. Box 406. 1119 12th St, N. W.
Dean, Richard Crain (a)
De Cain dry, William Augustiu.
De Land, Theodore Louis.
Dewey, George (r)
Doolittle, Myrick Hascull.
Navy Department. 1705 Rhode Island
Ave. N. W.
Navy Yard, New York
Commissary General's Office. 924
19ih St. N. W.
Treasury Dept. 126 7th St. N. E
Dorr, Fredric William (d)
Dunwoody, Henry Harrison Chase.
Dutton, Clarence Edward
Dyer, Alexander B. (d)..
Coast and Geodetic Survey Office.
1925 I St. N. W.
Army Signal Office. 1803 G St. N. W.
Geological Survey. 23 Lafayette
Square.
Eastman, John Robie .
Eaton, Amos BEEBE(d).
Eaton, John
Naval Observatory. 930 18th St. N.W.
Eldredge, Stewart (a)
Elliot, George Henry (r).
Elliott, Ezekiel Brown...
Emmons, Samuel Franklin
.
Endlich, Frederic Miller (a)
Ewing, Charles (a)
,
Ewing, Hugh (a)
Bureau of Education, Interior Dept.
712 East Capitol St.
Farquhar, Edward.
Farquhar, Henry....
Ferrel, William....
Fletcher, Robert..
Flint, Albert Stowell.
Flint, James Milton
Foote, Elisha (d)
Foster, John Gray (d)
French, Henry Flagg (?•)..
Fristoe, Edward T
,
Office of Government Actuary, Treas-
ury Department. 1210 G St. N. W.
Geological Survey. 915 16th St. N.W,
Smithsonian Institution
Lancaster, Ohio
Patent Office Library. 1915 H St. N.W.
Coast and Geodetic Survey Office.
Brooks Station, D. C.
Army Signal Office. 471 C St. N. W...
Surgeon Genl's Office, U. S. A. 1326
L St. N. W.
Naval Observatory. 1209 Rhode Island
Ave. N.W.
Smithsonian Inst. Riggs House
1434 N St. N. W..
1874, Jan. 17
1871, Mar. 13
1872, Nov. 16
1871, Mar. 13
1882, Feb. 25
1871, Mar. 13
1S83, Mar. 24
1874, Apr. 11
1880, Dec. 4
1882, Feb. 25
1877, Feb. 24
1882, Mar. 25
1874, Apr. 11
1871, Mar. 13
1879, Oct. 21
1880, Feb, 14
1871, Jan. 17
1871, Mar. 13
1873, Jan. 4
1879, Nov. 22
1871, Mar. 13
1874, Mar. 28
1871, Apr. 29
1871, Mar. 13
1874, Jan. 17
1880, June 19
1872, Apr. 23
1881, Apr. 30
1880, Dec. 18
1879, Feb. 15
1876, Feb. 12
1874, Jan. 17
1873, Dec. 20
1872, Jan. 27
1871, Mar. 13
1871, May 27
1871, Mar. 13
1874, May 8
1871, June 9
1871, Mar. 13
1871, Mar. 13
1883, Apr. 7
1873, Mar. 1
1874, Jan. 17
1874, Jan. 17
1876, Feb. 12
1881, May 14
1872, Nov. 16
1873, Apr. 10
1882, Mar. 25
1881, Mar. 19
1871, Mar. 13
1873, Jan. 18
1882, Mar. 25
1873, Mar. 29
XVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
NAME.
Gale, Leonard Dunnell (d).
Gallaudet, Edward Miner.
Gannett, Henry
Gardiner, James Terry (a)
Garnett, Alexander Young P. (r)..
Gihon, Albert Leary
Gilbert, Grove Karl
Gill, Theodore Nicholas
Godding, William Whitney.
Goode, George Brown
Goodfellow, Edward.
Goodfellow, Henry (r)
Gore, James Howard
Graves, Edward Oziel (a)
Graves, Walter Hayden \a)
Greely, Adolphus Washington (a).
Green, Bernard Richardson
Green, Francis Mathews (a)
Greene, Benjamin Franklin (a)....
Greene, Francis Vinton
Gunnell, Francis M.
Hains, Peter Conover (a)
Hall, Asaph
Hanscom, Isaiah (d)
Harkness, William
Hassler, Ferdinand Augustus (a)...
Hayden, Ferdinand Vandeveer (a).
Hazen, Henry Allen
Hazen, William Babcock
Henry, Joseph (d)
Henshaw, Henry Wetherbee..
Hilgard, Julius Erasmus
Hill, George William
Holden, Edward Singleton (a)...
Holmes, William Henry
Hough, Franklin Benjamin (a).
Howell, Edwin Eugene (a)
Humphreys, Andrew Atkinson (d)..
Jackson, Henry Arundel Lambe (a)
James, Owen (a)
Jeffers, William Nicolson (r)
Jenkins, Thornton Alexander...
Johnson, Arnold Burges
Johnson, Joseph Taber
Johnston, William Waring.
Kampf, Ferdinand (d)
Keith, Reuel (a)
Kerr, Washington Carruthers.
Kidder, Jerome Henry
Kilbourne, Charles Evans
King, Albert Freeman Africanus....
King, Clarence (r)
Knox, John Jay
Kummell, Charles Hugo
Lane, Jonathan Homer (d).
Lawver, Winfield Peter
P. O. Address and Residence.
Deaf Mute'College, Kendall Green...
Geological Survey. 1881 Harewood
Ave., Le Droit Park.
State Library, Albany, N. W
Navy Department. 2019 Hillyer Place
N. W.
Geological Survey. 1424 Corcoran St.
Smithsonian Inst. 321-323 i]4 St. N.W,
Government Asylum for the Insane..,
National Museum. 1620 Mass. Ave.
N. W.
Coast and Geodetic Survey Office.
1330 19th St. N. W.
Columbian College. 1305 Q St. N. W.
Denver, Colorado
1915
1738 N St. N. W
Navy Department
West Lebanon, N. H
District Commissioners' Office.
G St. N. W.
Medical Director, U. S. N. 600 20th
St. N. W.
1824 Jefferson Place
Naval Observatory. 2715 N. St. N.W.
Naval Observatory. 1415 G St. N. W.
Tustin City, Los Angeles Co., Cal ,
Geological Survey. 1803 Arch St., Phil-
adelphia, Penn.
Army Signal Office. 1416 Corcoran St,
Army Signal Office. 1601 K St. N.W.
Bureau of Ethnology. P. O. Box 585.
Coast and Geodetic Survey Office.
1709 Rhode Island Ave. N. W.
Nautical Almanac Office. 314 Ind.
Ave. N. W.
Madison, Wisconsin ^™ ,
Geological Survey. 1100 O St. N. W...
Agricultural Department. Lowville,
N. Y.
Rochester, N. Y ,
War Department..
Hyde Park, Penn.
2115 Penn. Ave. N. W
Light House Board, Treasury Dept.
501 Maple Ave., Le Droit Park
926 17th St. N. W
1603 K St. N. W
Raleigh, N. C
Smithsonian Institution. 1816 N St.
N. W.
Army Signal Office. Lexington House
726 13th St N. W
Treasury Dept. 1127 10th St. N. W...
Coast and Geodetic Survey Office.
608 Q St. N. W.
Mint Bureau, Treasury Department.
1912 I St. N. W.
Date of
Admission.
1874, Jan. 17
1875, Feb. 27
1874, Apr. 11
1874, Jan. 17
1878, Mar. 16
1880, Dec. 18
1873, June 7
1871, Mar. 13
1879, Mar. 29
1874, Jan. 31
1875, Dec. 18
1871,
1880,
1874,
1878,
1880,
1879,
1875,
1871,
1875,
Nov. 4
Mar. 14
Apr. 11
May 25
June 19
Feb. 15
Nov. 9
Mar. 13
Apr. 10
1879. Feb. 1
1879, Feb. 15
1871, Mar. 13
1873, Dec. 20
1871, Mar. 13
1880, May 8
1871, Mar. 13
1882, Mar. 25
1881, Feb 6
1871, Mar. 13
1874, Apr. 11
1871, Mar. 13
1879, Feb. 1
1873, June 21
1879, Mar. 29
1879, Mar. 29
1874, Jan. 31
1871, Mar. 13
1875, Jan. 30
1880, Jan. 3
1877, Feb. 24
1871, Mar. 13
1878, Jan. 19
1879, Mar. 29
1873, Jan. 21
1875, Dec. 18
1871, Oct. 29
1883, Apr. 7
1880, May 8
1880, June 19
1875, Jan. 16
1879, May 10
1874, May 8
1882, Mar. 25
1871, Mar. 13
1881, Feb. 19
LIST OF MEMBERS. XIX
NAME. P. O. Address andkesidence. Date ofAdmission.
Lee, William
Lefavour, Edward Brown.
Lincoln, Nathan Smith..
Lockwood, Henry H. (r).
Loomis, Eben Jenks
2111 Penn. Ave. N. W
Coast and Geodetic Survey Office.
117 C St. S. E.
1514 H St. N. W
Lull, Edward Phelps
Lyford, Stephen Carr (r).
Nautical Almanac Office. 1413 Col-
lege Hill Terrace N. W.
Navy Department
MacCauley, Henry Clay (a)
McGee, W. J
MeGuire, Frederick Bauders ,
Mack, Oscar A. (d)
McMurtrie, William (a)
Mallery, Garrick ,
Helena, Montana
Geological Survey. 512 13th St. N. W
1306 F St. N. W. 614 E St. N. W
Champaign, 111
Bureau of Ethnology. P.O. Box 585.
1323 N St. N. W.
Marvin, Joseph Badger (a)
Marvine, Archibald Robertson (d).
Mason, Otis Tufton
Meek, Fielding Bradford (d)
Meigs, Montgomery (a)
Meigs, Montgomery Cunningham...
Milner, James William (d)
Morgan, Ethelbert Carroll
Morris, Martin Ferdinand (a)
Mussey, Reuben Delavan
Myer, Albert J. (d)
Myers, William (a)
Columbian College. 1305 Q St. N.W.
War Department. Rock Island, 111.
1239 Vermont Ave.N. W ...
918 E St. N.W
P.'b" Box"618." 5085th St." N.W
!
Newcomb, Simon ,
Nichols, Charles Henry (a)..
Nicholson, Walter Lamb
Nordhoff, Charles
War Department
Navy Department. Stoddart Street.
Osborne, John Walter
Otis, George Alexander (d).
Parke, John Grt/bb
1322 I St. N. W
Alpine, Bergen Co., N. J.
212 Delaware Ave. N. E..,
Parker, Peter
Parry, Charles Christopher (a)..
Patterson, Carlile Pollock (d)
Paul, Henry Martyn
Peale, Albert Charles
Peale, Titian Ramsay (a)...
Peirce, Benjamin (d)
Peirce, Charles Sanders (a)
Engineer Bureau, War Department.
16 Lafayette Square.
2 Lafayette Square
Burlington, Iowa ,
Naval Observatory.
Geological Survey.
N. W.
Philadelphia, Penn.
917 R St. N. W..
1210 Mass. Ave.
Pilling, James Constantine.
Poe, Orlando Metcalfe
Pope, Benjamin Franklin....
Porter, David Dixon (r)
Powell, John Wesley
Prentiss, Daniel Webster....
Pritchett, Henry Smith (a).
Rathbone, Henry Reed (a)..
Rathbun, Richard
Renshawe, John Henry
Riehey, Stephen Olin
Ridgway, Robert (a)
Riley, Charles Valentine
Riley, John Campbell (d)
Ritter, William Francis McKnight.
Rodgers, Christopher Raymond
Perry (a)
Rodgers, John (d)
Rogers, Joseph Addison (a)
Russell, Israel Cook
Coast and Geodetic Survey Office.
Baltimore, Md.
Geological Survey. 918 M St. N. W.
34 Congress St. West, Detroit, Mich.
Surgeon General's Office, U. S. A.
2029 P St. N. W.
Geological Survey. 910 M St. N. W...
1224 9th St. N. W
Washington University, St. Louis, Mo,
Smithsonian institution. 1622 Mass.
Ave. N. W.
Geological Survey. 1221 O St. N. W..
1426 N. Y. Ave. N. W
Smithsonian Inst. 1214 Va. Av. N.W
Agricultural Dept. 1700 13th St. N.W
Nautical Almanac Office. 16 Grant
Place.
1723 I St. N. W
Naval Observatory
Geological Survey. 1424 Corcoran St.
1874, Jan. 17
1882, Dec. 16
1871, May 27
1871, Oct. 29
1880, Feb. 14
1875, Dec. 4
1873, Jan. 18
1880, Jan.- 3
1883, Nov. 10
1879, Feb. 15
1872, Jan. 27
1876, Feb. 26
1875, Jan. 30
1878, May 25
1874, Jan. 31
1875, Jan. 30
1871, Mar. 13
1877, Mar. 24
1871, Mar. 13
1874, Jan. 31
1883, Oct. 13
1877, Feb. 24
1881, Dec. 3
1871, Mar. 13
1871, June 23
1871, Mar. 13
1872, May 4
1871, Mar. 13
1879, May 10
1878, Dec. 7
1871, Mar. 13
1871, Mar. 13
1871, Mar. 13
1871, May 13
1871, Nov. 17
1877, May 19
1874, Apr. 11
1871, Mar. 13
1871, Mar. 13
1873, Mar. 1
1881, Feb. 19
1873, Oct. 4
1882, Dec. 16
1874, Apr. 11
1874, Jan. 17
1880, Jan. 3
1879, Mar. 29
1874, Jan. 17
1882,
1883,
1882,
1874,
1878,
1877,
1879,
Oct. 7
Feb. 24
Oct. 7
Jan. 31
Nov. 9
May 19
Oct. 21
1872, Mar. 9
1872, Nov. 16
1872, Mar. 9
1882, Mar. 25
XX PHILOSOPHICAL SOCIETY OF WASHINGTON.
NAME. P. O. Address and Residence. Date ofAdmission.
Russell, Thomas.
Salmon, Daniel Elmer
Sampson, William Thomas
Sands, Benjamin Franklin (d).
Saville, James Hamilton
Schaeiter, George Christian (d)..
Schott, Charles Anthony
Searle, Henry Robinson (d)...
Seymour, George Dudley (r)
.
Shellabarger, Samuel
Sherman, John
Sherman, William Tecumseh (r)
.
Shufoldt, Robert Wilson
Sicard, Montgomery (a)
.
Sigsbee, Charles Dwight.
Skinner, John Oscar
Smiley, Charles Wesley
Smith, David (a)
Smith, Edwin
Spofford, Ainsworth Rand.
Stearns, John (a) ..,
Stone, Ormond (a).
Taylor, Frederick William.
Taylor, William Bower
Thompson, Almon Harris ..
Tilden, William Calvin (a)..
Todd, David Peck (i)
Toner, Joseph Meredith
True, Frederick William.....
Twining, William J. (d)
Upton, Jacob Kendrick (r)
Upton, William Wirt
Upton, Winslow (a)..
Vasey, George (r)
Walcott, Charles Doolittle.
Waldo, Frank
Walker, Francis Amasa (a).
Walling, Henry Francis.
Ward, Lester Frank
Webster, Albert Lowry..
Welling, James Clarke
Wheeler, George M. (a)
Wheeler, Junius B. (a)
White, Charles Abiathar...
White, Zebulon Lewis (a).
Williams, Albert, Jr
Wilson, Allen D. (o)
Wilson, James Ormond.
Army Signal Office. 904 M St. N. W.
Agricultural Dept. 1121 1 St. N. W...
Naval Observatory
342 D St. (La. Ave.) N. W. 1315 M St.
N. W.
Coast and Geodetic Survey Office.
212 1st St. S. E.
Room 23 Corcoran Building. 812 17th
St. N. W.
1319 K St. N. W
Surgeon Genl's Office, U. S. A. 1619
K St. N. W.
Ordnance Bureau, Navy Department.
Hydrographic Office, Navy Depart-
ment. 3319 U St. N. W.
1739 F St. N. W
U. S. Fish Commission, 1443 Mass.
Ave. 1207 11th St. N. W.
Navy Department
Coast and Geodetic Survey Office
Library of Congress. 1621 Mass. Ave.
N. W.
Leander McCormick Observatory,
University of Virginia.
Smithsonian Institution
Smithsonian Inst. 306 C St. N. W.
Geological Survey
Army Medical Museum
Amherst, Mass
615 Louisiana Ave
National Museum
2d Comptroller's Office, Treasury
Dept. 810 12th St. N. W.
Army Signal Office. 1441 Chapin St.
N. W.
Winlock, William Crawford
Wolcott, Christopher Columbus (r).
Wood, Joseph (a)
Wood, William Maxwell (a)
Geological Survey. 1116 N. Y. Ave.
N. W.
Army Signal Office. 1427 Chapin St.
N. W.
Mass. Inst, of Technology, Boston,
Mass.
Geological Survey
Geological Survey. 1464 R. I. Ave.
N. W.
Johns Hopkins University, Balti-
more, Md.
1302 Connecticut Ave
Engineer Bureau, War Department..
West Point, New York
Geological Survey. LeDroit Park
Providence, Rhode Island
,
Geological Survey. 23 Lafayette
Square.
Newport, R. I
Franklin School Building. 1439 Mass.
Ave. N. W.
Naval Observatory. 733 20th St. N.W..
Asst. Eugineer B. & P. R. R.
Navy Department
1883, Feb. 10
1883, Nov. 24
1883, Mar. 24
1871, Mar. 13
1871, Apr. 29
1871, Mar. 13
1871, Mar. 13
1877, Dec. 21
1881, Dec. 3
1875, Apr. 10
1874, Jan. 17
1871, Mar. 13
1881, Nov. 5
1877, Feb. 24
1879, Mar. 1
1883, Mar. 24
1882, Oct. 7
1876, Dec. 2
1880, Oct. 23
1872, Jan. 27
1874, Mai. 28
1874, Mar. 28
1881, Feb. 19
1871, Mar. 13
1875, Apr. 10
1871, Apr. 29
1878, Nov. 23
1873, June 7
1882, Oct. 7
1878, Nov. 23
1878, Feb. 2
1882, Mar. 25
1880, Dec. 4
1875, June 5
1883, Oct. 13
1881, Dec. 3
1872, Jan. 27
1883, Feb. 24
1876, Nov. 18
1882, Mar. 25
1872, Nov. 16
1873, June 7
1871, Mar. 13
1876, Dec. 16
1880, June 19
1883, Feb. 24
1S74, Apr. 11
1873, Mar. 1
1880, Dec. 4
1875, Feb. 27
1875, Jan. 16
1871, Dec. 2
LIST OF MEMBERS. XXI
NAME. P. O. Address and Residence. Date ofAdmission.
Woodward, Joseph Janvier
Woodward, Robert Simpson
Woodworth, John Maynard (d)..
Yarnall, Mordecai (d).
Yarrow, Harry Crecy ..
Zumbrock, Anton.
Armv Med. Museum. 620 F St. N.W..
Naval Observatory. 1125 17th St. N.W.
814 17th St. N. W.
Coast and Geodetic Survey Office.
455 C St. N. W.
1871, Mar. 13
1883, Nov. 24
1874, Jan. 31
1871, Apr. 29
1874, Jan. 31
1875, Jan. 30
Number of founders 44
" members deceased 3G
" " absent 55
" " resigned 10
" " active 149
Total number enrolled 250
XXII PHILOSOPHICAL SOCIETY OP WASHINGTON.
ANNUAL REPORT OF THE TREASURER.
Washington City, December 31, 1883.
To the Philosophical Society of Washington
:
I have the honor to present herewith my annual statement as
Treasurer for the year ending December 31st, and to express my
regret that owing to absence from the city I was not able to present
this report at the proper time on the occasion of the recent annual
meeting, December 22d.
By the kindness of Messrs. Riggs & Co. the Society has been
enabled to invest in another $1,000 United States 4 per cent, bond,
but in this case a few weeks in advance of the regular winter accu-
mulation of its revenue. The balance shown by Riggs' books
against the Society is, therefore, with their assent, and in fact at
their suggestion, and will probably be met during January.
The total invested fund of the Society is, therefore, $2,500, of
which $1,000 is at 4? per cent, and $1,500 at 4 per cent.
The further assets of the Society consist of unpaid annual dues
to the amount of $185 for 1883 and $90 for 1882. The total.active
membership remains at about one hundred and fifty, and the prob-
able income for the next year may be estimated at $900, nearly all
of which Avill be needed to pay current expenses and the bills for
printing Volume VI.
Early in the year one hundred and fifty-five copies of Volume IV
and two hundred and eighty-five of Volume V were distributed to
the active members and to about fifty domestic and eighty-five for-
eign recipients.
The list of recipients is a slightly amended copy of that printed
in Volume IV of the Bulletin of the Society. Occasional copies of
the earlier volumes have been distributed to those whose sets had
accidentally become imperfect, or were otherwise entitled to them.
As custodian of the library and property, I have the honor to
report that the Society occasionally receives scientific publications
by way of exchange with similar organizations. The accession cata-
logue of the library now includes a hundred and two numbers or
titles, being an increase of thirty-one during the year.
By order of the General Council, the Treasurer was in 1881
instructed to initiate the keeping of a record book containing a
sketch of the life and services of the individual members of the
Society ; this record volume is now prepared, and a notice will be
sent to each member asking for the necessary data.
Very respectfully,
Cleveland Abbe,
Treasurer.
TREASURER S REPORT. XXIII

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL ADDRESS OF THE PRESIDENT.

ANNUAL ADDRESS OF" THE PRESIDENT,
J. \V. Powell,
Delivered December 8, 1883.
THE THREE METHODS OF EVOLUTION.
In the early history of research attention was chiefly given to
phenomena of co-existence. In late years the phenomena of sequence
have received the larger share of attention. The investigation of
the phenomena of sequence has led to the invention of a number of
hypotheses. In the past history of scientific research three of these
have each led to a long series of important discoveries. These are
the nebular hypothesis, the atomic hypothesis, and the hypothesis
of the development of life. The nebular theory is an hypothesis
of astronomic evolution ; the atomic theory has gradually assumed
the shape of an hypothesis of chemical evolution ; and the develop-
ment theory has been elaborated and re-stated as the hypothesis of
biologic evolution. The time has come when in all fruitful research
evolution in some form is postulated by each investigator in his own
field. Yet many scientific men, though admitting the doctrines of
evolution in their own special fields, ofttimes reject them elsewhere;
and there is some disagreement even among the greatest thinkers
as to the extent to which the hypotheses of evolution can be carried,
but all postulate evolution in some form and to some degree.
An attempt will be made in this address to point out what is be-
lieved to be the fact—that there are three grand classes of phe-
nomena, constituting three kingdoms of matter and representing
three stages of evolution ; or, stated in another way, that there has
been an evolution of the methods of evolution, so that the methods
discovered in the first stage have been superseded by those discov-
red in the second, and these superseded by the methods of the third
stage. It is proposed to indicate and, as clearly as possible within
the limits of an address, to define, in terms of matter and motion,
the three kingdoms of matter and the three methods of evolution.
As precedent to the general statement it will be well, therefore,
briefly to consider the kinematic hypothesis.
XXVII
XXVIII PHILOSOPHICAL SOCIETY OP WASHINGTON.
THE KINEMATIC HYPOTHESIS.
That motion is persistent is the kinematic hypothesis. In the
early history of research many modes or varieties of motion were
directly observed. To account for these motions they were said to
be caused by forces, and Force was sometimes defined as that which
produces motion. Something, therefore, was conceived to exist
—
not matter, not motion—an existence that would produce motion.
Then arose the question, What is Force—this antecedent of Motion?
The researches inaugurated from this standpoint led again and
again to the discovery that the antecedent of motion is some other
motion, and one after another of the so-called " forces " were thus
resolved into motions, until at last only gravity and affinity, and
perhaps magnetism, remain as unexplained antecedents of motion.
But gravity, affinity, and magnetism are included under one term,
" attraction," by those who hold that there is yet a force—something
other than motion which produces motion. Attraction, then, is left.
Sometimes these same philosophers speak of " attraction and repul-
sion." If, then, all forces the actions of which are thoroughly
known are resolved into antecedent motions, it is indeed an induc-
tive hypothesis worthy of consideration that the antecedents of the
phenomena of attraction and repulsion may also be regarded as
modes of motion.
But this hypothesis is reached by another method. It is known
that motions may be transmuted from one kind or mode into an-
other. Affinity can be transmuted into motion, and motion into
affinity. If we wish to obtain the mode of motion called electricity,
we may derive it from mechanical motion through friction, or we
may derive it through affinity in the voltaic cell. If we combine a
gramme of hydrogen with oxygen, 34,000 units of heat—a mode of
motion—are developed. If a gramme of hydrogen be combined
with iodine, 3,600 units of heat—a mode of motion—are absorbed.
But why introduce single illustrations? A large part of all the
powers used by man in the industries of the world are derived from
affinity. Affinity, therefore, is the equivalent of motion. By a
similar process it is shown that gravity can be transmuted into mo-
tion and motion into gravity, and the trasmutation of magnetism
into motion and of motion into magnetism is well known.
It is thus seen that while motion may be derived from the so-
called forces, gravity, affinity, and magnetism, these so-called force
ANNUAL ADDRESS OF THE PRESIDENT. XXIX
may also be derived from motion. In all other cases where a mode
of motion is transmuted, it is but changed into another mode. It
is therefore an inductive hypothesis that gravity, affinity, and mag-
netism are also modes of motion.
This hypothesis is reached by yet another inductive process.
There is a vast multiplicity of properties which bodies present to
the mind through touch, taste, smell, hearing, and sight
—
properties
at first explained as occult. During the progress of scientific re-
search, one after another of these properties has been resolved into
motion, until at last two remain unexplained—rigidity and elasticity.
By those who hold with most tenacity to older explanations of such
phenomena, these two remaining properties are attributed to attrac-
tion and repulsion ; but those who have fallen into the current of
modern thought believe that they can be explained as the results of
the composed motion of the constituent parts of the bodies which
exhibit them, together with molecular impact. That some such ex-
planation will eventually be fully established is highly probable as
an inductive hypothesis.
When these various methods of induction are combined they
lead to an hypothesis of the highest character, and we may reasonably
expect that all forces will ultimately be resolved into motions. The
term force will still be of value in science, to be used in each case as
denoting the antecedent motion.
Intimately related to the kinematic hypothesis is the hypothesis
of an ether, which has also been reached by a variety of inductive
methods, i. e. from converging lines of research. In fact, the kine-
matic hypothesis and the ethereal hypothesis are identical, the first
being stated in terms of motion, the second in terms of matter.
Intimately related to the ethereal hypothesis is the nebular hypo-
thesis, also reached through a series of converging lines of induc-
tion.
Every fact that lends probability to one lends probability to all.
Thus each strengthens the other. It must be understood that how-
ever probable they may be, they are yet hypotheses, and for their
complete demonstration the mode of action must be specifically
pointed out in each case.
The ethereal hypothesis furnishes the original homogeneous matter
in motion from which the various aggregates have been segregated.
The nebular hypothesis takes up this matter while it is yet in a
3 a
XXX PHILOSOPHICAL SOCIETY OP WASHINGTON.
molecular condition and derives from it the more compounded ag-
gregates and their motions, in obedience to the law of the persis-
tence of motion, which is the kinematic hypothesis. Thus there are
bodies of men engaged in researches relating to molecular physics,
other bodies of men in researches relating to molecular physics and
astronomy, and others in molecular physics and chemistry, all of
whose researches converge in the kinematic hypothesis. It is there-
fore reached by a consilience of many inductive methods.
In the statement thus made concerning the kinematic theory
there is no attempt to assemble the data on which it rests. Such
task could not be performed in an address, as volumes would be
needed for their presentation. An attempt has been made simply
to characterize the processes of inductive reasoning by which the
hypothesis is reached.
If the kinematic hypothesis should be demonstrated, it would be
a veritable explanation. The dynamic hypothesis is no explana-
tion. To exhibit this fact it must be briefly analyzed.
Philosophy is the science of opinion, and the philosopher has for
the subject-matter of his science the origin and nature of opinions,
and he discovers that they may be broadly grouped in three classes
—
mythic, metaphysic, and scientific. Mythic opinion arises from the
attempt to explain the simple in terms of the compound—that is,
to explain biotic and physical phenomena by their crude analogies
to human activities. Early man, discovering that his own activi-
ties arose from design and will, supposed that there was design and
will in all function and motion. Through this method of explana-
tion have arisen the mythologies of the world.
But in the early civilization of the Aryan race a multitude of
mythic systems were thrown together and studied by the same body
of men, originally for the purpose of deriving therefrom the com-
mon truth. The resulting comparison and investigation led to the
conclusion that they were all false, and in lieu thereof a new system
of explanation was invented. These earlier philosophers of the
cities of the Mediterranean, while engaged in the comparison of
mythologies, were also engaged in the comparison of languages, and
they discovered many profoundly interesting facts of linguistic
structure, and the intimate relations between language and thought
by which the form of thought itself is moulded. These great
facts appearing at the same time that mythic philosophy was dis-
ANNUAL ADDRESS OF THE PRESIDENT. XXXI
solving into idle tales, led to the origin of a new philosophic
method. The men of that day supposed that the truth is in the
word, and that a verbal explanation could be constructed ; that the
philosophy of the universe could be based on language; and to
them verbal statement was explanation, final and absolute, and be-
ing was but ideal.
But metaphysic philosophy was displaced by the increase of
knowledge—the development of scientific philosophy. In this sys-
tem the phenomena of co-existence and sequence are objectively
discerned and classified.
This bare statement of the three methods can be made more lucid
by an illustration. Unsupported bodies above the earth fall, and
such phenomena are seen so often as to challenge every man's atten-
tion. Early man, whose mind was controlled by mythic opinions,
subjectively knew that if he wished to move a body he must push
or pull it, and to him there was no other method of originating
motion.
Some years ago I was with a small body of Wintun Indians on
Pitt River, the chief tributary of the Sacramento, engaged in the
study of mythology. I had gone among the rocks for the purpose
of awakening echoes, that I might elicit from my dusky philosophers
an explanation thereof. Unexpectedly I fell upon an explanation
of gravity. We had climbed a high crag, and I sat at the summit
of the cliff with my feet overhanging the brink. An Indian near
me, who could speak but imperfect English, seemed solicitous for
my safety, and said : " You better get out ; hollow pull you down."
I had previously been intent on watching the operations of his mind
for the purpose above mentioned, and this expression seemed to me
strange ; and it started a line of investigation which I eagerly pur-
sued. I soon discovered that he interpreted the fall of bodies by
purely subjective analogies. He who stands on a rock but slightly
elevated above the earth feels no fear, but if standing a thousand
feet above the base of the cliff, he attempts to look over, fear curdles
his blood, and he seems to be pulled over. As he climbs a lofty
pine, at every increase of altitude there is an increase of fear, and
he seems to be pulled down by a stronger force. When he rests
upon the solid earth he feels no " pull," but when elevated above it
he interprets his subjective feelings as an objective pull. Vacuity
is personified and believed to be an actor.
In the early winter of 1882 I was with a party of Indians in the
XXXII PHILOSOPHICAL SOCIETY OP WASHINGTON.
Grand Cafion of the Colorado. Some of the young men were
amusing themselves by trying to throw stones across a lateral gorge.
No one -could accomplish the feat, though they could throw stones
even farther, as they believed, along the level laud. Chuar, the
chief, explained this to me by informing me that the canon pulled
the stones down. The apparent proximity of the opposite wall was
believed to be actual, and vacuity was personified and believed to
exert a force.
Metaphysic explanations of gravity are found. By that method
an absolute up and down is predicated, and bodies have a tendency
to fall down. This is an explanation in words, the words expressing
no meaniug but believed to be themselves thoughts. It is per-
haps the earliest form of the metaphysic explanation of gravity.
But with the progress of knowledge the absolute disappears, and
positions are found to be but relative ; there is no absolute up and
down ; and other facts with regard to gravity are discovered. And
finally the metaphysician says bodies attract. Now the term fall,
as used by the early metaphysicians, was the name of a motion
observed, and it was held to be a complete explanation as long as
up and down was supposed to be absolute, not relative ; and the
explanation was abandoned as insufficient when the ideas of abso-
lute up and down were abandoned. But the word attraction does
not involve this error. It is simply a name for the phenomenon,
without the manifestly fallacious implication of " up and down."
And it is a good name for the specific phenomenon to which it is
applied. But it must not connotate any other idea; in so far as
it does, it is vitiated. Yet the metaphysician will suppose that by
using the term " attraction " he explains gravity. The scientific
philosopher uses the term purely as the name of the phenomenon,
and does not suppose that thereby the phenomenon is explained
;
and having named it, he still seeks for its explanation—that is, he
still seeks to resolve that which is manifestly a complex phenom-
enon, exhibited in the relations of positions of bodies, into its most
simple elements. Whenever this is done he will say that attraction,
or gravity—they being synonyms for the same phenomenon—is
explained.
The kinematist uses " attraction " as a synonym for " gravitation."
The dynamist uses " attraction " as a verbal explanation of Gravi-
tation. The mythic philosopher uses the term to connotate the still
further idea that bodies exert a " pull " on one another ; and this
ANNUAL ADDRESS OF THE PRESIDENT. XXXIII
latter concept is do less mythic than that of the Indian who believes
that the vacuity between them exerts the pull.
It is fortunate for science that every discovery and every induc-
tive hypothesis is rigidly criticised, as this leads to the careful
examination of the verity of facts discerned and of the legitimacy
of hypotheses derived therefrom. Against the kinematic theory of
force much good rhetoric has been hurled, which may be somewhat
imitated in the following manner :
Here is a quotation from Bagehot, with an interpolation of my
own: " This easy hypothesis of special creation [occult force] has
been tried so often
#
and has broken down so very often, that
in no case probably do any great number of careful inquirers very
firmly believe it. They may accept it provisionally, as the best
hypothesis at present, but they feel about it as they cannot help
feeling as to an army which has always been beaten ; however
strong it seems they think it will be beaten again."
The venerable gentlemen who constitute the elder school tell us
that motion is not persistent; that energy constitutes a class of
things including two groups, the forces on the one hand and the
motions on the other ; that the total amount of energy is persistent,
but that the total amount of motion is changeable. And by their
definition force is that which produces motion, i. e. force can create
or destroy motion. But manifestly where there is more motion there
must be less force, therefore force can destroy itself; and when there
is more force and less motion, force can create itself.
The moon that passes through the sky of the gentlemen of the
old school is moon from the eastern to the western horizon. Then
the dragon, which exists not, destroys the moon and thus creates
itself, and passing through the cave from west to east it mounts to
their horizon, and in the twinkling of an eye commits suicide by
creating a moon. It is not strange that the thaumaturgics of such
philosophy should lend signal aid to its rhetoric.
The use of hypothesis in science is not only legitimate but an
absolute necessity. The science of psychology, as distinguished
from metaphysic speculation, points out this fact: that all increase
of knowledge is dependent upon hypothesis. Objective impressions
made by the phenomena of the universe upon the organ of the mind
are discerned only by the aid of comparison, and are added to
knowledge only by being combined with previously discerned phe-
XXXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
nomena. Phenomena imperfectly discerned are such as are com-
bined by superficial analogies
;
phenomena clearly discerned are
such as are combined by essential homologies. With all discern-
ment, therefore, there is comparison, and comparison is reflection
and reflection is reason. Now, scientific research is not random
observation and comparison, but designed discernment and classifi-
tion ; it is research for a purpose, and the purpose is the explanation
of imperfectly discerned phenomena. Phenomena not understood,
because imperfectly discerned and classified, are made the subject of
examination by first inventing a hypothetic explanation of the
same. With this, the investigator proceeds to more careful obser-
vation and comparison, devising new methods of discrimination
and of testing conclusions. Under the impetus of this hypothetic
explanation, discernment and comparison proceed, and additions to
knowledge are made thereby, and it matters not whether the hypo-
thesis be confirmed or overthrown.
On this rock much research is wrecked. When an hypothesis
gains such control over the mind that phenomena are subjectively
discerned, that they are seen only in the light of the preconceived
idea, then research but adds to vain speculation. A mind con-
trolled by an hypothesis is to that extent insane ; the rational mind
is controlled only by the facts, and contradicted hypotheses vanish
in their light.
There is another rock on which research is wrecked—the belief
which ofttimes takes possession of the mind that the unknown is
unknowable, that human research can penetrate into the secrets of
the universe no farther. It is the despondency of unrewarded
mental toil.
Yet another rock on which research is wrecked is the definition
of the unknown. Phenomena appear, but whence is not discovered,
and resort is had to verbal statement, and the verbal statement oft
repeated comes to be held as a fact itself. This is the vice of all
metaphysics, by which words are held to be things—spectral imagin-
ings that haunt the minds of introverted thinkers as devils possess
the imaginations of the depraved.
In the midst of the sea of the unknown stand the three rocks : the
controlling hypothesis, the unknowable unknown, and the verbal
definition, and in the waters about them are buried many wrecks.
ANNUAL ADDRESS OF THE PRESIDENT. XXXV
COMBINATION OF MATTER.
When the various bodies known to mind are resolved into their
constituent parts to the utmost of art and knowledge, such parts
are found to be so minute as almost to disappear in the perspective
toward the infinitesimal. The molecular bodies thus dimly discerned
"are combined and re-combined, until substances are produced that
come distinctly within the cognizance of our senses, so that we are
able to observe their forms and motions. These molar bodies
are again combined, until at last bodies of such magnitude are pro-
duced that they are but dimly discerned in the perspective toward
the infinite—stellar systems that appear not to the eye, but only to
the mind's eye.
INORGANIC COMBINATION.
Matter is primarily combined by chemical affinity. The sub
stances thus produced appear in three states : gaseous, fluid, and
solid, but are not clearly demarcated. That chemically combined
matter which is found in the solid state is further combined by crys-
tallization and lithifaction. It may be that these methods are parts
of the same process, and further, that they are one with chemical
affinity ; at any rate it is impossible clearly to demarcate them.
They are also influenced by gravity, and to a large extent act under
its control. Thus it is that gravity, and affinity with its concomi-
tants, unite in molecularly combining matter into inorganic sub-
stances. Again, these bodies are mechanically combined into geo-
logic formations, bodies of water, and bodies of air, and such com-
binations result from gravity. Finally they are all combined into
an aggregate, the earth itself, solid, fluid, and gaseous. This also
results from gravity.
In the succession of combinations thus briefly reviewed, the first
natural aggregate reached is the earth. Below that we have chemi-
cal and mechanical substances, which do not constitute integers, but
only integral parts. The earth itself is a whole—an aggregation,
as the term is here used.
Again, the earth is one of the bodies of the solar system, which
is a combination of worlds. This aggregation, also, is controlled by
gravity. Other higher astronomic aggregates may exist.
ORGANIC COMBINATION.
Portions of the matter combined by affinity and gravity are seg-
LIBRAKY
SfcP 6 I
XXXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
regated to be combined by vitality, giving organic bodies or aggre-
gates, as plants and animals. These bodies do not permanently re-
main such, as the matter of which they are composed sooner or later
returns to the condition of combination due solely to affinity and
gravity. They live and die.
SUPERORGANIC COMBINATION.
There are certain biotic bodies whose activities are combined.
The first step in combination is the biologic differentiation of the
sexes, giving a group of co-operative individuals for the activities
of reproduction—male and female, parent and child. This initial
combination is crudely developed into still larger combinations of
co-operative individuals among the lower animals. With mankind
it is developed to a much higher degree, resulting in a great variety
of co-operative activities.
There is found, then, a variety of methods of combination, in-
cluded under three classes : physical, due to affinity and gravity
;
biotic, due to vital organization ; and anthropic, due to related activ-
ities. Physical combinations result in the production of substances
and aggregates, and the existence of a physical body is preserved
by preserving identity of form and identity of constituent matter.
Biotic combination also produces substances and aggregates, and
the existence of a biotic body is continued by the preservation of
identity of form, but not of identity of constituent matter. In an-
thropic combination, substances and aggregates, as the terms are
here used, are not produced, but biotic aggregates are interrelated
in their activities through the agency of mind.
In physical aggregates the relation of parts is that of interde-
pendence, so that the constitution and form of each part are de-
pendent on the constitution and form of every other part. This
interdependence may be better comprehended by means of an illus-
tration. In the aggregate the earth, the interdependence is exhib-
ited in the relations existing between the incompletely aggregated
bodies of minerals, known as geologic formations; the incompletely
aggregated bodies of water, known as seas, lakes, streams, and
clouds ; and the incompletely aggregated bodies of air, known as
winds. Air-currents gather the waters from the seas and pour them
upon the lands. Rains and rivers disintegrate the rocks and carry
them to the sea. Currents in the sea distribute the detritus over
ANNUAL ADDRESS OF THE PRESIDENT. XXXVII
the bottom. By the loading of areas of sea-bottom they are de-
pressed, and by the degradation of land-areas they are unloaded
and rise. Change in the geography of the land effects a change in
wind-currents and in bodies of water, and a change in the latter
effects a change in sedimentation. In like manner, throughout all
physical nature, an interdependence of parts is exhibited. Part
acts on part.
In biotic aggregates the same interdependence of parts is shown.
Any change affecting the digestive apparatus affects the circulatory
apparatus, and these again are influenced by the respiratory appara-
tus. But in addition to this interdependence of parts, there is also
an organization of parts—that is, special functions are performed
by the several parts, and each is the organ of its function. And
this organization is of such a nature that each works for the others.
The digestive apparatus digests for itself and all the organs, the
heart propels for all the body, the eye sees for all the body, the ear
hears for all the body, the hand touches for all the body. Thus the
organic parts act on and for one another.
In activital combination, aggregates, as the term is here used, do
not appear, but the same interdependence is observed. By associa-
tion the sanitary state of the husband affects that of the wife, and
the condition of the mother affects the child ; and on through the
different combinations of animals and men this interdependence is
observed. The relation of organization also exists by the differen-
tiation of industries. The husband brings food to the wife and
children, and the wife prepares the food. And this differentiation of
industries, or "division of labor" as it is termed in political science,
is carried on to an elaborate condition in civilized life. Then men
are related to one another as constituent members of society ; one
commands and another obeys. Then men are related to one another
through language ; one speaks, another hears ; one writes, another
reads. Then men are related to one another through opinions;
having common opinions, they form common designs and act for
common purposes. It will thus be seen that superorganic or an-
thropic combination arises from the establishment of four classes of
relations, corresponding to the four classes of activities represented
by arts, institutions, languages, and opinions. The arts are human
activities directed to the utilization of the materials of nature and
the control of its powers, for the purpose of securing happiness. In-
stitutions are human activities arranged for the purpose of securing
XXXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
peace and establishing justice, and thereby increasing happiness
Languages are activities devised for the purpose of communicating
thought, and thereby securing happiness. Opinions arise from
psychic activities, the purpose of which is to learn the truth, that
happiness may ensue.
In physical, biotic, and anthropic combinations the parts control
one another. It will therefore be convenient to speak of three
kingdoms of matter: the mineral or physical kingdom, the organic
or biotic kingdom, and the anthropic or activital kingdom.
MODES OF MOTION.
All bodies, however combined, are discovered to be in motion.
Among the bodies of the mineral kingdom, a, variety of modes
of molecular motion are exhibited, having various distinguishing
characteristics. These are heat and light, electricity and magnetism,
then sound and that motion in gases by which through impact they
retain their rarefied state. Again, a variety of molar motions are
observed in gases, liquids, and solids ; and finally stellar motions
are observed in astronomic systems.
In the biotic kingdom plants and animals exhibit many varieties
of organic motions, called functions. These are superadded to the
physical motions, which appear alike in the physical and biotic
kingdoms. Physical bodies exhibit motions ; biotic bodies exhibit
motions and functions, the latter being highly organized motions.
In the anthropic kingdom there is a complexity of motions arising
from biotic functions, which are arranged and combined so as to
produce activities. These activities are represented by arts, institu-
tions, languages, and opinions.
Thus there are three great classes of motions corresponding to the
three great classes of combinations, namely, physical motions ; biotic
motions, or functions ; and anthropic motions, or activities.
THE RELATION OF MOTION TO COMBINATION.
It will at once be seen that anthropic combination is such by
virtue of human activities. Activital combination is manifestly
composed motion.
Again, biotic aggregates are such by virtue of continuous combi-
nation and dissolution. Within proper limits a biotic body may be
compared to a river ; it is a form through which matter passes. In
ANNUAL ADDRESS OF THE PRESIDENT. XXXIX
plants some of this passing matter becomes fixed for a time, but
eventually returns from the biotic to the mineral kingdom. Among
animals this passage of physical matter through the biotic form is
more rapid. The organic functions, also, of these bodies are but
arranged or organized motions. Life is motion—the specific motion
called function.
Again, among the aggregations of the physical kingdom, stellar
systems are aggregates by virtue of motion. The combination ob-
served is due to composed motion. Of the mechanical combina-
tions, that exhibited in the atmosphere is such by virtue of motion
—
that is, the gaseous state is preserved by the interference of molecu-
lar motions, and the bodies into which it is imperfectly differen-
tiated, i. e., currents of air, are such by virtue of motion. Again,
the imperfectly aggregated bodies of water are such by virtue of
motion. This is seen to be true of the clouds floating in the air,
and of rivers rolling to the seas. Lakes with outlets are bodies of
water in motion, forever fed from the clouds, forever discharging
into the sea ; and mediterranean seas without outlet are perpetually
receiving and discharging their waters ; and so far as the sea is
differentiated into currents, these are bodies imperfectly aggregated
by motion.
There yet remain certain molecular combinations of inorganic
substances, due to affinity and gravity, the nature of which is not
so immediately perceived. Now, as all societies and other anthropic
combinations are such by virtue of their motions, known as activi-
ties, and as all biotic bodies are such by virtue of their functions,
and as all stellar combinations are such by virtue of stellar motion,
and as finally all mechanical combinations are such by virtue of
motion, it is at once suggested as an inductive hypothesis that those
combinations the nature of which is yet unknown are also such by
virtue of motion. It is an hypothesis worthy of consideration, that
affinity and gravity are also due to motion. It has even been sup-
posed by some that chemical and barologic methods of combination
are but diverse modes of the same process ; that affinity and gravity
constitute but one method of combination, and that we call it
affinity when the combination involves minute bodies, below our
sense perceptions, and gravity when larger bodies are involved.
An attempt has thus been made to define the three kingdoms of
matter in terms of matter and motion, showing that there are three
XL PHILOSOPHICAL SOCIETY OF WASHINGTON
methods of combination, and that the parts combined are related
by three corresponding methods, aud that in each kingdom motions
of a distinctive class are discovered. The constitution of physical
bodies is due to composed motion ; the constitution of biotic bodies
is due to composed transmutations of motion ; anthropic combina-
tions are due to related activities.
In order that there be evolution, there must be change in com-
bination of matter and in mode of motion. The sole property of
matter is motion, and motion itself is change of position. But this
change of position results in chauge of combination, and change of
combination results in change of mode of motion. These changes
must now be set forth.
CHANGE OF COMBINATION.
If the mind could discern and classify all the bodies of the uni-
verse at any one moment, only space conditions would enter therein
;
but bodies change from time to time, so that there are sequences of
combination. Substances and aggregates of matter are such by rea-
son of an arrangement in position of their constituent parts. Sub-
stances and bodies change in external relations aud in internal rela-
tions. Change in external relations is chauge of position in relation
to external things. Change in internal relations is the change in
relative arrangement of constituent parts. And this change of posi-
tion is always motion, the first and only property of matter.
Chemical, crystalline, and lithical combinations are decomposed
and otherwise re-composed, mechanical combinations are broken
up and otherwise re-arranged, and stellar aggregates are believed
to have been gradually formed. With physical bodies internal
chauge is the direct result of external change. This is their dis-
tinctive characteristic, that all their chauges of constitution result
directly from agencies without themselves.
Biotic bodies exhibit the same changes as mineral bodies, and
also a series peculiar to themselves. First, biotic substances are
segregated from the mineral kingdom
—
i. e., mineral substances are
changed into biotic substances. Second, biotic bodies begin, grow,
decline, aud die. This is a progressive chauge of structure. Third,
the structure of biotic bodies is preserved by continuous change in
their constituent matter. Form and structure are preserved while
the matter is forever changing. Life is a determined, systematic
sequence of transmutations of motion, transformations of matter, and
ANNUAL ADDRESS OF THE PRESIDENT. XLI
transfigurations of body. Life is change. Fourth, as the individ-
uals are not persistent, the method of aggregation continues by the
processes of reproduction of like forms. But these like forms are
made unlike
—
i. e., changed—by two processes. In the biotic repro-
duction of the higher forms the bisexual method prevails, so that
each individual is the offspring of two parents, like both so far as
they are alike, but differing from the one or the other so far as they
are unlike. Fifth, the individual has its constitution determined
by its parents, but subject to changes which may be brought about
by external relations differing from those to which the parents were
subjected ; and within limits these are transmitted to offspring.
Thus it is seen that biotic changes are caused by external and in-
ternal agencies.
This may be put in another form. In mineral bodies the same
matter is changed in structure. In biotic bodies the same or nearly
the same structure remains and the constituent matter changes; yet
there is a slow change in structure from birth to death, and a still
further change in structure from generation to generation ; but
there is more rapid change of constituent matter. Anthropic ag-
gregates arise, not by a combination of matter, but by a combina-
tion of the activities of biotic bodies. These biotic bodies them-
selves change, as individuals disappear and new ones take their
places. Thus family group succeeds family group, and generations
of people succeed generations of people. In the same manner arts
change. Old arts are abandoned and new arts appear. Various
societies cease to exist and new societies are organized. The organ-
ization due to the differentiation of operations steadily increases by
the division of labor; and the grouping of bodies of men into states,
i. e., tribes and nations, is in constant flux. So, languages change
—
they grow and die. And opinions change with each individual and
from generation to generation. All these changes are determined
by the will of the individual units who are actors—that is, activi-
ties change because the actors so desire. Anthropic change is due
to psychic agencies.
CHANGE OF MOTION.
That motion is persistent is a fundamental axiom. But while it
does not change in quantity it changes in quality in diverse ways.
First, motion may be changed in direction. Simple motion is the
motion of a body in a straight line, and change of such motion of
XLII PHILOSOPHICAL SOCIETY OF WASHINGTON.
the lowest order is change in direction, and this is accomplished by
the combination of two or more motions having different directions.
Then motion may be transmitted from one body to another. The
molecular motions—heat, light, electricity, sound, etc.—are motions
propagated by transmission from molecule to molecule. In the
kinematic hypothesis of gravity it is held that atomic motion is
transmitted from atoms to combined and aggregated bodies by im-
pact; and here we reach another method of change—that by trans-
mutation. One mode of motion may be transmuted into another,
as molar motion into heat, and heat into electricity.
By the combination of matter motion is composed. Mineral sub-
stances and aggregates exhibit this composition of diverse modes of
motion. Biotic bodies exhibit composition of modes of motion, and
also composition of transmutations of motion, and it is this latter
characteristic which distinguishes biotic from physical motion.
Activital combinations exhibit a composition of modes of motion,
and a composition of the transmutations of motion, and a compo-
sition by co-operative action. It is the last characteristic which
distinguishes activital motion from biotic.
The changes of motion exhibited in the mineral kingdom are
changes in direction by combination, changes in relative quantity
by transmission, changes in mode of motion through transmutation,
and changes in the combination of modes of motion.
In the biotic kingdom the same changes are found as in the min-
eral kingdom, but to them are added changes in the composition of
transmutations of motion.
In the anthropic kingdom all the changes in the other kingdoms
appear, together with changes in the composition of activities.
EVOLUTION DEFINED.
As matter is indestructible, when one combination or aggregation
is dissolved some other must appear, and vice versa. Existing
bodies must have antecedents. In tracing backward the history of
bodies, lines of sequences are followed. Many such are known, and
the first important characteristic to be noted of them is they are
orderly. Like bodies have like antecedents. From this results one
of the highest inductions of science, namely, that from consequents
antecedents can be restored, and from antecedents consequents can
be predicted. The second important characteristic of these sequences
ANNUAL ADDRESS OF THE PRESIDENT. XLTTT
of change is that many are in a definite direction, which is gradually
becoming known. This general course of change is denominated
Evolution, and the term must be defined.
Evolution is progress in systemization. It must be noted that
not all changes are progressive ; some are retrogressive. It is only
progressive change that is here called evolution ; retrogressive change
is dissolution. As the term is here used, a System is an assemblage
of interdependent parts, each arranged in subordination to the
whole so as to constitute an integer. Evolution may therefore be
defined in another way. It is progress in differentiation by the
establishment of unlike parts, and in the integration of these parts
by the establishment of interdependence. Dissolution is retrogres-
sion by the lapsing of integration through the destruction of inter-
dependence, and the lapsing of differentiation through the loss of
heterogeneity in parts.
EVOLUTION IN THE PHYSICAL KINGDOM.
Under the kinematic hypothesis, which embraces the ethereal and
nebular hypotheses, portions of discrete matter have been segregated
to be combined and aggregated. The process precedent to evolu-
tion, then, is combination and aggregation, by which substauces
and integers are produced.
Whatever may be the fate of the explanation of the origin of
substances and aggregates through the kinematic and concomitant
hypotheses, the fact remains that such bodies exist, and the evolu-
tion of matter, as it is hereafter dealt with, starts from this point.
Given substances and aggregates as they are known to exist in
nature, and given changes which they are known to undergo, it is
proposed to point out by what methods evolution is attained.
The terms substance and aggregate have been used as distin-
guishing two orders of combination. It should be noted that they
cannot be clearly demarcated. Substances are composed of homo-
geneous, non-interdependent parts, but this homogeneity is never
absolute, and some slight degree of interdependence may always be
discovered. Aggregates, on the other hand, are composed of hetero-
geneous, interdependent parts, but degrees of heterogeneity and
interdependence appear. Combination is the bringing together of
dissociated matter ; and it is in the combinations, separations, and
re-combinations of matter that evolution appears.
XLIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
In mineral bodies combinations proceed by molecular, molar, and
stellar methods. It has been shown that the changes in these bodies
are due to external conditions or forces. If a given body be in
harmony with external conditions no change occurs in its constitu-
tion, but if it be out of harmony the impinging agencies effect such
modifications as will produce harmony. This may be done by a
change in the body as a substance or aggregate, or by its separation
and re-combination in some more harmonious form. The evolution
of mineral bodies is thus accomplished by direct adaptation to
external conditions.
If it is permitted hypothetically to conceive of a universe of
ethereal matter
—
i. e., matter composed of discrete atoms in motion,
such atoms would remain in an attenuated condition by atomic im-
pact. In matter thus constituted, motion could be transmitted from
atom to atom, but no new mode of motion would result therefrom.
The mass of matter thus constituted would be absolutely homoge-
neous. But if by some method several such atoms should be com-
bined, so as to move together as a common body, and so that
their interspaces could not be penetrated by other atoms, the motion
of an impinging atom would not only be transmitted to the larger
body, but it would also be transmuted into another mode or kind of
motion. If other such molecules were formed by the segregation of
atoms from the homogeneous mass, the new kind of motion would
be set up in all the matter thus segregated, and the motions of these
bodies would react one upon another. If, again, some of these
molecules were segregated, to be combined in larger bodies, with or
without such a diminution of interspaces as to prevent the inter-
penetration of atoms, a third mode of motion would be established
;
and if diverse methods of aggregation should occur, diverse modes
of motion would be established thereby ; and in all combining and
re-combining, aggregating and re-aggregating, new modes and com-
plexities would arise.
It is a well-known law that a moving body passes in the direction
of the least resistance. Diverse modes of motion may exist in a
body, due to the complexities of its organization. In the trans-
mission of motion to such a body from another by impact, the
motion transmitted is transmuted into that mode which gives it
the least resistance. This is illustrated on every hand. When
a smaller body impinges against a larger, the inequality between
the two may be so great that molar motion is not set up in the
ANNUAL ADDRESS OP THE PRESIDENT. XLV
larger body, but the whole of the imparted motion is transmuted
into heat or some other molecular motion.
This law, that motion passes in the direction of least resistance,
is the equivalent of the law of adaptation in the evolution of mat-
ter. When evolution is considered from the standpoint of matter,
it is convenient to use the term Adaptation ; when considered from
the standpoint of motion, it is more convenient to use the term Least
Resistance.
EVOLUTION IN THE BIOTIC KINGDOM.
In biotic bodies it has been seen that change is the result of in-
ternal as well as external conditions. As external conditions, or the
environment, are changing, these bodies change to a limited extent,
in the same manner as do mineral bodies ; but there is also a change
brought about indirectly by the environment, through certain in-
ternal changes in the constitution of biotic bodies. Through this
internal constitution individuals are changed in time—one genera-
tion dies and another succeeds.
There is yet another method of change in biotic bodies, which
steadily increases from the lowest to the highest—that is, the change
in their constituent matter. While structure changes slowly from
birth through growth and decadence to death, the constituent matter
changes with much greater rapidity. In this change the minute
elements of structure change much more rapidly than the larger
into which they are compounded ; so that every part of the organ
must be supplied with new material to replace that which is steadily
becoming effete and passing away. Now the rate of this change in
any integral part of an organism is dependent upon the activity of
the organ. Exercise increases the rate of change in the constituent
matter of a biotic organ, and thus the slow change in its structure,
which proceeds from life to death, is accelerated. This accelerated
change results in increased differentiation of the organ, and it thereby
becomes more and more efficient in the performance of its function.
This change, therefore, results from exercise. Organs that are ex-
ercised increase in efficiency, by non-exercise they decrease in effi-
ciency. This change in the organization of any one individual is
but slight, but as the slight changes pass from one generation to
another, continuous exercise of one set of organs greatly modifies
them ; continuous neglect of exercise in another set modifies them
also, until at last they are atrophied. Thus by exercise and non-
4a
XLVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
exercise important structural changes are produced when conjoined
with the changes due to heredity.
All these changes result in progress, from the fact that those indi-
viduals whose change is in a direction out of harmony with the en-
vironment ultimately perish, while those whose change is in a direc-
tion in harmony with the environment survive. This method of
adaptation or evolution in biology is called " the survival of the
fittest."
The rate of evolution by survival is greatly accelerated by another
condition. Each pair of biotic bodies reproduce a large number of
new bodies, so that reproduction from generation to generation is in
a high geometric ratio. The earth having become occupied with
all the biotic beings that can derive sustentation therefrom, but a
small fraction of the beings produced in a generation can live. Few
survive, many succumb. Survival by adaptation is therefore made
more efficient by competition.
There are other changes in the biotic kingdom brought about by
adaptation. The multiplicity of biotic beings, causing over-popula-
tion, has crowded them into every conceivable habitat—in the air,
on the land, and in the water; and living beings have become
adapted thereto by the development of wings, legs, fins, and correl-
ative organs. Thus by exercise organs have been developed, and
by non-exercise other organs have been atrophied, until living be-
ings have become specialized for a vast diversity of habitats—for
life on the mountain and in the valley, in the light and in the dark,
in the cold and in the heat, in humid regions and in arid re-
gions. Living beings have also been adapted to various kinds of
food and to various methods of acquisition—in fine, to a great
variety of conditions.
This specialization by development, through exercise and non-
exercise, must be clearly distinguished from the processes of evolu-
tion. The heterogeneous living beings thus produced are but multi-
plied and diverse forms, animals and plants alike being as often de-
graded as evolved in the processes of specialization. Degradation
is especially to be noticed in parasitic animals and others adapted
to extremely abnormal habitats ; but it should be understood that
a form thus produced may, in the process of its production and sub-
sequent existence, make progressive change in the system of its
structure by the methods of evolution already characterized.
Specialization is greatly accelerated by a peculiar method. As
ANNUAL ADDRESS OP THE PRESIDENT. XLVII
all the highei animals are physically discrete, psychic relations
must be established, in order that they may meet for the act of re-
production. These psychic relations gradually develop into choice,
or sexual selection, and by methods which have been clearly pointed
out by biologists the minute increments of change that result there-
from eventually accumulate into strong variations, always adapted
to the conditions of the environment. Thus the survival of the
fittest is accelerated by sexual selection.
EVOLUTION IN THE ANTHROPIC KINGDOM.
If attention is directed exclusively to animal life, we notice that
evolution has proceeded pari passu with specialization. Of the
forms that have been specialized from time to time some have be-
come extinct, some have been degraded, and some have been evolved
in varying degree. One form, not the most specialized, made the
greatest progress in evolution, until an organism was developed of
so high a grade that this species became more independent of en-
vironment than any other, and, by reason of its superiority, spread
widely throughout the land portion of the globe. This superior
animal was early man, when he first inhabited all the continents
and the great islands. The production of this superior, i. e. more
highly systematized organism, was the antecedent to the inauguration
of new methods of evolution.
It has been shown that the great efficiency of the biotic method
of evolution by survival depends upon competition for existence in
enormously overcrowded population. Man, having acquired superi-
ority to other animals, passed beyond the stage when he had to
compete with them for existence upon the earth and into the stage
where he could utilize plants and animals alike for his own pur-
poses. They could no longer crowd him out, and to that extent
the law of the survival of the fittest in the struggle for existence
was annulled in its application to man. , He artificially multiplies
such of the lower animals as are most useful to him, and domesti-
cates them, that they may be more thoroughly under his control,
and modifies them, that they may be more useful, and uses such as
he will for beasts of burden ; and the wild beasts he destroys from
the face of the earth. In like manner he cultivates useful plants,
and destroys such as are worthless to him. He does not compete
with other biotic species, but utilizes them for his welfare. Yet
XLVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
the law of the survival of the fittest applies in so far as it is not
dependent upon competition, and slow evolution may still result
therefrom. But at this stage new methods spring up of such great
efficiency that the method by the survival of the fittest may be
neglected because of its insignificance.
In anthropic combinations the units are men, and men at this
stage are no longer passive objects, but active subjects ; and instead
of man being passively adapted to the environment, he adapts the
environment to himself through his activities. This is the essential
characteristic of anthropic evolution. Adaptation becomes active
instead of passive. In this change certain parts of the human or-
ganism are increasingly exercised from generation to generation.
This steadily increasing exercise results in steadily increasing
development, and the progress of the unit—man—in this higher
organization depends upon development through exercise. But the
progress by exercise depends upon the evolution of activities.
Man is an animal, and may be studied as such ; and this branch
of science belongs to biology. But man is more than an animal.
Though an animal in biotic function, he is man in his anthropic
activities ; for by them men are combined
—
i. e., interrelated—so that
they are not discrete beings, but each acts on, for, and with, his
fellow-man in the pursuit of happiness. Human activities, thus
combined and organized, transcend the activities of the lower ani-
mals to such a degree as to produce a new kingdom of matter. The
nature of these activities must here be set forth.
The first grand class is composed of those which affect the exter-
nal world, and by them men are interrelated through their desires.
These activities are the Arts. The arts have been evolved by human
invention, and man has been impelled thereto by his endeavor to
supply his wants. In the course of the evolution of the arts, man
has progressively obtained control over the materials and powers of
nature. All the arts of all the human period are the inventions of
men. But invention has proceeded by minute increments of growth.
A vast multiplicity of arts have been devised, of which compara-
tively few survive in the highest civilization. As the inventions
have been made, the best in the average has been chosen. Man has
therefore exercised choice. The evolution of the arts has thus been
by the method of invention and choice, in the endeavor to gratify
desire, and by them man has adapted the environment to himself.
Second. There is a grand class of activities through which men
ANNUAL ADDRESS OP THE PRESIDENT. XLIX
are interrelated in respect to their conduct. These activities result
in Institutions. Through them men are associated for a variety of
purposes. Every institution is an organization of a number of in-
dividuals, who work together for a common purpose, as, for exam-
ple, to prosecute some industrial enterprise, to co-operate in the
pursuit of pleasure, to promote some system of opinions, or to wor-
ship together under the forms of some religion. All such institu-
tions constitute a class denominated Operative Institutions. A second
class are the institutions which man has organized for the direct reg-
ulation of conduct. These are States and their subordinate units,
with their special organs of government, and rules for the regulation
of conduct, called Laws.
Institutions have been developed from extreme simplicity to ex-
treme complexity. They are all the inventions of mankind, and
their evolution has been by minute increments of growth. Their
invention has been wrought out that men might live together in
peace and render one another assistance ; and gradually, by the
consideration of particulars of conduct as they have arisen from
time to time, men have sought to establish justice, that they might
thereby secure peace. Of the vast multiplicity of institutions
—
forms of state, forms of government, and provisions of law—which
have been invented, but few remain in the highest civilization, and
these few have been selected by men. Men have thus exercised
choice. Institutions, therefore, have been developed by invention
and the choice of the just in the endeavor to secure peace.
Third. There is another fundamental group of activities through
which men are interrelated in respect to their thoughts. These are
the activities of mental intercommunication, and result in Lan-
guages. Languages, also, are inventions by minute increments of
growth. Many languages have been invented, and in each language
many words and many methods of combining linguistic devices have
been invented. In the languages of the most civilized peoples, but
few of these survive ; and there are spoken by all the peoples of the
earth but few languages in comparison to the many that existed in
the early history of mankind ; and the method of survival, when
analyzed, is found also to be choice. Men have chosen the economic
in the expression of thought. Languages, therefore, have devel-
oped by invention and choice in the struggle for expression.
Fourth. There is a grand class of activities by which men are
interrelated in respect to their designs. Men arrive at Opinions, and
L PHILOSOPHICAL SOCIETY OF WASHINGTON.
these have always reacted upon languages, institutions, and arts, and
largely led them in their courses of progress. Because of their opin-
ions, men are willing to work together, and thus have common designs.
There have been many opinions and many systems of philosophy. Of
all that have existed, but few remain in the highest civilization. A
careful analysis of the facts relating to the growth of opinions re-
veals this truth, that opinions also are invented, and that the final
survival of the few has been due to the human act of choice in the
selection of the truth. Opinions, therefore, have been developed by
invention and choice in the struggle to know.
Fifth. Opinions are formed as the direct activities of the Mind.
Languages, institutions, and arts have arisen through the action of
the mind and the exercise of other corporeal functions. All these
activities, therefore, are dependent upon the mind. On the other
hand, these objective activities react upon the mind, so that mental
operations are controlled thereby. Through the exercise of the
mind in the prosecution of activities it is developed. These
mental activities are perception and comparison, or reflection, as it
is more usually called. The subjective evolution of the mind is
therefore the product of the objective evolution of activities.
These five great classes of activities are interdependent in such a
manner that one is not possible without the others ; they arise to-
gether, and their history proceeds by a constant interchange of
effects. All the five classes of activities react upon man as an ani-
mal in such a manner that his biotic history subsequent to his
differentiation from the lower animals is chiefly dependent thereon.
The evolution of man as a being superior to the beast is therefore
due to the organization of activities.
It has been shown that man does not compete with the lower
animals for existence. In like manner, man does not compete with
man for existence ; for by the development of activities men are
interdependent in such a manner that the welfare of one depends
upon the welfare of others ; and as men discover that welfare must
necessarily be mutual, egoism is transmutted into altruism, and
moral sentiments are developed which become the guiding princi-
ples of mankind. So morality repeals the law of the survival of
the fittest in the struggle for existence, and man is thus immeasur-
ably superior to the beast. In animal evolution many are sacrificed
for the benefit of the few. Among mankind the welfare of one
depends upon the welfare of all, because interdependence has
been established.
ANNUAL ADDRESS OP THE PRESIDENT. LI
It has thus been shown that there ai*e three stages in the combina-
tion of matter and motion, and that each stage is characterized by
a clearly distinct method of evolution. These may be defined as
follows
:
First, physical evolution is the result of direct adaptation to en-
vironment, under the law that motion is in the direction of least
resistance.
Second, biotic evolution is the result of indirect adaptation to the
environment by the survival of the fittest in the struggle for exis-
tence.
Third, anthropic evolution is the result of the exercise of human
faculties in activities designed to increase happiness, and through
which the environment is adapted to man.
These may be briefly denominated : evolution by adaptation,
evolution by survival of the fittest, and evolution by endeavor.
Civilized men have always recognized to some extent the laws of
human evolution,—that activities are ideologically developed, and
that happiness is increased thereby. In the early history of man-
kind the nature of teleologic endeavor was so strongly impressed
upon the mind that the theory was carried far beyond the truth, so
that all biotic function and physical motion were interpreted as
teleologic activity. When this error was discovered, and the laws
of physical and biotic evolution established, vast realms of phe-
nomena were found to have been entirely misunderstood and falsely
explained, and teleologic postulates have finally fallen into disrepute.
Men say there is progress in the universe by reason of the very laws
of nature, and we must let them alone. Thus, reaction from the
ancient false philosophy of teleology has carried men beyond the
truth, until they have lost faith in all human endeavor ; and they
teach the doctrine that man can do nothing for himself, that he
owes what he is to physical and biotic agencies, and that his inter-
ests are committed to powers over which he has no control.
Such a philosophy is gradually gaining ground among thinkers
and writers, and should it prevail to such an extent as to control
the actions of mankind, modern civilization would lapse into a con-
dition no whit superior to that of the millions of India, who for
many centuries have been buried in the metaphysical speculations
of the philosophy of ontology. When man loses faith in himself,
and worships nature, and subjects himself to the government of the
LII PHILOSOPHICAL SOCIETY OF WASHINGTON.
laws of physical nature, he lapses into stagnation, where mental and
moral miasm is bred. All that makes man superior to the beast is
the result of his own endeavor to secure happiness.
Man, so far as he is superior to the beast, is the master of his
own destiny, and not the creature of the environment. He adapts
the natural environment to his wants, and thus creates an environ-
ment for himself. Thus it is that we do not discover a biotically
aquatic variety of man, yet he dwells upon the sea and derives
sustentation from the animals thereof by means of his arts. *A
biotically arboreal variety of man is not discovered, but the forest
are used in his arts and the fruits of the forests for his susten-
tation. An aerial variety of man is not discovered, but he uses
the winds to propel his machinery and to drive his sails ; and, in-
deed, he can ride upon the air with wings of his own invention.
A boreal variety of man is not discovered, but he can dwell among
the everlasting snows by providing architectural shelter, artificial
warmth and bodily protection.
Under the influences of the desert a few plants secure a constitu-
tion by which the moisture imbibed during brief and intermittent
rains is not evaporated ; they become incrusted with a non-porous
glaze, or contract themselves into the smallest space and exist with-
out life until the rain comes again. Man lives in the desert by
guiding a river thereon and fertilizing the sands with its waters, and
the desert is covered with fields and gardens and homes. Every-
where he rises superior to physical nature. The angry sea may not
lash him with its waves, for on the billows he builds a palace, and
journeys from land to land. When the storm rises it is signaled
from afar,and he gathers his loved ones under the shelter of his
home, and they listen to the melody of the rain upon the roof.
When the winds of winter blow he kindles fossil sunshine on his
hearth, and sings the song of the Ingleside. When night covers
the earth with darkness he illumines his path with lightning light.
For disease he discovers antidote, for pain nepenthe, and he gains
health and long life by sanitation ; and ever is he utilizing the
materials of nature, and ever controlling its powers. By his arts,
institutions, languages, and philosophies he has organized a new
kingdom of matter, over which he rules. The beasts of the field,
the birds of the air, the denizens of the waters, the winds, the
waves, the rivers, the seas, the mountains, the valleys, are his
subjects; the powers of nature are his servants, and the granite
earth his throne.
BULLETIN
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
GENERAL MEETING.

BULLETIN
GENERAL MEETING
227th Meeting. January 13, 1883.
The President in the Chair.
Twenty-six members present.
Mr. H. Farquhar completed a communication begun at the
224th meeting on
EXPERIMENTS IN BINARY ARITHMETIC,
in which he showed that simple addition involved carrying on sev-
eral distinct mental operations almost simultaneously and a capital
of more than fifty propositions committed to memory. Believing
that the difficulty in mastering, and the mental strain and liability
to error in conducting, this most important of mathematical pro-
cesses could be proved to be unnecessarily great, he had compared
the time occupied in adding a few dozen numbers of six or eight
figures each with that required when these numbers were expressed in
powers of 2, the mental work being, in the latter case, reduced to
counting similar marks and halving their sums. He had found it
best to give different forms to the marks denoting neighboring powers,
so as to avoid confusion of columns, and had combined two or more
of them into one written figure for brevity of expression. About
seventy combinations of various shapes had been tried, but very few
of them found economical. In the best notation, however, the addi-
tion required only three-fourths the time taken with the ordinary
figures. Had the computer practised as many weeks with the new
notation as years with the old, the difference would have been much
more marked ; as it was in fact when one unskilled in arithmetic,
to whom the binary notation had just been taught, tried the two
additions. The gain in accuracy, with this observer, was even
3
4 PHILOSOPHICAL SOCIETY OF WASHINGTON.
more striking than the gain in speed. There could be very little
doubt, therefore, that a fair degree of skill in arithmetic with a
binary notation could be acquired by many to whom it is impossible
under the present system.
The only practicable division of arcs and angles, and the most
natural division of all things, is by continued bisections. This is
shown by the ratio of value in our coins, weights, and capacity
measures ; by any table of prices ; and by the prevalent subdivision
of lowest nominal units, as of the carpenter's inch into eighths and
sixteenths, and of percentages into quarters, etc., in stock quotations,
where convenience of calculation by our present arithmetic seems
almost gratuitously sacrificed. The American coinage is inconve-
nient in practice, because of the awkward fractional ratio 1\, which
it introduces between successive pieces ; and there would be the
same difficulty in a decimal system of weights or of measures, should
it be imposed upon us. We have thus another powerful reason for
endeavoring to introduce a binary arithmetic.
In the remarks which followed, Mr. E. B. Elliott expressed the
hope that Congress would adopt the metric system of weights and
measures for international purposes. It would be better to secure
what advantage could be gained from uniformity and consistency,
even though the basis of consistency was an arithmetic not ideally
the best attainable. Such a course would not prevent, but might
pave the way for a better arithmetic.
Mr. W. B. Taylor said the world was losing so much by the
employment of the denary arithmetic that he thought even a single
generation might find economy in substituting the octonary. The
introduction of decimal measures, while it would aid the computer,
would injure the remainder of the community. The paper of Mr.
Farquhar had an especial value, in that it proved the ability of
binary systems to compete with the established system in rapidity
of computation.
Other remarks were made by Messrs. Bareness, Mussey, Pow-
ell, and Gilbert.
The next communication was by Mr. S\ M. Burnett on
REFRACTION IN THE PRINCIPAL MERIDIANS OF A TRIAXIAL ELLIP-
SOID
J
REGULAR ASTIGMATISM AND CYLINDRICAL LENSES ;
and he was followed by Mr. W. Harkness on
GENERAL MEETING. 5
THE MONOCHROMATIC ABERRATION OF THE HUMAN EYE IN
APHAKIA.
These two papers are complementary, and are published in the
Archives of Ophthalmology, Vol. XII, No. 1.
228th Meeting. January 27, 1883.
The President in the Chair.
Thirty-seven members present.
The Auditing Committee, appointed at the Annual Meeting, re-
ported through its chairman, Mr. Antisell, that it had examined
the accounts of the Treasurer for 1882, and found them correct.
The report was accepted.
The communication of the evening was by Mr. H. H. Bates on
THE NATURE OF MATTER,
and was discussed by Mr. W. B. Taylor and Mr. Powell.
This paper is published in the Popular Science Monthly for
April, 1883.
229th Meeting. February 10, 1883.
The President in the Chair.
Forty-two members and visitors present.
It was announced that reports of the scientific proceedings would
hereafter be furnished to Science.
Mr. W. H. Dall announced that an opportunity would be
afforded members to contribute to the Balfour Memorial Fund.
A communication was then read by Mr. A. F. A. King on
THE PREVENTION OF MALARIAL DISEASES, ILLUSTRATING, inter alia,
THE CONSERVATIVE FUNCTION OF AGUE.
[Abstract.]
The various theories thus far presented in explanation of the
6 PHILOSOPHICAL SOCIETY OF WASHINGTON.
phenomena of malaria were unsatisfactory and insusceptible of
scientific demonstration.
' According to the best medical authorities the most generally
admitted facts upon which the present orthodox theory of malaria
rests were as follows: 1. Malaria affects by preference low and
moist localities. 2. It is almost never developed at a lower tem-
perature than 60° F. 3. Its evolution or active agency is checked
by a temperature of 32° F. 4. It is most abundant and most
virulent as we approach the equator and the sea-coast. 5. It has
an affinity for dense foliage, which has the power of accumu-
lating it, when lying in the course of winds blowiug from malarious
localities. 6. Forests or even woods have the power of obstructing
and preventing its transmission under these circumstances. 7. By
atmospheric currents it is capable of being transported to consider-
able distances
—
probably as far as five miles. 8. It may be devel-
oped in previously healthy places by turning up of the soil, as in
making excavations for the foundations of houses, tracks for rail-
roads, and beds for canals. 9. In certain countries it seems to be
attracted and absorbed by bodies of water lying in the course of
such winds as waft it from the miasmatic source. 10. Experience
alone can enable us to decide as to the presence or absence of
malaria in any given locality. 11. In proportion as countries,
previously malarious, are cleared up and thickly settled, periodical
fevers disappear, in many instances to be replaced by typhoid
fever (?) 12. Malaria usually keeps near the surface of the earth.
It is said to " hug the ground," or " love the ground." 13. It is
most dangerous when the sun is down, and seems almost inert
during the day. 14. The danger of exposure after sunset is greatly
increased by the person exposed sleeping in the night air. 15. Of
all human races the white is most sensitive to marsh fevers, the
black least so. 16. In malarial districts the use of fire, both in-
doors and to those who sleep out, affords a comparative security
against malarial disease. 17. The air of cities in some way renders
the poison innocuous ; for, though a malarial disease may be raging
outside, it does not penetrate far into their interior. 18. Malarial
diseases are most prevalent towards the latter part of summer and
in the autumn. 19. Malaria is arrested not only by trees, but also
by walls, fences, hills, rows of houses, canvas curtains, gauze veils,
mosquito nets, and probably by fishing nets. 20. Malaria spares
no age, but it affects infants much less frequently than adults.
GENERAL MEETING. 7
These generally admitted facts were insusceptible of scientific
explanation by the marsh fever hypothesis of Lanscisci ; but were
capable of explanation by the theory that marsh fevers are pro.
duced by the bites of proboscidian insects, notably in this and in
some other countries by mosquito bites.
A review of the natural history, habits, and geographical distri-
bution of the mosquito was next presented in explanation of the
twenty statements above quoted.
In discussing statement 15, it was maintained that the compara-
tive immunity of the black races was largely due to color, the dark
complexion of the skin being another illustrative instance of " pro-
tective coloring " so often observed in other animals, and by which,
in this instance, the negro was protected from the sight, and conse-
quently from the bite of the mosquito ; a similar protection being
further secured by the offensive odor and greasiness of his cutaneous
secretions, aided by artificial inunction of the body with grease,
paint, pitch, &c, which last probably constituted the initial step in
the evolution of dress. Hence malarial melanosis was considered
to be the designed natural termination of ague—its conservative
function—destined to modify the individual by defensive adaptation
against the mosquito, whose penetrating proboscis, like an inoculat-
ing needle, infected the body with malarial poison, no matter
whether this last was mosquital saliva, the Bacillus malarice of
Klebs and Crudelli, or some other element as yet unknown.
The spleen, whose function is not yet settled by physiologists,
was regarded as the chief pigment-forming organ, and was designed
for this purpose in the economy of the organism. Generally con-
sidered a superfluous organ, capable of removal without any great
interference with the functions of the organism, it was naturally
designed to meet the emergency of variation in skin-color to secure
" protective coloring " against fever-producing proboscidian insects
as before indicated. The natural process, however, required expo-
sure of the naked body to the sun during the chill stage, in order
to secure deposit of the newly formed pigment in the skin. Nature
had not anticipated the artificial appendage of dress, and the organ-
ism had not inherited from ancestral progenitors any provision for
so unexpected an addition. Chills do not occur at night, but only
between the rise and setting of the sun ; sunlight during the chill
stage being a necessary requirement, in order that nature's design
of cutaneous chromatogenesis may be consummated. Other racial
8 PHILOSOPHICAL SOCIETY OF WASHINGTON.
differences between the whites and blacks—such as even cerebral
capacity and variations in the skeleton—might be susceptible of
explanation by blood changes resulting from malaria. The marrow
of bones was also a pigment-forming tissue, and the aching of bones
during ague, especially in so-called " break-bone " fever, suggested
congestion and modified nutrition in the osseous structures, such as
might eventually lead to modification in the skeleton. The inhabi-
tants of oriental countries especially were more vigorous and intel-
ligent if they lived in elevated regions, than were others inhabiting
mosquito-infected lowlands and sea coasts.
In further support of the mosquital origin of malarial fevers
numerous noted medical authorities were cited, showing that, in
all parts of the world where these diseases prevail, immunity was
secured by protecting the body from mosquito bites. The geo-
graphical distribution and seasonal evolution of mosquitoes and
other proboscidian insects were shown partially to agree with the
times and places in which malarial diseases prevail ; though from
lack of information conclusive evidence on this point was yet
wanting. There was, however, a general admission on the part of
medical authorities that swarms of these insects in almost any
locality were a pretty sure sign of malignancy.
On the other hand numerous instances were adduced from " Nar-
ratives " and " Travels " in which the bodies of persons had been
covered with pustules, " resembling small-pox," from mosquito bites
without any subsequent occurrence of fever having been recorded
by the narrating authors.
This opposing evidence was inconclusive, (1) because the authors
cited were not in search of medical information ; (2) because the
period of incubation, being often long and uncertain, fever may
have occurred after the mosquito bites had been forgotten; (3)
the insect proboscis (like a vaccine lancet unarmed with virus)
might be uncontaminated with fever poison, or fever germs ; and
(4) successful inoculations of specific germ poisons are not usually
followed by immediate local suppuration at the point of puncture,
but only after a certain period of incubation, the immediate local
inflammation being rather preventive of subsequent blood infection.
The possible spread of yellow-fever contagion by the inoculating
proboscis of the mosquito carrying infecting matter drawn from
the blood of yellow-fever patients to unaffected persons was sug-
gested. In epidemics, the spread of the disease stopped as soon as
a freezing temperature paralyzed the mosquito, &c.
GENERAL MEETING. 9
The spread of spotted-fever, typhus-fever, in jails, ships, &c, was
referred to the inoculating instrument of fleas, &c.—these insects
usually prevailing among filthy people thickly crowded together.
That malarial diseases were ever produced solely by the inhala-
tion of supposed poisonous vapors was held to be untenable. Ex-
perimenters, who had demonstrated the existence of specific poisons
for special fevers, had equally proven that the mode by which such
poisons, when obtained, could be introduced into the body for the
artificial production of disease, was by inoculation through the skin.
These experiments were imitations of insect inoculation. The pro-
boscis of the mosquito was Nature's inoculating needle.
The modus operandi of the eucalyptus tree in preventing malarial
diseases was ascribed tentatively to the tree being destruetive to, or
interfering directly or indirectly with, the propagation and develop-
ment of mosquitoes.
From the foregoing conceptions as to the origin of malarial dis-
ease, the following prophylactic measures were deducible
:
1st. Personal protection from all winged insects, especially during
evening and night, by gauze curtains, veils, window-blinds, or
clothing impenetrable by the proboscis of inoculating insects ; and
further, personal protection both from these and all creeping insects,
especially during epidemics, endemics, and in crowded jails, ships,
&c, by daily inunction of the whole body with some terebinthinate,
camphorated, or eucalyptalized ointment or liniment.
2d. Domiciliary protection (a) exteriorly, by screens of trees, walls,
fences, &c, interposed at some distance between dwellings and the
supposed sources of malaria, or mosquito nurseries ; and with fires
or lamps arranged as traps for the attraction and destruction of
such winged insects as may encroach nearer. A further protection
(b) in the interior of dwellings being secured by the use of smoke
(as of tobacco or prethrum) or of some volatile aromatic substance,
as of camphor, assafoetida, garlic, &c, which may be offensive to
proboscidian intruders.
3. Municipal protection by groves of trees (pines, cedars, or eucal-
yptus) planted between cities and the sources of malaria and mos-
quitoes, together with cordons of electric or other lights, between
said grove and the marsh, the lights to be arranged as fly-traps for
the retention and destruction of such winged insects as may be thus
secured.
5
10 PHILOSOPHICAL SOCIETY OF WASHINGTON,
With relation to the city of Washington, it was suggested that
the Washington monument would afford a good opportunity (by
placing illuminated fly-traps at different elevations on its exterior)
for ascertaining the height at which mosquitoes fly, or are brought
by the wind from the adjacent Potomac flats. The proposed re-
clamation of the flats could scarcely do more than mitigate malarial
disease, so long as our summer and autumn southern breezes come,
laden with mosquitoes, from the miles of unreclaimed swamps
farther down the river, as at Four-mile Run and other nearer local-
ities.
Mr. Billings remarked that, since ague did not invariably
result from insect bites, the most that could be claimed was that
they accomplished an accidental inoculation with malarial poison.
The subject was also discussed by Messrs. Doolittle, Toner,
and Antisell.
The meeting closed with an exhibition by Mr. C. E. Dutton of
a series of oil paintings illustrative of the Hawaiian Islands.
230th Meeting. February 24, 1883.
Vice-President Billings in the Chair.
Thirty members and visitors present.
The Chair announced the election of Mr. Thomas Russell to
membership.
The first communication was by Mr. G. K. Gilbert on
the response of terrestrial climate to secular variations
IN solar radiation.
[Abstract.]
Secular variations of climate may theoretically be caused (1) by
the internal heat of the earth and (2) by changes in the constitu-
tion or volume of the atmosphere. They have unquestionably been
wrought (3) by changes in the limits and configuration of ocean
bottoms and land surfaces, (4) by changes in the movements of the
earth with reference to celestial bodies, and (5) by variations of
GENERAL MEETING. 11
solar radiation. Attention will here be restricted to the last-men-
tioned cause.
An augmentation of the strength of solar radiation (a) will cause
a general rise in the temperature of the atmosphere, (b) will heighten
the contrast between warm and cold regions, thereby stimulating
oceanic and atmospheric circulation, and (c) will heighten the con-
trast between wet and dry regions, making the wet wetter and the
dry drier, (d) It will also diminish glaciation. This has been dis-
puted by some writers, but is sustained by a quantitative discussion.
A computation, based on the annual curves of precipitation and tem-
perature at St. Bernard, close to the glaciers of the Alps, shows that
a general rise in the temperature of the air, while it will increase the
total precipitation, will slightly diminish the snow-fall ; that it will
very greatly increase the rate of melting. The ratio of snow-fall
to evaporation is reduced one-half by 6° C rise of temperature;
the ratio of snow-fall to melting is reduced one-half by a rise of
1£°
; and, assuming that evaporation actually dissipates twice as
much snow as does melting, the ratio of snow-fall to snow dissipa-
tion (or the tendency to glaciation) is reduced one-half by 4f° rise
of temperature.*
(e) Increase of solar radiation will also, through its general
effects, influence the distribution of winds, and thus produce sec-
ondary effects of a local nature.
Mr. Dall remarked that ice was rendered more plastic and
fluent by the presence of water; so that the movement of ice and
the consequent- extent of glaciers are favored by rain. If Mr.
Gilbert by the term " glaciation " referred to the extent of glaciers,
some limitation of his conclusions might be necessary.
Other remarks were made by Messrs. Antisell, Doolittle, H.
Farquhar, and Elliott.
The next communication was by Mr. J. W. Chickering on
THE THERMAL BELTS OF NORTH CAROLINA.
[Abstract.]
In the agricultural volume of the Patent Office Report for 1861
is an article written by Mr. Silas McDowell, of Franklin, Macon
county, N. C, bearing this title. He was a man of much intelli-
* The computation is given in full in " Science " for March 16, 1883.
12 PHILOSOPHICAL SOCIETY OF WASHINGTON.
gence, an enthusiastic student in geology and botany, a companion
and guide of several botanists in their early explorations of the
southern Appalachians, and a farmer by profession. He died in
1882, at the ripe old age of 87.
He states that in the valley of the Little Tennessee river, in
Macon county, lying about 2,000 feet above tide water, when the
thermometer in the morning indicates a temperature of about 26°,
the frost line extends about 300 feet in vertical height, but that then
comes a belt extending about 400 feet in vertical height up the
mountain side, within which no frost is seen, delicate plants remain-
ing untouched. Above this, frost again appears. So sharp is the
dividing line that sometimes one-half of a shrub may be frost
killed, Avhile the other half is unaffected.
A small river, having its source in a high plateau 1,900 feet above
this, runs down into this valley, breaking through three mountain
barriers, and consequently making three short valleys, including
the plateau, rising one above the other, each of which has its own
vernal zone, traversing the hillsides that enclose it, and each
beginning at a lesser elevation above the valley, as the valleys
mount higher in the atmosphere, so that around the plateau, a
beautiful level height, containing 6,000 acres of land, and lying
3,900 feet above tide water, the loAver edge of the thermal belt is
not more than 100 feet above the common level of the plateau.
Not only does vegetation within this zone remain untouched by
frost, so that the Isabella, the most tender of all the native grapes,
has not failed to produce abundant crops in twenty-six consecutive
years, but mildew, blight, and rust, which often attack vines in the
lower valleys, are here unknown, while the same purity and dry-
ness of the air which favor the grape, make this a refuge for the
consumptive, as diseases of the lungs have never been known to
originate among the inhabitants.
Mr. McDowell adds : " The thermal belt must exist in all coun-
tries that are traversed by high mountains and deep valleys, and
the only reason why its visible manifestations are peculiar to our
southern Alleghanies, is the fact that their precocious spring vegeta-
tion is sometimes killed by frost, while the same thing does not
happen in the mountains further north."
These statements are corroborated by similar testimony respect-
ing another such belt along the Tryon mountain range in Polk
county, N. C. ; the specific claim being that such a belt is found
GENERAL MEETING. 13
for eight miles in length, extending from 1,200 feet to 2,200 feet
above tide water, within which the leaves of plants, shrubs, and
flowers remain untouched by frost until the latter part of Decem-
ber, and after a snow storm not a particle of snow remains within
the belt, while the tops and sides of the mountains above and the
valleys below will be covered.
The verification of these alleged facts would be matters of interest
in their economical and sanitary aspects, and would supply data
for some interesting researches respecting the nocturnal stratifica-
tion of the atmosphere.
It is earnestly to be hoped that at some time we may have reli-
able and continuous thermometrical observations at these and simi-
lar stations, to determine the existence, extent, and temperature of
such belts.
Remarks were made on this communication by Mr. Alvord.
Mr. C. E. Dutton then made a communication on the
GEOLOGY OF THE HAWAIIAN ISLANDS.
[Abstract.]
On the slopes of Mauna Loa are sea beaches, terraces, coral
sands, and other evidences of shore action at various levels. The
highest that can be positively announced has an altitude of 2,800
feet above the ocean. It can be traced a large part of the way
around the island, being discernible even when covered by more
recent lava. It does not now lie horizontal, but descends from
2,800 to 400 feet, while on the adjoining island, Maui, there is
evidence of submergence. On the farther (western) side of Maui,
and on other islands beyond, there is again evidence of upheaval.
All the lavas of the islands are basaltic. Those of Mauna Loa
and Kilauea are abnormally basic and are related to certain lavas
of New Zealand, called by Mr. Judd " ultra-basalts." The New
Zealand rock consists chiefly of olivine ; that of Mauna Loa is
sometimes more than half olivine, and contains much magnetite
and hematite. A Greenland lava, classed also as ultra-basalt,
contains the only known native iron of telluric origin. As this
suggests the iron meteorites, so the basalts of New Zealand and
Mauna Loa suggest the stony meteorites.
The volume of the eruptions of Mauna Loa is enormous ; that of
1855 would nearly build Vesuvius, and two of prehistoric date
14 PHILOSOPHICAL SOCIETY OP WASHINGTON.
were greater still. The lava has a high liquidity and flows forty
to fifty-five miles, spreading at the base of the cone into a broad
sheet. There are no explosive phenomena and no fragmental pro-
ducts. The slope of the mountain is 4° along the major and 7°
along the minor axis. Kilauea has a few cinder cones on its flanks.
-Mauna Kea consists chiefly of them, and has an average slope of
7J° to 11°.
Kilauea is always active, maintaining lakes of liquid fire.' Over
one of these a crust is formed, black, but flexible, which after a
while breaks up and suddenly sinks, the process being repeated at
intervals of 1§ to 2i hours. The great interior pit described by
observers from 1823 to 1841 is now filled.
Mauna Loa is not active more than one-third or one-fourth of
the time, but compensates by the magnificence of its phenomena.
Great fountains of lava are projected hundreds of feet into the air.
Mr. Dutton's communication was interrupted by the arrival of
the hour for adjournment. In response to a question by Mr. Tay-
lor, he stated that the crust over a lava lake acquired a thickness
of five or six inches before breaking up.
Mr. Antisell inquired whether there is any basalt on the
islands, and Mr. Dutton explained that they are composed exclu-
sively of that material.
231st Meeting. March 10, 1883.
Vice-President Welling in the Chair.
Thirty-four members and visitors present.
The Chair announced that Messrs. Albert Williams, Jr.,
John Henry Renshawe, and Henry Francis Walling had
been elected to membership.
Mr. M. H. Doolittle read a communication on
SUBSTANCE, MATTER, MOTION, AND FORCE,
which was discussed by Messrs. W. B. Taylor, Elliott, Hark-
ness, and Welling.
Mr. E. B. Elliott then communicated
GENERAL MEETING. 15
FORMULAS FOR THE COMPUTATION OF EASTER.
In the calendar the vernal equinox is considered as invariably
occurring on the 21st of March.
The Paschal full moon is the full moon which (according to the
calendar) occurs on or first after the 21st of March.
Easter Sunday in any year is the first Sunday which occurs after
the Paschal full moon ; that is, first after the full moon which,
according to the calendar, occurs on or first after March 21st.
To find the date of Easter Sunday for any year, A. D., New Style.
Let c denote the complete hundreds of years in the number de-
noting any year, and y the number of remaining years. Thus in
the year 1883, e = 18 and y = 83, the number for the entire year,
1883, being denoted by 100 c + y.
In the following formulas w, as a subscript after a division, de-
notes that only the whole number of the quotient is to be retained,
and r, as a subscript, denotes that only the remainder after the
division is to be retained ; thus [ _j =4; and (-j-J =2.
n (the golden number less one)
_ (I^l\ /100 c -f- y \ (5j_±y\ (5c-\- y\
- \ 19 ) T ~ \ 19 ) r ~ \ 19 /r — V20 -l) t
=
T9 L
5 \W T + \W T J r
This number (n~) pertains to a lunar cycle of 19 years.
--=Mf).-C + -p>-),
Inspection of the formula for s will show that, for any year from
1700 A. D. New Style to 1899 A. D., both inclusive, the value of
s is zero (0). For any year Old Style the value of s is the con-
stant number 22.
/23 + s
-f- 19 n\q=[ 30 j r ;also,
/23-f 5-ll7l\
-V 30 ) r
»-(a).+*=i(A).(n).
16 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The value of h may be shown to be zero (0) for any year from
1700 A. D. to 1899 A.. D., both inclusive, during New Style, and
for all years during Old Style.
p = q — h = the interval in days from March 21st to the date
of the Paschal full moon, or the number of days to be added to
March 21st to find the date of the Paschal full moon.
If p = zero (0), the Paschal full moon accordingly falls on the
21st of March.
j.( l + »(T) r -»-(i).+ fe).)
L denotes the number (in alphabetical order) of the Dominical
or Sunday letter. Thus, the number corresponding to the Domini-
cal letter A is 1, to B is 2, to C is 3, to D is 4, to E is 5, to F is 6,
and to G is 7 or (zero).
The term ( tq ) gives a correction to the Gregorian value when
the year exceeds 4000 A. D. ; for any year less than 4000 the
value of this corrective term is obviously zero (0).
,_i_(!=ft£)
f
-(Lt^±^
i
t denotes the number of days which elapse after the date of the
Paschal full moon to the date of Easter Sunday.
Easter Sunday = March (21 + 1 + p 4- 1 — 1)
= March (21 + p + t)
= April (p + t — 10)
To find the date of Easter Sunday for any year, A. D., Old Style.
/year\ /100 c
-\-y\
n
=\-W) r =K—W-) r
The formula for n is the same as in New Style.
/23 4-22 + 19 n\ ( lb + 19 n\ /15 — 11 n\
<*= P = { 30 ) t - I 30^ A - V 30 ) r
£=( 8 + «-y-(i)w )
^ 1 = (l=^)
r
l(i±^LX)
r
GENERAL MEETING. 17
Easter Sunday = March (21 + 1 + p + t — 1)
= March (21+ja + f)
= April (jp + t — 10) '
Example 1.
—
Required the day of the month on which Easter Sunday
falls in the year 1883 A. D., New Style.
Q r = 18or-l ; 5(i|) p = 90oi-S .
©. -(**£")-»
n =-5 + 7 = 2
20 n = 40
19 n = 20 n — n = 38
.-K^-ftV(M+1
-f^). )_
= 10-4- (~i~
)
w
= 10-4-6 =
/23 + s + 19 »\ /'23 + + 38\
*
- V 30 J r - I 30 ) t "
X
A =(219) w+ 2^- I (i) w (n) w= + 28 x°xo=o+o = o
_
/I + 2 X 2 — 83 — 20 + \ _ / l + 4 — 6 — 6 \
t - 1 = (-fi)
r
=(-i±i)
r:
/
•Easter Sunday = March (21 + 1+^ + ^—1)
= March (22 + 1 + 2)
= March 25
18 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Example 2.—Required the date of Easter Sunday for the year 1884
A. D., New Style.
5
m
-_
(
84=«
20
n=8— 5=3
20 w = 60
20 — n= 19 n — 57
s =
_
/ 23 + + 57 \
»-©.%=* (l),(n).
=0+9x0X0=0+0=0
p = g-/i = 20-0 = 20
x =
(
* + »(¥),-"-(?).+ Q.
)
.( 1 + 4 -?- 0+0) r -6
( _ 1=(3^±5)r : (^)r=2
Easter Sunday = March (21 + 1 + 20 + 2)
= March 44
= April (44 — 31)
= April 13
Example 3.
—
Required date of Easter Sunday for the year 3966
A. D., New Style.
39 1 66
2X 19 = 38 | 57 = 3X19
1 I 9
c-tfve-^pv*
20 n = 280
19 n = 20 n — n = 266
GENERAL MEETING. 19
t=3^-(f)„-(^TT-m,.)
= 31 - 9 - ( 3
*) — 31 - 9 - 13 = 9
? - I 30 J r = I 30 J r =
28
=0+lXl Xl=0+l=l
p=2_/i=28 — 1 = 27
£= / 1 + 2 (-) r _ 6e_(^ + (|)X
/ l + 2x3-3-2 + \
=2
Easter Sunday = March (21 + 1 + 27 + 6)
= March 55
= April (55 — 31 =) 24
Example 4.
—
Required the date of the Paschal full moon {March
21 + p), and the date of Easter Sunday (March 21 + p + t or
March 21 + 1 +p + (t — 1) for the year 2152 A. D., New Style.
/2152\
19 n= 95
s= 1
23= 23
19n + s+23 = 119
r(giyg),-(ii),-'
^=1+0x0x0= 1
p=q — h= 28
20 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Pascbal full moon — March (21 + 28 =) 49
= April (49 -31=) 18
z-( * + 'ffl,-»-(?).+ (S).
)
/!
-f 2~xT— 52 — 13 + \
Easter Sunday = March (21 + 1 + 28 + 4 =) 54
= April (54 -31=) 23
The Julian or Old Style Calendar was established by the Council
of Nice A. D. 325 ; the first year of the Gregorian or reformed
calendar was A. D. 1582, and the first year in which the reformed
calendar was adopted in England was A. D. 1752.
In Russia, and in other countries where the religion of the Greek
Church now obtains, the New Style of reckoning has not been
adopted, but the Old Style is still in force.
In Alaska, Old Style was employed until after the cession of that
country by Russia to the United States in the year 1869.
Example 5.
—
Find the date of Easter Sunday for the year 1582
A. D., Old Style.
15 | 82
5-f- 15 | =75
20-1) 157 * (7
140 - 7
17 + 7 = 24 = 19
-f- 5
n = 5
19 n = (20— 1) n = 100 — 5 = 95 = 3 X«30 + 5
/19n + 15\ /5 + 15\
/3 + 15 - 82 - 20\
= (18^6X=(18-nx =
GENERAL MEETING. 21
'3 - 20 + 0>
-'-m,-
Easter Sunday = March (22
-f 20 -f 4 =) 46
= April (46 - 31 =) 15
232d Meeting. March 24, 1883.
"Vice-President Welling in the Chair.
Forty-three members and visitors present.
The first communication was by Mr. J. R. Eastman on
THE FLORIDA EXPEDITION FOR OBSERVATION OF THE TRANSIT
OF VENUS.
[Abstract. ]
The observing station of the Florida expedition was upon Way
Key, the largest of the group of islands known as Cedar Keys.
The principal instruments employed were a portable transit, a
five-inch equatorial telescope, and a photoheliograph. The first
two require no description. The photoheliograph consisted of an
objective of five inches aperture and about forty feet focus, a helio-
stat for throwing the sun's rays on the objective, and a plate holder
at the focus of the objective. The accessory apparatus consisted
of a measuring rod, permanently mounted, for accurately measuring
the distance from the objective to the photograph plate ; a movable
slide with a slit of adjustable width, for exposing the plates; and a
circuit connecting with a chronograph, so arranged that when the
exposing slide was moved to expose the plate, and when the center
of the slit was opposite the center of the plate-holder, the circuit
was broken and the record made on the chronograph. A black
disk was painted on one side of the slide, and so placed that when
the slide was at rest at one end of its course and the image of the
sun was adjusted concentric with this disk, it would fall on the
center of the plate-holder when the slide was moved. The adjust-
ments having been completed the exposing of the plates was a sim-
ple matter. The image of the sun was thrown by the heliostat
upon the black disk and centered, the sensitive plate was fixed in
22 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the plate-holder, the operator moved the exposing slide, and the
time of exposure was recorded on the chronograph.
For observing contacts I used an eye piece, magnifying 216 diam-
eters, attached to a Herschel solar prism, and a sliding shade-glass
with a density varying uniformly from end to end. The time of
my signals was taken by assistant astronomer Lieut. J. A. Norris,
U. S. N., from a chronometer ; while, with an observing key, I also
made a record on the chronograph as a check.
About 40 seconds before the computed time of first contact a
narrow stratus cloud passed on to the southeastern edge of the sun
and shut out all the light. The cloud remained about 3 minutes,
and when it passed off, the notch in the sun's limb was plainly
marked. Two photographs were taken to test the apparatus and
the plates, and then the time before second contact was devoted to
an examination of the limbs of Venus and the sun. Both were
perfectly steady. In observations of the sun for the last twenty
years I never saw it better. At about 13 minutes after first contact
the outline of the entire disk of Venus could be seen, and seemed
perfectly circular. About 2 minutes later a faint, thin rim of
yellowish light appeared around the limb yet outside the sun. This
rim was at first broadest near the sun's limb, but soon the width of
the light became uniform throughout. The light was wholly ex-
terior to the limb of Venus ; that is, the black limb of Venus on
the sun and the dark limb outside formed a perfectly circular disk,
with the rim of light or halo, outside the portion off the sun. As
the time of second contact approached, Lieutenant Norris again
took up his station at the chronometer. As the limbs neared geo-
metrical contact, the cusps of sunlight began to close around Venus
more rapidly; and the perfect definition of the limbs and the steady,
deliberate, but uniformly increasing motion of the cusps, convinced
me instantly that the phenomena attending the contact would be
far more simple than I had ever imagined. I had only to look
steadily to see the cusps steadily but rapidly extend themselves into
the thinnest visible thread of light around the following limb of
Venus and remain there without a tremor or pulsation. At the
moment the cusps joined I gave the signal and also made the
record on the chronograph. Still keeping my eye at the telescope,
I saw nothing to note save the gradually increasing line of light
between the limbs of the two bodies. The disk of Venus on the
sun was black.
GENERAL MEETING. 23
A re-examination was then made of all the photographic appara-
tus, and about 10 minutes after the second contact the principal
photographic work was commenced ; and this was continued with
slight interruption until about 10 minutes before third contact;
150 dry plates and 30 wet ones being exposed. One of the inter-
ruptions was for the purpose of making measurements of the
diameter of Venus, which was done with a double-image micrometer
attached to the 5-inch telescope.
On going to the telescope to observe the last contacts, I found the
limbs of Venus and the sun as steady as in the morning, and though
there was now some haze over the sun it did no harm. The. third
contact was observed with great accuracy, nothing occurring to
obstruct or complicate the very simple and definite phenomena,
which were in the reverse order of those seen at second contact.
The rim of light appeared around Venus as soon as the limb was
visible beyond the sun, and was seen for nearly 10 minutes. The
complete outline of Venus was visible for 2 minutes longer. No
phenomena worthy of note were seen between third and fourth con-
tacts. The lapping of the limb of Venus over that of the sun
gradually but steadily decreased until the final separation, which
was observed with great accuracy for such a phenomenon. Soon
after the last contact the entire apparatus was again carefully
examined and the necessary observations made to determine the
errors of the chronometers.
In the observations of interior contacts there was no trace of any
tremor or fluctuation of the light in the cusps as they closed around
the limb of Venus ; and it is almost needless to say that there was
no trace of a shadow or a black drop or ligament between the
limbs at second and third contacts. The probable error for the
second and third contacts was estimated at 0".3 ; for fourth con-
tact, 0".5.
Observers of transits of Venus and Mercury have written so
much in regard to the obstacles encountered from the apparition of
the shadow, or black drop, between the limbs of the two bodies at
second and third contacts, and so full has been the testimony in
favor of the existence and the almost necessary occurrence of this
phenomenon, that at the transit of Mercury, in 1878, many ob-
servers claimed, as evidence of their skill, that they did see it
;
while others, less fortunate, apologized for not seeing it. Observers
of the black drop were so generally confined to those with imperfect
24 PHILOSOPHICAL SOCIETY OF WASHINGTON.
apparatus or to those unaccustomed to observation of the sun's
limb or disk that the true nature of the obstacle was pretty well
understood before it was carefully investigated. It is now quite
well settled that the " black drop " is due to bad eyes, imperfect
apparatus, or the inexperience of the observer. With good eyes
and proper apparatus a good observer never should see the black
drop. When it is seen there is something wrong ; it is a spurious
phenomenon.
One of the negatives was exhibited to the Society.
In reply to a question by Mr. E. J. Farquhar, Mr. Eastman
said the halo about Venus was believed to be due to the atmosphere
of the planet.
The next communication was by Mr. Cleveland Abbe on
DETERMINING THE TEMPERATURE OF THE AIR.
He stated that the question now to be considered is not where to
place a thermometer so as to obtain the temperature most proper
for the use of the meteorologist, but is rather the purely physical
question of how to determine the temperature of the air at any
given location. He described the methods and defects of the for-
mer and present meteorological methods of exposure, viz : (1) Ther-
mometers hung in the open air. (2) Those placed in shady loca-
tions. (3) The Glaisher screen. (4) The Stevenson screen and
the double louvre screens in general. (5) The double metallic cylin-
drical shelters of Jelinek and Wild. (6) The silver thimble screen
of Regnault. (7) The whirling thermometer of Saussure, Arago,
Bravais, and the French observers (exhibiting Babinet's arrange-
ment as made by Casella.) (8) Joule's method, depending on a
balance in the temperature and density of two columns of the air.
He then gave a description of the method devised by him in
1865 and used for a short time at Poulkova; this consisted in con-
structing a very perfect louvre screen, within which were established
black bulb and bright or silvered bulb thermometers having very
diverse coefficients of radiation and conduction. These thermom-
eters were in air, not in vacuo, as this latter arrangement was proper
only for the determination of the direct solar radiation, as in the
Arago-Davy method, whereas in the present case the temperature
of the air and the radiation from terrestrial objects were the special
objects of study.
GENERAL MEETING. 25
The air temperature (ta ) was found from the indications of the
bright and black bulbs (t 8 and tb) by the empirical formula
ta =te + C(tb—
t
s)
where C is a small coefficient, to be determined experimentally,
and is nearly constant. This arrangement of bright and black
bulbs can be used by meteorologists and physicists without a
screen, and even in the sunlight, if the. theory of the action of the
bright and black bulbs is perfectly understood. A similar for-
mula will give the temperature (T) of a single radiating body whose
effect is equal to the total effect that is shown by the black bulb
:
T= tb + C'(tb— ts.)
He then stated that the theoretical basis of this method has quite
recently been further elucidated by Professor Ferrel, who has shown
that the approximate nature of the relation between the above con-
stant C, the radiating, absorbing, and conducting powers of the
thermometers, and the velocity of the wind is given by the following
equation
:
„
1+
B'+ B"v
\j—
where rb and rs are the radiating (and absorbing) powers of the
blackened and silvered bulbs, respectively, v is the velocity of the
wind or currents flowing past the bulbs, and B B' B" are constant
coefficients depending on the size, conductivity, and specific heat
of the substance of the bulbs.
In reply to a question of Mr. Gilbert, he stated that the differ-
ence between the bright and black bulbs had rarely exceeded a
few tenths of a degree in the delicate shelter made of oiled paper,
as used by him at Poulkova, the maximum occurring February 22,
1866, at 10 a. m., when, the louvre box being in the full sunshine,
the bright bulb was at 14°.9 Cent, and the black bulb at 14°. 3,
showing that the latter had been slightly warmed by the warm sides
of the box.
In reply to a question of Mr. Harkness, the author explained,
that although it was conducive to accuracy that these thermometers
should be placed within a shelter, yet this was not necessary ; if
we take advantage of the more accurate method of determining
26 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the co-efficient constant C, as given by Prof. Ferrel's theory,
the two thermometers placed anywhere within doors or without
would still give data for determining temperatures of the loca-
tion ; it should be borne in mind that the temperature thus ob-
tained belongs specifically to the air in contact with the themome-
ters and is not an average value for any extensive portion of the
atmosphere. As it is an advantage to conduct observations under
uniform conditions, it is recommended that a pair of bright and
black bulb thermometers be attached to the whirling table, whereby
the effect of a current of air may be on the one hand determined
and on the other hand kept as uniform as possible.
Mr. Harkness said that the object practically sought by meteo-
rologists was to learn the average temperature of a considerable
body of air, but their efforts were thwarted by the irregularity and
inconstancy of the distribution of temperature. So long as the air
in contact with the thermometer is not precisely representative of
the air of the vicinage it was useless to refine methods of observa-
tion, unless by that refinement errors of a constant nature were
eliminated. For the determination of mean monthly or annual
temperatures he considered the reading of the nearest half degree
as sufficient, and regarded the reading of the tenths of a degree as
a useless refinement.
The advantage of reading to tenths was further discussed by
Messrs. Abbe, Doolittle, and Kummell. Mr. Kummell
pointed out that where a difference of temperature is observed as
an indication of the moisture of the air, the tenths are worthy of
record.
The following communication by Prof. Charles E. Munroe,
of Annapolis, Md.g was then read by the Secretary
:
DETERMINATION OF THE SPECIFIC GRAVITY OF SOLIDS BY THE
COMMON HYDROMETER.
Having occasion some time since to devise methods for the ex-
amination of coal on board ship, I was obliged, as my first con-
sideration, to work with such materials and apparatus as are usually
found in ships' stores, and then to arrange the methods so that they
could be used under the restricted conditions which prevail. The
unsteadiness of the ship makes balance methods for the determina-
tion of specific gravities difficult, even when a suitable balance is at
GENERAL MEETING. 27
hand, while hydrometers may be steadied so that the instrument
may be read with a reasonable degree of precision, as is shown in
its constant use in the determination of the degree of saturation of
the water in the steam-boiler, and in other instances.
To use the hydrometer for the determination of the specific
gravities of solids I take advantage of the fact that, when a body
floats in a liquid in which it is wholly immersed, the specific gravi-
ties of the liquid and the solid are the same, and we have simply to
determine the value for one of them.
The process is carried out by taking a dense solution, dropping
in it the solid to be determined, (which must be light enough to
float on the surface,) and then diluting slowly with water until the
solid floats immersed, stirring the mixture constantly. The solid
is now removed and the hydrometer inserted and read. For the
determination of the specific gravities of the bituminous coals and
lignites a thick solution of cane sugar was used, while for the
heavier anthracite concentrated sulphuric acid, diluted with dilute
sulphuric acid, was employed. The increase in temperature in the
latter case causes no appreciable error if the reading is quickly
taken. The following results were obtained by the method des-
cribed, the specific gravity of each specimeu having first been de-
termined by Jolly's balance
:
By Jolly's balance. By mixture.
Anthracite 1.5640 1,560
Bituminous coal 1,3008 1,310
Bituminous coal 1,3000 1,300
Gas coal 1,2790 1,285
Cannel coal (ligniform) I
>
1 55° I > 1 55
Cannel coal 1,1292 1,120
Lignite 1,0909 1,090
Mr. Dutton remarked that the same principle had recently been
successfully applied to the separation of the component minerals of
crystalline rocks. A sample is powdered and then placed in a very
heavy liquid (a solution of mercuric iodide and potassium iodide),
the density of which is gradually diminished, until the particles of
the heaviest mineral sink to the bottom. A repetition of the process
eliminates each mineral in turn.
28 PHILOSOPHICAL SOCIETY OF WASHINGTON.
233d Meeting. April 7, 1883.
Mr. Wm. H. Dall in the Chair.
Thirty-six members and visitors present.
The Chair announced that Messrs. Edward Sandpord Burgess
and Sumner Homer Bodfish had been elected members.
The General Committee reported to the Society that " a Mathe-
matical Section had been organized by the election of Mr. Asaph
Hall as Chairman and Mr. Henry Farquhar as Secretary. All
members of the Society who are interested in mathematics are in-
vited to attend and take part in its meetings, announcements of
which will be sent to those who notify the Secretary of a desire for
them."
The first communication was by Prof. W. C. Kerr on
THE GEOLOGY OF HATTERAS AND THE NEIGHBORING COAST.
[Abstract.]
The notable projection of Hatteras, beyond the general line of
trend of the Atlantic coast, has, of course, a geological origin.
The study of the changes now taking place, and of the phenomena
which have left their recent traces on the surface, readily furnish
the data for the solution of the problem. Nearly one-half of this
eastern inter-sound region of North Carolina is water surface, and
the land surface lies for the most part below ten feet (much of it
below five.)
A large part of this low-lying surface is covered with beds of
peat, which thicken towards the centre on the divides or swells be-
tween the bays and sounds, rising, in some cases, to ten and fifteen
feet, and in the Dismal Swamp on the northern border of the State
to twenty-two feet. These beds of peat are in process of forming
by the decay of plants growing on the surface, chiefly cypress and
juniper. Many tiers of the undecayed logs of these timbers are
piled upon one another through the whole thickness of the deposit,
which is soft and yielding, so that a fence-rail may be thrust down
beyond its length. Vast tracts of such peat swamps (and of marsh
and savanna on which only water grasses and small shrubs and
scrub pines grow and decay) are found throughout this coast region.
Here we have the first stage in the formation of a coal bed. Another
notable fact is that many of the rivers which empty into the sounds
GENERAL MEETING. 29
increase in depth of channel at a distance from their mouths
;
while the sounds are 12 to 15 and 20 to 22 feet deep, the rivers are
often 30 and 40 feet and upwards. This can only be accounted for
by supposing a subsidence of the region to be in progress, the
sounds and open bays being silted up by the deposits brought down
by the floods of the Roanoake and other large rivers, while no
particle of sediment can reach the sheltered depths of the narrow
windings of the upper reaches of these minor streams. This theory
of subsidence is abundantly confirmed by the disappearance under
water of large tracts of swamp bordering the rivers, as the Chowan,
within the observation of men now living, and by the existence
of rooted stumps of cypress and juniper in the bottom of the bays
and sounds, even to the depth of 15 and 20 feet, and also by the
vertical and crumbling shores of the sounds, undermined and
eroded by the advancing waves.
The Atlantic ocean is walled off from this region by a narrow
fringe of sand islands, or dunes, blown shoreward by the wind and
thrown up into reefs and hillocks like snow-drifts 50, 80, and even
more than 100 feet high. The movement of these sand .waves
being inland, the sounds are silting up next the sea, and are in
many places converted into marshes 3 to 5 miles wide. The reef is
increasing in continuity and breadth, most of the inlets above Hat-
teras that were open 300 years ago being closed and obliterated.
An inspection of the form of the curves of the submarine contours
off Hatteras and adjoining coasts will show that the action of the
tides and ocean currents, the Gulf stream and Arctic current meet-
ing at this point, accumulate upon Hatteras the river silt which
reaches the sea by way of the Chesapeake as well as that of the
rivers which discharge their burdens through the inlets about this
point and southwards. Which amounts to this—that Hatteras may
be described as a sort of delta, whose materials are derived from the
drainage of more than 100,000 square miles of the Atlantic slope.
A subsidence of about 20 feet would bring the sea again
over the entire Sound region and carry the shore 75 miles inland,
bringing Hatteras to coincide with Cape Lookout. A sand reef,
like that north of Hatteras, marks the line of the ancient shore,
when these conditions obtained. A depression of fifty feet would
move the shore 100 miles west of Hatteras and carry the point of
meeting of the conflicting ocean currents and waves to Cape Fear.
A subsidence of 500 feet, as in the glacial period, would carry
30 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Hatteras more than 200 miles west of its preseut position. This
horizon is marked by an immense saud reef, still retaining its wind
and wave marks, and rising to a height of more than 500 feet above
tide, the reef itself being at least 100 feet deep and many miles in
length. The sea must have remained at this level for a very long
period.
But Hatteras is not a modern phenomenon. It is at least as old
as the cretaceous; the quaternary as well as the tertiary of this
coast region of North Carolina are laid down upon an eroded
surface of cretaceous rock, while the artesian borings, at Charleston,
reach this formation at 700 feet, and at the mouth of the Chesa-
peake they do not seem to have touched it at 1,000 feet.
Mr. Ward remarked that, in traversing the Jericho canal of the
Dismal Swamp in a row boat, he had observed an outward flow at
both ends of the canal, showing that, by continuous water passage,
a divide was crossed between Lake Drummond and the James river.
He criticised the doctrine taught in text-books aud popular writ-
ings that the preservation of leaves in a fossil state is due ordinarily
to river action and delta formation. More favorable conditions
are to be found in swamps.
Other remarks were made by Messrs. Dutton and Hough.
The second communication was by Mr. H. F. Walling on
TOPOGRAPHICAL INDICATIONS OF A FAULT NEAR HARPER'S FERRY.
[Abstract.]
A description was given of a break in the continuity of the Blue
Ridge, where its disconnected portions, extending side by side for a
few miles, are cut by the Potomac river, near Harper's Ferry, the
gorges so formed presenting a striking feature of the scenery.
The two ridges, here about 12,000 feet apart, stretch for hundreds
of miles in nearly parallel directions, one to the south and the
other to the north ; the latter being known in Pennsylvania as the
South Mountain. The strike of the rocks is parallel to the ridges,
about N. 30° E., and the prevailing dip is eastward* averaging not
more than 30°. The ridges are composed of hard sand-rock;
the adjacent region, of lime-stone and other rocks more easily dis-
integrated or dissolved.
Supposing the sand-rock of the Blue Ridge and South Mountains
to have been originally a continuous formation, it will be readily
GENERAL MEETING. 31
seen that a vertical fault in easterly dipping strata, having its
direction somewhat nearer the meridian than the present strike
and its downthrow on the west side of the fault, would produce a
lateral discontinuity like that here observed, the upthrown part of
any stratum cropping out on the east of the downthrown part at a
distance depending upon the amount of the vertical displacement.
All this would depend upon whether the sand rocks were origi-
nally continuous in the two ridges—a question which was left for
the geologists to decide. The writer, however, took occasion to
suggest that great longitudinal faults might be formed near coast
lines when the gradual overloading of the balanced crust by depo-
sitions of sediment produced a strain too great to be relieved by flex-
ure. A rupture would then occur, the strata going • down on the
overloaded side of the fault and up on the other until equilibrium of
pressure upon the yielding magma below was restored by lateral
displacement of the magma. The fault so formed would present a
diminished resistance to dislocation, and if the action which origi-
nated it should continue, it would be likely to increase in dimensions
both in length and in the amount of vertical displacement. This
action might even continue after the emergence of the region above
the surface of the water, provided a more rapid denudation of the
landward than of the seaward side of the fault took place, in which
case a continued disturbance of equilibrium would be accompanied
by vertical yielding, increasing the amount of dislocation, and by sub-
terranean movements of the supporting magma, whereby a restora-
tion of material would be effected from overloaded to denuded areas.
Moreover, the hypothesis of a constant restoration of disturbed
equilibrium makes it easier to understand why the folding of strata
should grow steeper, even to a, folding under, as the axis of a moun-
tain chain is approached. A diagram exhibiting the so-called
" fan-like structure of the Alps," enlarged from a figure by Rogers,
(see Rogers' Report on the Geology of Pennsylvania, Vol. II, p.
902, ) was shown in illustration. The gradual subterranean move-
ments inward under a mountain chain, as the upper portions were
removed and the remainder elevated, would carry the strata along
on a support of diminishing width until they were folded upward
and backward.
The gradual increase towards the east in the amount of corrugation
and steepness of dips, together with the supposed reversed folding by
which the rocks of the eastern part of the Appalachian region seem to
32 PHILOSOPHICAL SOCIETY OF WASHINGTON.
dip under older rocks, still further east appear, therefore, to favor the
notion that the paleozoic rocks of the Appalachian region and the
eastern part of the Mississippi basin were derived from the erosion
of highlands formerly existing east of the Appalachian chain, now,
perhaps, submerged in the Atlantic ocean. The downthrow of a
fault, if formed in the manner supposed in the region under con-
sideration, would accordingly be on its western side, as suggested
above.
The third communication was by Mr. S. F. Emmons on
^ ORE DEPOSITION BY REPLACEMENT.
[Abstract.]
After a few introductory remarks upon the relatively unsatis-
factory condition of that branch of geology which treats of ore de-
posits, considering the early date at which it was taken up, the
speaker briefly reviews the existing theories and classifications, and
shows that they are mainly based on the idea that each ore deposit
is the filling of some pre-existing cavity or opening in the rock in
which it is now found ; that so-called fissure veins, for instance, were
once actually open cracks, and that irregular deposits in limestone
have been made by the filling up of open caves, such as so fre-
quently occur in these rocks. The result of his studies of the so-
called " carbonate deposits " of Leadville, Colorado, has been to
show that they are not the filling up of pre-existing cavities ; the
caves there have been formed since the ore was deposited, as is
proved by their crossing indiscriminately ore bodies and limestone.
They belong to a class of deposits for which he proposes the name
metamorphie deposits, or those which have been formed by a meta-
somatic interchange between the vein and original rock material.
In Leadville the principal deposits are an actual replacement of
the limestone itself at or near the contact of this stratum with an
overlying sheet of porphyry. This replacement action has in places
proceeded so far that the entire stratum of ore-bearing limestone or
dolomite, originally 150 to 200 feet thick, has been changed into
vein material, which consists of silica and metallic minerals. This
vein material was brought in solution by percolating waters, which
had taken it up during their circulation through the adjoining and
generally overlying eruptive rocks. A more detailed description
of the phenomena of these deposits will be found in his paper en-
GENERAL MEETING. 33
titled " Abstract of a Report on the Geology of Leadville," in the
Second Annual Report of the Director of the United States Geo-
logical Survey.
While the speaker's studies have thus far been mainly confined to
limestone deposits, he has reason to believe that essentially the same
process has produced a large proportion of ore deposits in crystal-
line and eruptive rocks, and that to the class of metamorphic de-
posits belong most of the so-called fissure veins of the Rocky Moun-
tain region. That is, that they are not the filling in of pre-existent
open fissures by vein materials foreign to the adjoining rocks, but
simply a metamorphic change of these rocks themselves along
channels of easy access to percolating waters ; and according to the
character of the material held in solution by these waters, these
rocks have been more or less changed into quartz and metallic min-
erals, to a greater or less width, as the case may be. Numerous
instances of such veins will be found in the forthcoming Census
Report upon the Statistics and Technology of the Precious Metals,
by Mr. G. F. Becker and the speaker.
234th Meeting. April 21, 1883.
Vice-President Billings in the Chair.
Forty members present.
The Chair announced that Messrs. Washington Carruthers
Kerr and Samuel Franklin Emmons had been elected members.
Mr. W. H. Dall addressed the Society on
GLACIATION IN ALASKA,
illustrating his remarks by maps of the territory and of the glacial
areas of the St. Elias Alps and Kachekmak Bay, Cook's Inlet, the
latter being from surveys made by him under the direction of the
U. S. Coast Survey.
He called attention in the first place to the wide differences in
the character of the masses of ice resulting from the consolidation
of snow by gravity (which would usually be classed as glaciers),
as observed by him during nine years' exploration in Alaska.
These might be classed under several heads : as plateau-ice, filling
34 PHILOSOPHICAL SOCIETY OP WASHINGTON.
large areas of depression and without motion as a whole, but when
sufficiently accumulated overflowing the edges of its basin in various
directions ; as valley-ice, filling wide valleys of gentle incline both
as to their axes and their lateral slopes, producing masses of ice
moving in a definite direction but without lateral and sometimes
even without terminal moraines ; as ice-cascades, formed in sharp nar-
row ravines of very steep inclination, usually without well-defined
surface moraines ; as typical glaciers, showing neve and lateral and
terminal moraines ; and lastly, as effete or fossil glaciers, whose
sources have become exhausted, whose motion has therefore ceased,
and whose lower portions have become smothered by the accumu-
lation of non-conducting debris. The very existence of one of these
last has remained unknown for half a century, though the plateau
underwhich it is buried has been described and mapped by explorers.
Another form under which ice appears in Alaska is that of solid
motionless layers, sometimes of great thickness, interstratified with
sand, clay, etc. A deposit probably of this character is described
by Nordenskiold, on the Asiatic coast, near Bering Strait. In
Alaska this formation, in which ice plays the part of a stratified
rock, extends from Kotzebue sound, where the greatest known
thickness of the ice-layer, about three hundred feet, has been noted,
around the Arctic coast, probably to the eastern boundary. In
Kotzebue Sound the ice is surmounted by about forty feet of clay
containing the remains of fossil horses, buffaloes (Bos latifrons, etc.),
mountain sheep, and other mammals. Farther north the ice is
covered with a much thinner coat of mineral matter or soil, usually
not exceeding two or three feet in thickness, and rarely rises more
than twelve or fifteen feet above high water mark on the sea coast.
Its continuity is broken between Kotzebue Sound and Icy Cape by
rocky hills composed chiefly of carboniferous limestones, which
bear no glaciers and do not seem to have been glaciated. The
absence of bowlders and erratics over all this area has been noted
by Franklin, Beechey, and all others who have explored it. The
remarkable extent and character of the formation was unknown
previous to the speaker's investigations, though the ice cliffs of
Kotzebue Sound had attracted attention from the time of their first
discovery.
Mr. Dall desired especially to emphasize the distinction between
these strata of pure ice and the "frozen soil" so often alluded to
by arctic explorers. The absence of frozen soil in the alluvium
GENERAL MEETING. 35
of the Yukon Valley, far north of Kotzebue Sound, was noted, as
well as the fact that this valley has, for some unexplained reason,
a mean temperature considerably above the normal, so that its
forests extend well beyond the Arctic circle.
The distribution of glaciers, properly so-called, in Alaska, as far
as our present knowledge goes, is confined to the region of the
Alaskan range and the ranges parallel with it south of the Yukon
Valley, but particularly to the coast mountains bordering on the Gulf
of Alaska and the Alexander Archipelago, of which the Saint
Elias Alps form the most conspicuous uplift.
The distribution of stratified ice is all north of the Yukon Val-
ley, which divides the two regions. Hence, for the glacial epoch,
it may be presumed that the one is the equivalent of the other, and
the fact that Arctic Alaska is marked by stratified ice, rather than
glaciers such as those of Greenland, must be due to local geological
and climatic peculiarities existing at the time. On the Asiatic
coast, especially at Holy Cross Bay, in nearly the same latitude and
with not very different topographic conditions, glaciers are abun-
dant at the present time.
On the mainland, facing the Alexander Archipelago, especially
toward Lynn Canal, Icy Strait and the Stikine region, local glaciers
are abundant, and traces of others, now dissolved, may be found
on the lowlands of most of the islands. That these were always
local, though doubtless very extensive, and that they were the pro-
geny of the topography instead of being its parent, is obvious to
anyone who has seen the coasts of Maine or Norway, which have
been submitted to general glaciation, and will compare their
rounded, worn, and moutonnee aspect with that of the sharp cliffs,
beetling crags, narrow valleys, and scanty lowlands of the Alaskan
islands.
The speaker concluded, from his observations, that the extent of
the Alaskan glaciers is greatly diminished from its former state,
and is probably still diminishing; that the southern portion of the
Territory is probably nearly or quite stationary, while the northern
part is undergoing elevation ; and that, from the nature of the case,
the area of stratified ice cannot be expected to increase or di-
minish materially without changes in geological or climatic con-
ditions too great to be anticipated.
Mr. Alvord remarked that on Point Barrow frozen ground had
been penetrated to a depth of thirteen feet.
36 PHILOSOPHICAL SOCIETY OF WASHINGTON.
In reply to a question by Mr. Antisell, Mr. Dall said that
little was known of the humidity of the interior of Alaska ; 23
inches of precipitation, nearly all in snow, had been observed in a
single year at one point and 12 inches at another.
Mr. F. B. Hough then read a paper on
THE CULTIVATION OF THE EUCALYPTUS ON THE ROMAN
CAMPAGNA,
which was discussed by Messrs. E. B. Elliott and H. Farquhar.
It is published in the American Journal of Forestry for June, 1883.
235th Meeting. May 5, 1883.
Vice-President Billings in the Chair.
Twenty-seven members and visitors present.
The Chair announced the election to membership of Messrs.
William Thomas Sampson, John Oscar Skinner, and Thomas
Ceowder Chamberlin.
The first communication was by Mr. H. A. Hazen on
HYGROMETRIC OBSERVATIONS.
[Abstract. ]
After describing the various devices by which the moisture of •
the air has been measured, and especially the novel and valuable
apparatus of Crova, the speaker illustrated the difficulty of the
subject by contrasting synchronous determinations made at four
points within a radius of two miles, and then described some ex-
periments tending to show the inaccuracy of the wet and dry bulb
hygrometer, as ordinarily observed. The value of the wet bulb
reading is enhanced by blowing on the bulb with a bellows, or
otherwise subjecting it to a brisk current of air.
Mr. Harkness remarked first, that Mr. Hazen's experiments
appeared to prove the insufficiency of Regnault's formula, for they
showed the difference between the indications of the wet bulb and
dry bulb to be a function not only of the humidity, but of the
velocity of wind ; second, that height of station above the ground
GENERAL MEETING. 37
was a condition to which too little attention had been given ; and
third, that there seemed a possibility of obtaining a slightly erro-
neous vapor tension with Crova's apparatus.
Mr. E. J. Farquhar then read a paper on
DREAMS IN THEIR RELATION WITH PSYCHOLOGY.
[Abstract.]
Several theories of dreams were considered and none found en-
tirely sufficient ; not because a new and complete one was to be
proposed, but because all seemed a little too partial and limiting in
their scope. After touching on the relation of dreams to sleep and
to waking, as intermediate between them, discrediting many recorded
experiments on the ground of their being vitiated by a special pur-
pose latent in the mind, and pointing out that the usual supposition
of our being often waked by the intensity of a dream appears to
put cause for effect, since it must be the fact of waking that effects
the dream, perhaps by slow degrees—the character of mental opera-
tions in dreams was discussed. Dissent was expressed from the
opinion that the dreaming state is devoid of such originating power
as belongs to the waking ; this position was maintained by showing
first, the extreme vividness and lastingness of impression often per-
taining to dreams, apart from any features of horror; then the
coherence, far from being unknown among them, yet of a peculiar
kind ; and, finally, the true significance occasionally appearing in
them, generally by figurative shape, amounting sometimes to a real
enlightenment of the mind. Regarding the faculties or aspects of
mind most apt to display themselves in dreams, it was held that all
were liable to the exercise in turn, though some of the higher ones,
especially the moral sense and judgment, less than others ; since these
expressed a rarer and more distinctive force evolved and laid up by
and for our relations with actual life, while other powers whose
exercise is less of an expenditure from the most important vitalities
of mind were freer at the time—the principles of conservation and
struggle for existence being thought to apply among the mental
elements. Thus, to a certain degree, the mind may be seen more
clearly in its true character by means of dreams than awake,
though in very partial views at a time. Unconscious mental action
was reviewed in this connection, and it was held that not only the
lower processes, called reflex, but many of the highest functions
38 PHILOSOPHICAL SOCIETY OF WASHINGTON.
largely partake of this attribute. A great number of other points
in regard to dreams were merely named as illustrating the fertility
of the subject.
236th Meeting. May 19, 1883.
Vice-President Hilgard in the Chair.
Forty members and visitors present.
It was announced from the General Committee that the following
rules had been adopted :
I. If the author of any paper read before a section of the Society
desires its publication, either in full or by abstract, it shall be re-
ferred to a committee, to be appointed as the section may determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the secretary of the section, together with any
action of the section taken thereon.
II. Any paper read before a section may be repeated, either en-
tire or by abstract, before a general meeting of the Society, if such
repetition is recommended by the General Committee of the So-
ciety.
Mr. Robert Fletcher made a communication entitled
RECENT EXPERIMENTS ON SERPENT VENOM.
It is published in the American Journal of the Medical Sciences
for July, 1883.
Mr. H. Farquhar then made a communication on
FURTHER EXPERIMENTS IN BINARY ARITHMETIC,
showing that the relation between the vertical and horizontal di-
mensions of the characters used in the biuary notation is a factor
in determining its economic value. He presented, also, the results
of a series of comparative tests showing that the binary notation
enables some persons, after brief practice, to perform addition more
rapidly than with denary notation, while with others it requires a
longer time. The latter class includes practiced computers, gene-
rally, and the former those less accustomed to the use of figures.
GENERAL MEETING. 39
Mr. Doolittle remarked that the most instructive results would
be obtained by experimenting with young persons; and the subject
was further discussed by Messrs. W. B. Taylor, E. B. Elliott,
and C. A. Schott.
237th Meeting. June 2, 1883.
Vice-President Hilgard, and afterward Mr. Harkness, in the
Chair.
Twenty-two members present.
It was announced that the next meeting would be held October
13th.
Mr. "W. Lee made a communication, with illustrations, entitled
SKETCHES FROM MEDALLIC MEDICAL HISTORY.
[Abstract.]
The paper was prefaced by remarks on the value of coin and
medal collecting as a profitable means of instruction, and by a recog-
nition of the danger to which collectors are exposed of develop-
ing a mania for collecting odd and curious things which cease to
be instructive. An extended interest in numismatics commenced
to show itself in this country in 1858, at which time there were
probably not as many as one hundred coin collectors in the United
States. The interest has grown rapidly, however, until now there
must be on the books of the United States Mint the names of at
least one thousand collectors who receive yearly the issue of
the mint, with a special proof polish. In New York alone, during
the year 1882, there were thirty-nine collections sold at public
auction, the amount realized being '$68,441.36. The largest of
these was the Bushnell collection, which realized $13,900.47. Sev-
eral of our large cities have numismatic societies, some of which
are designated as numismatic and archaeological societies ; and a
number of periodicals devoted simply to the interest of numis-
matics obtain a satisfactory circulation.
The modes of striking off coins and medals were given somewhat
in detail, and attention was then called to the important part which
medals struck in honor of medical men and to commemorate im-
40 PHILOSOPHICAL SOCIETY OF WASHINGTON.
portant events bearing directly upon the history of medicine have
played throughout the history of the world. The illustrations of
the paper included a hundred and fifty examples of the medals
themselves, in regular sequence, from the days of Roman and
Greek medicine down almost to the date of the paper itself, an
interesting commemoration of events and individuals marking
epochs in the history of medicine. These medals were taken up
seriatim, references were made to the lives of individuals and the
scientific work done by them, and descriptions were given of the
occasions which called for the striking of medals.
The paper closed with an expression of hope that the Society
might be stimulated at the sight of so many handsome and perma-
nent memorials of the men and times of the past, to attempt to
preserve the features of its first president, Joseph Henry, in a
similar enduring form.
The bibliography of the subject was discussed at some length,
and the following works were referred to
:
Mead, Richardi.—Dissertatio de Nummis quibusdam a Smyrnaeis
in medicorum honorem percussis. Naples, 1752.
Rudolphi, C. A.—Index numismatum in virorum de rebus medi-
cis vel physicis meritorum memoriam percussorum. Berlin,
1st edition 1823, 2d edition 1825, 12mo., XII, 131 pp, 3d
edition 1828, 4th edition 1829. (This work (2d edition)
comprises the description of 523 medals struck in honor of
350 scientific and medical men.)
Renauldin, Leop. Jos.—Etudes historiques et critiques sur les
Medicins Numismatistes, contenant leur biographie et l'an-
alyse de leurs ecrits. Paris, 1851, 8°, XVI, 574 pp. (This
work contains the names of 61 physicians).
Chereau (A).—Les mereaux et les getons de l'ancienne faculte de
medecine de Paris. L'Union Medicale. Paris, 1873, 3
Series, XV, pp. 309, 321.
Pfeiffer, (L) und Ruland (C).—Pestilentia in Nummis. Ges-
chichte der grossen Volkskrankheiten in numismatischen
Documenten. Ein beitrag zur Geschichte der Medicin und
der Cultur. Tubingen, 1882, 8° X, 189 pp. Mit zwei
Tafeln Abbildungen in lichtdruck.
Wroth, Warwick.—Asklepios and the C«ins of Pergamon. From
the Numismatic Chronicle and Journal of the Numismatic
Society. London, 1882, Part I, Third Series, No. 5, pages
1 to 51, plates 3.
Moehsen, J. C. G.—The exact title of this author's work is not
known to the writer of the paper ; it was written in German,
GENERAL MEETING. 41
and embodies a description of a collection of medals in
Berlin struck in honor of physicians, giving 200 medals
struck after the 15th century.
Grotefend, C. L.—Die Stempel der Romischen Augenarzte.
Hannover, 1867.
Mr. T. N. Gill then made a communication on
ANALOGUES IN ZOO-GEOGRAPHY.
238th Meeting. October 13, 1883.
The Society, in accordance with the notice of adjournment at
the June meeting, resumed its sessions.
The President in the Chair.
Forty-four members and visitors present.
It was announced that during the vacation the Society had lost
by death Surgeon General C. H. Crane, one of its Vice-Presidents
;
Admiral B. F. Sands, one of its founders ; and Dr. Josiah Curtis.
It was further announced from the General Committee that Mr.
Garrick Mallery had been appointed Vice-President to fill the
vacancy occasioned by the death of Mr. Crane, and that Mr.
C. V. Riley had been added to the General Committee to complete
its number.
Mr. William B. Taylor read a paper entitled
NOTE ON THE RINGS OF SATURN.
[Abstract.]
After an historic sketch of the varying and apparently incon-
gruous observations by astronomers on the markings and aspects of
the Saturnian rings, down to those of Schiaparelli of the Milan
Observatory, (published in June last,) Mr. Taylor remarked that
since the mathematical discussion by Prof. J. Clerk Maxwell, in
1857,* both the rigid and the fluid ring theories have been aban-
doned ; and the discrete or meteoric constitution of the rings is now
accepted by all physical astronomers as conclusively established.
* On the Stability of the Motion of Saturn's Rings. 4:0. 71 pp. and I plate.
Cambridge, Eng., 1859.
7
I
42 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Reference was then made to the startling announcement by Otto
Struve, in 1851, that a careful comparison of the earlier with the
later measurements showed that during the two hundred years of
observation the rings had been widening, and the inner edge steadily
approaching the body of the planet.* Considering the necessarily
vast antiquity of the Saturnian system, such a change during the
brief iuterval of human existence seems a priori almost infinitely
improbable. The hypothesis of some that a meteoric ring has been
drawn in by Saturn's attraction, within comparatively recent ages,
seems entirely negatived by the circular symmetry of the system.
It is not surprising, therefore, that Struve's inference has been re-
ceived with an almost universal incredulity by the astronomical
world. Robert Main, of the Greenwich Observatory, from a dis-
cussion of his own measurements taken in the winter of 1852-'3,
and in 1854, disputed the accuracy of Struve's measures ; and con-
cluded that " no change has taken place in the system since the
time of Huyghens."f And Prof. F. Kaiser, in a paper on " The
Hypothesis of Otto Struve respecting the gradual increase of
Saturn's Ring," etc., arrives at the same conclusion, and believes
" there exists no reason whatever for supposing that the compound
ring of Saturn is gradually increasing in breadth." |
There seems to be little doubt of some unintentional exaggeration
in Struve's tabulated results, which range from 4".6 : 6".5 for the
ratio of ring breadth to space between ring and ball, in the time of
Huyghens, 1657, to 7".4 : 3".7 for the ratio of breadth to space, by
his own observation in 1851. Nevertheless it is a noteworthy fact
that all the early drawings of Saturn made in the seventeenth cen-
tury (many of which are figured by Huyghens in his Systema Sat-
urnium, 1659) plainly exhibit the width of the ring as sensibly
less than the dark space within ; while all modern observers would
agree that the bright ring is now wider than the dark space, in
about the ratio of 3 : 2 ; or were we to take the average of the esti-
*Recueil des Memoires presentes [etc.] par les Astronomes de Poulkova. 4to.
St. Petersburg, 1853. Vol. I, pp. 349-385. " Sur les Dimensions des Anneaux
de Saturne." (Memoir read before Acad. Sci. ) A brief abstract of the memoir
is given in the Monthly Notices, R. A. S., November 12, 1852. Vol. XIII, pp.
22-24.
f Monthly Notices, R. A. S., December 14, 1855. Vol. XVI, pp. 30-36.
\Mem. Acad. Sci., Amsterdam, 1858. A translation of the memoir is given
in the Monthly Notices, R. A. S., January II, 1856. Vol. XVI, pp. 66-72.
GENERAL MEETING. 43
mates of the last century, it would probably not vary far from
5".25:5".75; while the general average for the present century
would probably be about 6".5 : 4".5. There seems, therefore, to be
a real difference, not accounted for by inferiority of earlier instru-
ments and estimates, nor by the existing uncertainties of modern
measurements. The question will probably be definitely settled in
less than a century. Meanwhile there is a need of some explana-
tion of the apparently systematic and progressive divergence first
pointed out by Struve; and we naturally ask, What indications
are afforded by theory ?
The elder Herschel, in 1789, (at the Saturnian equinox, when the
edge of the ring was presented to view,) from supposed observation
of protuberances moving on the line, believed that he had detected
a rotation, whose period he estimated at lOh. 32m. 15s., for the
outer edge of the ring.* The correctness of this interpretation was
controverted by Schroeter, from observations at Lilienthal, on the
next passage of Saturn's equatorial node in 1803 ; as it was after-
ward questioned by Prof. G. P. Bond, of Harvard Observatory,
from observations in 1848."}" It is scarcely doubtful that Herschel's
period was derived from an entire misconception of the nature of
the ring—which he firmly held to be solid—and that it possesses no
scientific value whatever. A. Secchi, from certain recurrent irreg-
ularities of phase observed at Rome in 1854, 1855, and 1856, in-
ferred a rotation period of 14h. 23m. This is doubtless a nearer
approximation (for the outer edge of the ring) than Herschel's es-
timate. It is not probable, however, that the period of any portion
of the ring will be determined by observation.
Accepting the meteoric theory of the rings as now established,
we may by Kepler's law compute with confidence the period of
rotation of any part of the ring ; and we thus find
—
From the period of the inner Satellite (Mimas) 22I1. 37jm.
—
The period of outer edge of ring 14.I1. 30 m.
" dividing stripe - nh. 20 ra.
" inner edge of bright ring 7h. 12 m.
" inner edge of dusky ring 5I1. 45 m.
Mean period of ring (supposed solid) about ioh. 50 m.
The period of the planet Saturn is lOh. 14m.
* Phil. Trans. Roy. Soc. 1790: Vol. LXXX, p. 479; and 1792: Vol.
LXXXII, p. 6.
f Gould's AstronomicalJournal. 1850. Vol. I, pp. 20, 21.
44 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Thus regarding each constituent element of the ring as having
its own independent rotation, (a condition absolutely essential to
the stability of the system,) we may consider that from the compli.
cated and variable perturbations by the exterior satellites, no one
particle can revolve in a circular orbit, and hence that in a space
so crowded there must be a considerable amount of interference.
The collisions at intersecting orbits may result in heat or in disin-
tegration ; but in any event they must tend to a degradation of
motion, and hence to a slightly shortened mean radius-vector and a
shortened period.
Theoretically then such an effect as that indicated by Struve
would seem inevitable, whether as a matter of fact it has been
sufficient in a couple of centuries to be detected or not. And this
involves a modified conception as to the earlier condition of the
Saturnian rings. To suppose a fine web of nebulous matter con-
tinuously spun out from Saturn's equator, with an unchanging
balance of centrifugal and centripetal forces during the long ages
while the planet was slowly contracting to one-half its radius, is
certainly no easy task or plausible theory. If, however, we are
now beholding but a stage of transitional development of the ring,
we shall have to imagine its primitive radius considerably larger,
and its width as probably very much narrower—so narrow indeed
as to have a planetary or satellitic status, revolving in a single
definite period
—
possibly that of Mimas the nearest satellite. Such
a ring would present a condition of comparatively great stability
;
and it may have been that only the secular recurrence of rare and
remarkable conjunctions commenced upon it the work of disturbance
and disintegration.
When Galileo, the first to see the strange appendages to Saturn,
(though without being able to distinguish the ansae as parts of a
ring,) observed, in 1612, that they had entirely disappeared, he
wrote in some dismay, " Has Saturn possibly devoured his own
children ? " * So may perhaps the future astronomer, seeing but an
airy trace of the historic ring, repeat the saying, Saturn has indeed
devoured his offspring; not indeed completely, for a part will
probably still remain ; nor with violent catastrophe, for the scattered
fragments falling by their eccentricity will be absorbed as gently as
are the meteors daily falling on our earth.
* Third letter to Marc Velser, December I, 1 612. Opere di Galileo. 4tOi 4
vols. Padua, 1744: Vol. II, p. 123.
GENERAL MEETING. 45
A subsidiary point deserving of notice is the certainty that the
inner portions of the bright ring (and still more those of the dusky
ring) are revolving in periods three or four hours shorter than that
of Saturn himself. When Professor Hall made his brilliant discov-
ery of the satellites of Mars, and announced that the inner satellite
(Phobos) was found to have the short period of 7h. 38m. (or less
than one-third of that of Mars) the fact was at once proclaimed by
some as incompatible with the " nebular hypothesis." Everybody
knows that the rotation periods of the sun and planets do not con-
form to the third law of Kepler. Our own moon has an actual
velocity in its orbit more than double that of our terrestrial equator.
And had the moon a little less than one-third its present distance,
(that is, were its radius-vector less than 70,000 miles,) its angular
velocity would exceed that of the earth, or its period would be less
than 24 hours. Or, stated in another way, our earth, if expanded
to the orbit of the moon, (under the most favorable disposition of
form and of homogenous density,) would occupy considerably more
than a year in completing its rotation. The supposed nebular diffi-
culty is therefore just as pertinent to our own satellite as to those
of Saturn or of Mars. The obvious solution is, that all the planets
(without exception) have lost a very large amount of rotatory
energy ; and this may be largely or chiefly ascribed to the retarding
effects of internal friction resulting from solar tides. And, given
time enough, the rotation of every planet should be finally reduced
to the lunar condition of a precise accord of its diurnal and annual
periods. On any hypothesis whatever, it is certain that the rotations
of the planets are very much slower (notwithstanding too the
acceleration due to contraction) than they originally were. This
fact certainly offers no objection to the nebular hypothesis.
Mr. Dutton questioned the validity of Enuis' hypothesis, that
the rotation of a nebular mass could be initiated by purely internal
movements.
Other remarks were made by Mr. Frisby.
Mr. S. M. Burnett then made a communication on
THE CHARACTER OF THE FOCAL LINES IN ASTIGMATISM,
showing that the two lines which limit the focal interval of Sturm
have been erroneously assumed to be straight. There is only one
46 PHILOSOPHICAL SOCIETY OF WASHINGTON.
special case of the triaxial ellipsoid in which they are straight.
In all other cases they are curved.
The full text of this paper may be found in the Archives of
Ophthalmology, Vol. XII, Nos. 3 aud 4.
Mr. H. A. Hazen followed with a communication on
THERMOMETER EXPOSURE.
[Abstract.]
Without entering upon the question, Where in any locality shall
the air temperature be observed, it is proposed to discuss the even
more important question, What shall be the environment of a
thermometer that it may give the true temperature. The practice
has been very various : in England the Stevenson shelter is re-
garded as a standard : this is a double-louvred frame, wholly of
wood, 18 x 10 x 18 inches, and placed about 4 feet above grass. In
Russia we find a large wooden outside shelter of single louvres
open to the north, inside of which is placed a metallic screen, the
whole being exposed 12 or 13 feet above grass. In any exposure we
should seek, first, to allow the freest possible access of the outer air,
and second, to screen the thermometer from direct sun heat, from
precipitation, and from radiation, whether (a) from surrounding
objects by day or (b) to the sky at night.
It is important that we adopt some ready means of accurately
determining the air temperature which may answer as a standard
of comparison. This we have in the swung thermometer, which,
by its free motion through a large body of air shaded from direct
sunlight in the daytime, is calculated to give good results.
Experiments have been tried with a so-called "Pattern" shelter
constructed of wood, of single louvres, inclined 30° to the hor-
izontal, thus giving a good air circulation. The size is 4 x 3 x 3
feet, and it is erected at a height of 13 feet above a tin roof. In
order to determine the least admissible size for a shelter, thermom-
eters were placed in the Pattern 5 inches apart and running in an
east and west direction, and these were observed morning and after-
noon. It has been found that with a hot sun and still air the heat
from the louvres rapidly diminishes with distance and becomes in-
sensible at 15 inches. Comparisons have also been made for several
weeks between the Russian and Pattern shelters ; and the means
of 100 sets of continuous observations on a still day, and again on
a windy day, are shown n the following table:
GENERAL MEETING. 47
Dry ther- Wet ther- Relative humidity;
mometer. mometer. per cent.
Russian. Pattern. R. P. R.. P
Still air 74°.8 73°.5 64°.o 62°.7 52.4 51.
1
Light south wind.. 77 .2 77 .1 62 .0 61 .0 36.7 34.1
These results show directly the advantage of a good circulation
of air, and that after shielding from the sun and radiation to the
sky with a shelter at least 3 feet long, we may neglect other consid-
erations.
Experiments are still in progress to determine the proper height
above sod or roof, the proper exposure for a north window, and so
forth.
Mr. Antisell, referring to the general theme rather than to
the special subject of the paper, took occasion to note that the
practice of conducting meteorologic observations on the tops of
high4iouses, while it may well subserve the special purposes of the
Signal Service, renders their work of materially less value to the
medical profession. There is so much change, especially of the
moisture element, in the first few feet from the ground upward that
no observations can be depended upon as reporting the conditions
of the phenomena of disease unless they are made in the layer
actually occupied by man.
Mr. Taylor asked whether there might not be an error arising
from the set given to the glass of the bulb by the pressure of the
mercury of a whirled thermometer.
Mr. Hazen replied that he had tested the effect of pressure ap-
plied to the bulb with the finger, and found that the set produced
was of very brief duration. He had also tested the thermic effect
of the friction on the atmosphere incurred by rapid whirling, and
found it inappreciable with a velocity of about fourteen miles an
hour. On whirling a black bulb thermometer, he observed a change
of several tenths of a degree, which appeared clearly referable to
the greater coefficient of friction of the surface roughened by lamp-
black.
Mr. Graham Bell remarked that if we eliminate radiation and
learn the absolute temperature of the air at the point of observa-
tion, our knowledge is still limited to that point only, whereas for
meteorologic purposes it is important to ascertain the average tem-
perature of a body of air. He suggested the possibility of utilizing
for this purpose a measurement of the velocity of sound, which
48 PHILOSOPHICAL SOCIETY OF WASHINGTON.
velocity is dependent on atmospheric temperature and independent
of barometric pressure.
Mr. Dutton thought that the extreme delicacy of this observa-
tion would involve an uncertainty greater than the one which now
inheres in the determination.
239th Meeting. October 27, 1883.
The President in the Chair.
Forty-seven members and guests present.
The Chair announced the death of two members since the last
meeting
—
Leonard Dunnell Gale and Elisha Foote.
Announcement was also made of the election to membership of
Charles Doolittle Walcott.
Mr. T. N. Gill made a communication on
ICHTHYOLOGICAL RESULTS OF THE VOYAGE OF THE ALBATROSS.
Mr. Alexander Graham Bell made the following communi-
cation on
FALLACIES CONCERNING THE DEAF, AND THE INFLUENCE OF SUCH
FALLACIES IN PREVENTING THE AMELIORATION
OF THEIR CONDITION.
It is difficult to form an adequate conception of the prevalence
of deafness in the community. There is hardly a man in the
country who has not in his circle of friends and acquaintances at
least one deaf person with whom he finds it difficult to converse
excepting by means of a hearing-tube or trumpet. Now is it not
an extraordinary fact that these deaf friends are nearly all adults?
Where are the little children who are similarly afflicted? Have
any of us seen a child with a hearing-tube or trumpet ? If not,
why not? The fact is that very young children who are hard of
hearing, or who cannot hear at all, do not naturally speak, and this
fact has given origin to the term " deaf-mute," by which it is cus-
tomary to designate a person who is deaf from childhood.
"But are there no deaf children," you may ask, "excepting
those whom we term deaf-mutes ? " No ; none.. In the tenth census
GENERAL MEETING. 49
of the United States (1880) persons who became deaf under the
age of sixteen years were returned as " deaf and dumb." Such
facts as these give support to the fallacy that deafness, unaccom-
panied by any other natural defect, is confined to adult life, and is
specially characteristic of advancing old age.
So constant is the association of defective speech with defective
hearing in childhood that if one of your children whom you have
left at home, hearing perfectly and talking perfectly, should, from
some accident, lose his hearing, he would also naturally lose his
speech. Why is this, and why are those who are born deaf always
also dumb ?
Fallacies Concerning the Dumbness of Deaf Children.
The most ingenious and fallacious arguments have been advanced
in explanation. George Sibscota,* in 1670, claimed that the nerves
of the tongue and larynx were connected with the nerves of the
ear, " and from this Communion of the vessels proceeds the sympathy
between the Ear, the Tongue and Larynx, and the very affection of
those parts are easily communicated one with the other. Hence it
is that the pulling of the Membrane of the Ear causeth a dry Cough
in the party ; and that is the reason most deaf men * * * are
Dumb, or else speak with great difficulty ; that is, are not capable of
framing true words or of articulate pronunciation by reason, of the
want of that convenient influx of the animal spirits ; and for this
cause also, it is that those who are thick of Hearing have a kind of
hoarce speech."
The value of Sibscota's reasoning may be judged of by the
further information he gives us concerning the uses of the Eusta-
chian tube. " By this it is," he says, " that Smoakers, puffing up
their Bheeks, having taken in the fume of Tobacco, send it out at
their Ears. Therefore the opinion of Alcmaeon is not ridiculous,
who held that she-Goats did breathe thorough their Ears," &c, &c.
It is easy for us to laugh at the fallacies of the past, but are we
ourselves any less liable to error on that account? The majority
of people at the present day believe that those who are born deaf
are also dumb because of defective vocal organs. Now let us examine
* I have been informed that Sibscota's work, " The Deaf and Dumb Man's
Discourse," from which the above extracts are taken, is in reality a translation of
another work by Anthony Densing, published in 1656.
50 PHILOSOPHICAL SOCIETY OF WASHINGTON.
this proposition. It is a more ridiculous and absurd fallacy than
that of Sibscota and more easily disposed of.
The hypothesis that congenitally deaf children do not naturally
speak because their vocal organs are defective involves the assump-
tion that were their vocal organs perfect such children would natu-
rally speak. But why should they speak a language they have
never heard ? Do we speak any language that we have not heard?
Are our vocal organs defective because we do not talk Chinese? It
is a fallacy. The deaf have as perfect vocal organs as our own,
and do not naturally speak because they do not hear. I have my-
self examined the vocal organs of more than 400 deaf-mutes with-
out discovering any other peculiarities than those to be found
among hearing and speaking children. The deaf children of Italy
and Germany are almost universally taught to speak, and why
should we not teach ours? Wherever determined efforts have been
made in this country success has followed and articulation schools
have been established.
Fallacy Concerning the Intelligence of Deaf Children.
The use of the word " mute" engenders another fallacy concerning
the mental condition of deaf children. There are two classes of
persons who do not naturally speak—those who are dumb on account
of defective hearing and those who are dumb on account of defec-
tive minds. All idiots are dumb.
Deaf children are gathered into institutions and schools that
have been established for their benefit away from the general obser-
vation of the public, and even in adult life they hold themselves
aloof from hearing people ; while idiots and feeble-minded persons
are not so generally withdrawn from their families. Hence the
greater number of " mutes " who are accessible to public observation
are dumb on account of defective minds, and not of defective hear-
ing. No wonder, therefore, that the two classes are often con-
founded together. It is the hard task of every principal of an
institution for the deaf and dumb to turn idiots and feeble-minded
children away from his school—children who hear perfectly, but
cannot speak. Although it is evidently fallacious to argue that,
because all deaf infants are dumb, and all idiots are dumb ; there-
fore all deaf infants are idiots: still this kind of reasoning is un-
consciously indulged in by a large proportion of our population
;
and the majority of those who for the first time visit an institution
GENERAL MEETING. 51
for the deaf and dumb express unfeigned astonishment at the bright-
ness and intelligence displayed by the pupils.
Why Hearing Children who become Deaf also become Dumb.
I have stated above that children who are born deaf do not natu-
rally speak because they cannot hear. For the same reason chil-
dren who lose their hearing after having learned to speak naturally
tend to lose their speech. They acquired speech through the ear
by imitating the utterances of their friends and relatives, and when
they become deaf they gradually forget the true pronunciation of
the words they know, and have naturally no means of learning the
pronunciation of new words ; hence their speech tends to become
more and more defective until they finally cease to use spoken
words at all.
Adults who become deaf do not usually have defective speech,
for in their case the habit of speaking has been so fully formed
that the mere practice of the vocal organs in talking to friends
prevents loss of distinctness. We can learn, however, from the
case of Alexander Selkirk how important is constant practice of
the vocal organs. This man, after about one year's solitary resi-
dence upon an island, was found to have nearly forgotten his mother
tongue; and we find that deaf adults who shrink from society and
use their vocal organs only on rare occasions acquire peculiarities
of utterance that are characteristic of persons in their condition,
although the general intelligibility of their speech is not affected.
Fallacies Regarding the Nature of Speech.
The fallacies I have already alluded to respecting the difference
between those who become deaf in' childhood and those who become
deaf in adult life have their origin in a fallacy concerning the nature
of speech itself. To most people, who do not reflect upon the sub-
ject, it appears that speech is acquired by a natural process similar
to that by which we acquire our teeth. At a certain age the teeth
make their appearance, and at another age we begin to talk. To
unreflecting minds it appears that we grow into speech; that speech
is a natural product of the vocal organs, produced without instruc-
tion and education ; and this leads directly to the fallacy that where
speech is wanting or imperfect the vocal organs are defective.
I have already stated that this cause has been assigned in expla-
52 PHILOSOPHICAL SOCIETY OF WASHINGTON.
nation of the dumbness of children who are deaf. The idea gives
rise also to the popular notion that stammering and other defects of
speech are diseases to be " cured," and the attempt has been made
to do so, even by heroic treatment. It is not so very long ago that
slices have been cut from the tongue of a stammerer, in the vain
hope of " curing " what was, after all, but a bad habit of speech.
I have myself known of cases where the uvula has been excised to
correct the same defect. The dumbness of the deaf and the defect-
ive speech of the hearing are some of the penalties we pay for ac-
quiring speech ignorantly, by mere imitation. If parents realized
that stammering and other defects of speech were caused by igno-
rance of the actions of the vocal organs, and not necessarily through
any defect of the mouth, they would have their children taught the
use of the vocal organs by articulation teachers, instead of patron-
izing the widely-advertised specialty physicians, who pretend by
secret means to " cure " what is not a disease. Speech is naturally
acquired by imitation, and through the same agency defects of
speech are propagated. A child copies the defective utterance of
his father. A school-fellow mocks a stammering companion, and
becomes himself similarly affected. In the one case the fallacy that
the supposed disease is hereditary prevents attempts at instruction
and correction, and in the other the idea that the affliction is the
judgment of God in the way of punishment discourages the afflicted
person and renders him utterly hopeless of any escape excepting by
a miracle.
A practical illustration of the fact that defective speech is prop-
agated by imitation is shown in my own case. When I was a boy
my father was a teacher of elocution, and had living with him at
one time one or two pupils who stammered. While under the care
of my father, these boys spoke clearly and well, without any ap-
parent defect, but, owing to his being called away for a protracted
period of time, his pupils relapsed, and the boys commenced to
stammer as badly as at first. Upon my father's return he found a
house full of stammerers. Sis own sons were stammering too ! I
can well remember the process of instruction through which I
went before the defect was corrected in my own case.
Ignorance the Real Difficulty in the Way of Teaching Deaf Children
to Speak.
Speech is the mechanical result of certain adjustments of the
GENERAL MEETING. 53
vocal organs, and if we can teach deaf children the correct adjust-
ments of the perfect organs they possess, they will speak. The diffi-
culty lies with us. We learn to speak by imitating the sounds we
hear, in utter ignorance of the action of the organs that accompa-
nies the sounds. I find myself addressing an audience composed of
scientific men, including many of the most eminent persons in the
country, and I wonder how many there are in this room who could
give an intelligible account of the movements of their vocal organs
in uttering the simplest sentence? We must study the mechanism
of speech, and when we know what are the correct adjustments of
the organs concerned, ingenuity and skill will find the means of
teaching perfect articulation to the deaf.
The Old Fallacy—" Without Speech, no Reason."
I have already stated that children who are born deaf are also
always dumb. How, then, can they think ? It is difficult for us to
realize the possibility of a train of thought being carried on with-
out words ; but what words can a deaf child know, who has never
heard the sounds of speech ?
When we think, we think in words, though we may not actually
utter sounds. Let us eliminate from our consciousness the train of
words, and what remains ? I do not venture to answer the ques-
tion ; but it is this, and this alone, that belongs to the thoughts of
a deaf child.
It is hardly to be wondered at, therefore, that the fallacy should
have arisen in the past that there could be no thought without
speech ; and this fallacy prevented for hundreds of years any attempt
at the education of the deaf. Before the end of the last century
deaf-mutes were classed among the idiots and insane ; they had no
civil rights, could hold no property ; they were irresponsible beings.
Even those interested in the religious welfare of the world consigned
their souls to the wrong place, for " faith comes by hearing," and
how could a deaf child be saved ? I say that for hundreds of years
the old fallacy, that " without speech there could be no reason,"
hindered and prevented any attempt at the amelioration of the con-
dition of the deaf. But, strange to say, it was this very fallacy that
first led to their education. It was attempted, by a miracle to teach
them to speak.
In Bede's History of the Anglo-Saxon church we read " How Bish-
opp John cured a dumme man with blessing him."
54 PHILOSOPHICAL SOCIETY OF WASHINGTON.
" And when one weeke of Lent was past, the next sounday he
willed the poore man to come unto him ; when he was come, he
bydd him put out his tounge and show it unto him, and taking him
by the chiuue, made the signe of the holy crosse upon his tounge,
and when he had so signed and blessed it, he commauuded him to
plucke it in again, and speake saying, speake, me one word, say
gea, gea, which in the english tounge is a worde of affirmation and
consent in such signification as yea, yea.* Incontinent the stringes
of his tounge were loosed, and he said that which was commanded
him to say. The bishopp added certain letters by name, and bid
him say A; he said A; say B, he said B, and when he had said
and recited after the bishopp the whole cross rewe he put upon him
sillables and hole wordes to be pronounced. Unto which when he
answered in all pointes orderly, he commauuded him to speake long
sentences, and so he did ; and ceased not all that day and night
following, so louge as he could hold up his head from sleepe (as
they make report that were present) to speake and declare his secret
thoughtes and purposes, which before that day he could never utter
to any mau."f
Now, stripped of the miraculous, this is simply a case of articula-
tion teaching. In the other countries of Europe the first attempts at
the education of the deaf were also made by teaching them to speak,
and as the early teachers were monks of the Roman Catholic
Church, it is probable that these schools resulted from the attempts
to perform the miracle of healing the dumb. A large proportion
of the deaf and dumb who were thus brought together were success-
fully taught to articulate.
But now comes a marvel : It was found by the old monks that
their pupils came to understand the utterances of others by watch-
ing the mouth. Such a statement appears more marvelous to those
who understand the mechanism of speech than to those who are
ignorant of it ; and there is a general tendency to consider this ac-
complishment as among the fictitious embellishments of the old nar-
ratives. But the experience of modern teachers confirms the fact.
John Bulwer, who is said to have been the earliest English writer
upon the subject of the instruction of the deaf and dumb, published
* It will be remembered that the original of this was in Latin, and that " the
english tounge" here means what we now call the Anglo Saxon,
f American Annals of the Deaf and Dumb, vol. I, p. 23 (1S48).
GENERAL MEETING. 55
iii the year 1648 a treatise entitled "Philoeophus ; or, the Deaf and
Durabe Man's Friend. Exhibiting the Philosophicall verity of that
subtile Art, which may inable one with an observant Eie, to Ileare
what any man speaks by the moving of his lips. Upon the same
Ground, with the ad vantage, of au Historicall Exemplification, ap-
parently proving, That a Man Borne Deafe and Dumbe may be
taught to Ileare the sound of words with his Eie, and thence learn
to speak with his tongue."
Articulation Teaching in America.
In Europe at the present time deaf children are much more com-
monly taught to speak and understand speech than in this country.
In the majority of our schools and institutions articulation and
speech-reading are taught to only a favored few, and in these schools
no use is made of articulation as a means of communication. A
considerable number of the deaf children in our institutions could
once hear and speak, and those pupils who retain some knowledge
of spoken language have their vocal organs exercised for an hour
or so a day in an articulation class under a special articulation
teacher, but this is not enough exercise to retain the speech. I have
seen a boy who became deaf at 12 years of age, and who had previ-
ously attended one of our public schools, go into an institution for
the deaf and dumb talking as readily as you or I and come out a
deaf mute.
Few, if any, attempts are made to teach articulation to those who
have not naturally spoken, except at the special request of parents
who desire that the experiment shall be tried with their children.
I have seen a congenital deaf mute, who also had a sister deaf and
dumb, who was taught to speak in adult life, and I found upon ex-
periment that he could understand by ear the words and sentences
that he had been taught to articulate when they were spoken in an
ordinary tone of voice about a foot behind his head, yet this young
man had been educated at one of our best institutions without ac-
quiring articulation, and as a consequence he grew up a deaf mute
and married a deaf mute. He informed me himself that he could
hear the people talking in the workshop where he was employed,
but did not understand what they said.
As a matter of personal observation I am convinced that a large
proportion of the congenitally deaf are only hard of hearing, and
this belief is supported by the fact that it used to be the custom in
56 PHILOSOPHICAL SOCIETY OF WASHINGTON.
some of our institutions to summon the pupils from the play-ground
by the ringing of a bell! Does this not indicate that a large num-
ber of the pupils could hear the ringing of the bell, and that they
told the others who could not hear at all? Such pupils could have
been taught to speak at home by their friends if artificial assistance
had been given to their hearing. There was no necessity for their
ever becoming deaf and dumb.
It is only within the last fifteen years or thereabouts that schools
have been established in the United States where all the deaf chil-
dren admitted are taught articulation and speech-reading, but such
schools are rapidly increasing in number. Still, it is not generally
known that the experimental stage has passed, and that all deaf
mutes can be taught intelligible speech. This is now done in Italy
and Germany, and the international conventions of teachers of the
deaf and dumb held recently at Milan and Brussels have decided
in favor of articulation for the deaf.
I have stated before that the difficulties in the way of teaching
articulation are external to the deaf. They lie with us and in our
general ignorance of the mechanism of speech. A teacher who does
not himself understand the mechanism of speech is hardly competent
to produce the best results. So dense is the general ignorance upon
this subject that it is probable that of the 50,000,000 of people in
this country the number of persons who are familiar with all that
is known concerning the mechanism of speech might be numbered
on the two hands. Considering this, the success obtained in our
articulation schools is gratifying and wonderful.
Upon the Art of Understanding Speech by the Eye.
It has been found in the articulation schools of this country that
deaf children can acquire the art of understanding by eye the utter-
ances of their friends and relatives, and this fact has led some
teachers to suppose that speech is as clearly visible to the eye as it
is to the ear, and this fallacy tends to hinder the acquisition of the
art by their pupils.
When we examine the visibility of the elementary sounds of our
language we find that the majority can not be clearly distinguished
by the eye. How then, you may ask, can a deaf child who cannot
distinguish the elements understand words which are combinations
of these elements?
When the lips are closed we cannot see what is going on inside
GENERAL MEETING. 57
the mouth. The elementary sounds of our language, represented
by the letters P, B, and M, involve a closure of the lips. Hence
the differences of adjustment that originate the differences of sound
are interior and cannot be seen. But while the deaf child may not
be able to say definitely whether the sound you utter is P, B, or M,
he knows certainly that it must be one of these three, for no other
sounds involve a closure of the lips. And so with the other ele-
ments of our language. While he may not be able to tell definitely
the particular element to which you give utterance, he can gener-
ally refer it to a group of sounds that present the same appearance
to the eye. In the same manner he may not be able to tell the pre-
cise word that you utter, but he can refer it to a group of words
having the same appearance. For instance, the words " pat," " bat,"
and " mat " have the same appearance to the eye. While he can-
not tell which of these words you mean when it is uttered singly,
he readily distinguishes it in a sentence by the context. For in-
stance, were you to say that you had wiped your feet upon a " mat,"
the word could not be " pat " and it could not be " bat."
Here we come to the key to the art of understanding speech by
the eye—Context. But this involves, as a prerequisite, a compe-
tent knowledge of the English language ; and we may particularly
distinguish those children who have acquired the art from those
who have not, by their superior attainments in this respect. We
can, therefore, see why children who have become deaf after hav-
ing learned to speak, naturally acquire this power to a greater ex-
tent than those who are born deaf.
There are many cases of congenitally deaf children who have ac-
quired this art as perfectly as those who have become deaf from
disease; but in every case such children have been thoroughly
familiar with the English language, at least in its written form.
Fallacies Hegarding Speech-reading.
The fallacy that speech is as clearly visible to the eye as it is
audible to the ear hinders the acquisition of the art by causing the
teacher to articulate slowly and word by word, even opening the
mouth to its widest extent to make the actions of the organs more
visible. When we realize that context is the key to speech-read-
ing, theory asserts that ordinary conversational speech should be
more intelligible than slow and labored articulation. This is amply
proved by the experience of the most accomplished speech-readers.
58 PHILOSOPHICAL SOCIETY OF WASHINGTON.
I have been told by one who has acquired this art that when intro-
duced to strangers their speech is more readily understood if they
are not aware they are speaking to one who cannot hear. The
moment they are told they commence to speak slowly and open
their mouths to an unnatural extent, thus rendering their articula-
tion partially unintelligible. The change brought about by the
knowledge that the listener could not hear was sometimes sudden and
great.
I have lately made an examination of the visibility of all the
words in our language contained in a small pocket dictionary, and
the result has assured me that there are glorious possibilities in the
way of teaching speech-reading to the deaf, if teachers will give
special attention to the subject.
One of the results of my investigation has been that the ambigui-
ties of speech are confined to the little words, chiefly to monosylla-
bles. The longer words are nearly all clearly intelligible. The
reason is obvious, for the greater number of elements there are in a
word the less likelihood is there that another word can be found
that presents exactly the same outline to the eye.
We need never be afraid, therefore, of using long words to a deaf
child, if they are within his comprehension. We are apt to have
the idea that short words will be simpler, and we sometimes try to
compose sentences consisting as much as possible of monosyllabic
words, under the impression that such words are easy for the pupil
to pronounce and read from the mouth. It is more common, there-
fore, to present such sentences to beginners than to more advanced
pupils. Now, I do not mean to say that these sentences may not be
easier for a child to pronounce, but the words used are the most
ambiguous to the eye. Such a simple word as " man," for instance,
is homophenous with no less than thirteen other words.
A few years ago I dictated a string of words to some pupils, with
the object of testing whether they judged by context or were able
to distinguish words clearly by the eye. The results are instruct-
ive. Among the words dictated occurred the following : " Hit
—
rate— ferry— aren't—hat— four— that— reason— high— knit
donned—co." I told the pupils not to mind whether they under-
stood what I said or not, but simply to write down what they thought
the words looked like, and what do you think they wrote? Upon
examining their slates I found that nearly every child had written
the following sentence : " It rained very hard, and for that reason
GENERAL MEETING. 59
I did not go." I told the pupils to be very careful to observe
whether they could distinguish any difference between the words I
uttered and the words they wrote. I therefore went over the whole
string of words again, articulating them one by one very distinctly.
No difference whatever was detected.
The mother of one of my pupils was present, and was greatly as-
tonished to see her daughter writing down words so different from
those I had pronounced. She said that she could not have believed
that her daughter could have been so stupid ; but her surprise was
increased when she found that the other children had written the
same sentence. I told her that there was no difference in appear-
ance between the words I had uttered and the words they had writ-
ten. She desired to test the matter herself with her own child.
She asked her daughter to repeat after her the words I had written,
but the result was the same. The last part of the sentence she re-
peated at least a dozen times, without shaking her daughter's con-
fidence in the belief that the words she had uttered were precisely
the same as those spoken by her mother. To one who could hear,
it was a startling revelation to observe the confidence of the child
in the accuracy of her replies.
" Repeat after me," said the mother, as she pronounced the words
singly and with deliberate distinctness : " high ;" answer, " I ; " knit,"
ans., " did ;" " donned," ans., " not ; " " co," ans., " go./ "Are you
sure you have pronounced the words exactly as I have said them ?"
Ans. " Yes
;
perfectly certain." " Try again." " Knit," answer,
"did;" "donned," answer "not." "Are you sure I said that?"
Ans. " Yes ; absolutely sure." " Try again," and here the mother
mouthed the word " donned," ans., " not." The mother was con-
vinced, and she left the room with the remark that she felt that she
had been very cruel to her child through ignorance of the fact that
words that were very different to her ear looked alike to her child,
and could not possibly be distinguished, excepting by context.
I have seen a teacher attempting to impart instruction to a deaf
child by word of mouth. She would speak word by word, and the
pupil would repeat after her. Upon one occasiou the pupil gave
utterance to a very different word from that which had been spoken
by the teacher. The latter repeated the word a number of times,
opening her mouth to the widest extent, and the boy each time re-
peated the incorrect expression. The teacher grew annoyed at the
supposed stupidity of the pupil, and the pupil grew sulky, and was
60 PHILOSOPHICAL SOCIETY OF WASHINGTON.
discouraged in his attempt to read from the mouth ; whereas, in
reality, it was not the stupidity of the boy that was in the way of
his progress, but the ignorance of the teacher, who did not know
that the words that were so different to her ear were absolutely alike
to his eye.
Some teachers, in their anxiety to teach speech-reading to their
pupils, have the idea that they should refrain from every other
mode of communication, so that their pupils may be forced to ob-
serve the movements of the mouth, and the mouth alone. For in-
stance, it is easy to write an ambiguous word or to spell it by a
manual alphabet, but some teachers refrain from doing so, under
the impression that this practice leads the pupil to depend upon
the hand instead of the mouth.
Again, deaf persons gather an idea of the emotion that actuates
a speaker by the expression of his countenance. In fact facial
expression is to the eye what the modulation of the voice is to the
ear. It gives life to the inaudible utterances of the mouth ; but
there are some teachers who are so afraid that their pupils may
come to depend upon the face instead of the mouth, that they think
they should assume an impassive countenance from which nothing
could be inferred.
Requisites to the Art of Speech-reading.
If we examine the visibility of speech and the causes of its in-
telligibility, we shall find that there are three qualifications that
must be possessed by a deaf child in order that he may understand
readily the utterances of his friends. Omit any one of these quali-
fications and good speech-reading is an impossibility
:
I. The eye must be trained to recognize readily those movements
of the vocal organs that are visible. Has this ever been done ?
Have not pupils been required to grapple with all the difficulties of
speech-reading at once, and to observe not only the movements of
the vocal organs, but to find out the meaning of what is said ?
II. I have already explained that certain words have the same
appearance to the eye, and it is necessary, if the pupil is to under-
stand general conversation, that he shall know the words that look
alike, so that a given series of movements of the vocal organs shall
suggest to his mind not a single word, but a group of words, from
which selection is to be made by context.
An illustration will explain what I mean. There are many
GENERAL MEETING. 61
words which have the same sound to the ear, but different signifi-
cations. For instance, were I to ask you to spell the word " rane,"
you could not tell whether I meant " rain," " rein," or " reign."
These words sound alike, but they lead to no confusion, for they
are readily distinguished by context. In the same way " homo-
phenous words," or words that have the same appearance to the
eye, are readily distinguished by context.
As a general rule when a teacher finds that her pupil does not
understand a given word, she supposes the non-comprehension to
be due to an untrained eye, and this leads to the patient repetition
of the word with widely opened mouth, to make the action of the
organs more visible. This, unintentionally, enables the pupil to
acquire a knowledge of homophenous words ; for, when he fails to
understand in the first instance, he is requested to try again. He
then guesses at the meaning. He thinks of all the words that past
experience has taught him looked something like the word pro-
posed, and after a series of guesses generally succeeds in his at-
tempt to unravel the meaning.
In this way success comes at last, not in consequence of the pupil
seeing more than he saw at first, but in consequence of knowledge
gained by experience of failure. He learns what words present the
same appearance to the eye. Let teachers find out the words that
look alike, and teach them in groups to their pupils. In this way
instruction will take the place of painful experience.
III. The third requisite to good speech-reading is familiarity
with the English language. Familiarity with our language, either
in its written or spoken form, is absolutely essential in order that
a deaf person may make use of context in his attempt to decipher
our speech. It is a mental problem that the deaf child has to
solve and not solely a problem of vision. The eyes of the con-
genially deaf, if there is any difference at all, are rather stronger
and better than the eyes of those who become deaf from disease;
and yet, as a class, the congenitally deaf acquire the art of speech-
reading with much more difficulty than those who could speak be-
fore they became deaf. The reason is, that, as a class, the former
have not a vernacular knowledge of our language even in its writ-
ten form, while the latter have. Children who become deaf in
infancy from disease are at as great a disadvantage in this respect
as the congenitally deaf, and for the same reason.
I shall inquire more particularly into the cause of this lack of
62 PHILOSOPHICAL SOCIETY OF WASHINGTON.
familiarity with the English language, and I snail show that it
results from a wide-spread fallacy regarding the nature of language
and the means by which our language should be taught. In the
meantime I shall simply direct attention to the fact that those who
are deaf from infancy do not, as a general rule, become familiar
with the English language even in its written form.
It is obvious that if we talk to deaf children by word of mouth,
and refrain from explaining, by writing or some other clearly visi-
ble means, the words that are ambiguous, those pupils who are
already familiar with the language have very great advantages
over the others. They have a fund of words from which to draw,
they can guess at the ambiguous word and substitute other words
within their knowledge so as finally to arrive at the correct mean-
ing. But young children who have been deaf from infancy and
who never, therefore, have known our language, are not qualified
at once for this species of guess-work. They know no words ex-
cepting those we teach them, and have, therefore, no fund to draw
upon in case of perplexity. If we commence the education of
such children by speech-reading alone they are plunged into dif-
ficulties to which they have not the key.
To such children it becomes a matter of absolute necessity that
our language should be presented to them in an unambiguous form.
With such pupils, writing should be the main reliance, and speech-
reading can only be satisfactorily acquired by the constant accom-
paniment of writing, or its equivalent—a manual alphabet. I have
no hesitation in saying that the attempt to carry on the general
education of young children who are deaf from infancy by means
of articulation and speech-reading alone, without the habitual use
of English in a more clearly visible form, would tend to retard their
mental development. I do not mean to say that this is ever actu-
ally done, but I know there is a tendency among teachers of articu-
lation to rely too much upon the general intelligibility of their
speech. Let them realize that the intelligibility is almost entirely
due to context, and they will rely more upon writing and less upon
the mouth in their instructions to young congenitally deaf children.
After a probationary period, pupils who could speak before they
became deaf become so expert in speech-reading that the regular
instruction of the school-room can be carried on through its means
without detriment to the pupil's progress. The exceptional cases
of congenitally deaf persons who have become expert in this art
GENERAL MEETING. 63
assures us that, with all who are deaf from infancy, we can cer-
tainly achieve the same results if only we can give them a sufficient
knowledge of our language, at least in its written form. In the
early stages of the education of the congenitally deaf it appears to
me that written English should be made the vernacular of the
school-room, and that all words or sentences written should also be
spoken by the teacher and read by the pupils from the mouth.
When the English language has become vernacular there is no
reason why instruction should not also be given by word of mouth
alone (as in the case of those who could speak before they became
deaf) without interfering with mental development.
Before leaving this subject I would say that it is of importance
to remember that speaking and understanding speech by the eye
are two very different things. We can all of us speak very readily,
but I fancy it would puzzle most of us to be called upon to tell what
a speaker says by watching his mouth. The congenitally deaf can
certainly be taught to speak intelligibly even by persons unfamiliar
with the mechanism of articulation. Such pupils should therefore
be taught to articulate, and their vocal organs should be continually
exercised in the school-room by causing them to speak as well as to
write. The congenitally deaf can be taught to articulate even be-
fore they are familiar with English, but I do not think they can
acquire the power of understanding ordinary conversational speech
by watching the mouth, at least to any great extent, until after they
have become familiar with our language.
Gesture Language.
I have already stated that the old fallacy, " without speech there
can be no reason," prevented for hundreds of years any attempt at
the education of the deaf and dumb, and now I come to the mem-
orable experiment that forever exploded the fallacy. Towards the
latter end of the last century the Abbe de l'Epee, during the course
of his ministration in Paris, entered a room in which two girls were
sewing. He addressed some remarks to them, but received no reply.
These girls were deaf and dumb. At once the kind heart of the
good Abbe was touched, and he determined to devote his life to the
amelioration of the condition of the deaf and dumb.
He gathered together quite a number of deaf children, who made
their home with^him. He spent his time in their society and de-
voted to their comfort all that he possessed, reducing himself even
64 PHILOSOPHICAL SOCIETY OF WASHINGTON.
to poverty for their sake. He soon observed that these children
were communicating with one another, but not by speech. They
were inventing a language of their own, unlike any of the spoken
languages of the earth—a language of gestures. These children
were reasoning by means of this language ; they were thinking in
gestures instead of in words, and the idea occurred to the Abbe de
l'Epee that the old dogma that had for so many hundred years pre-
vented the education of the deaf was a fallacy. Here was nature
developing an instrument of reason with which speech had nothing
to do. Why should he not study this gesture language and assist
these children in their attempts to perfect a means of communica-
tion of this kind, and why should he not use this means of com-
munication so as to lead their minds to higher and ever higher
thoughts? He did so and succeeded in developing the "sign lan-
guage " that is now so extensively employed in this country in
the education of the deaf. The experiment at once attracted at-
tention. Kings and Emperors visited the humble abode of the
Abbe de l'Epee and were astonished by what they saw. He con-
versed with his pupils in the gesture language, and he taught them
through its means the meaning of written French, so that they were
enabled to communicate with hearing persons by writing.
The Fallacy that a Gesture Language is the only Form of Language
that is Natural to the Congenitally Deaf.
The old fallacy was done away with, but a new one immediately
took its place, which has been introduced into our country with the
language of signs, and is now the main obstacle to the acquisition
of English by the congenitally deaf. The fallacy to which I allude
is that this gesture language is the only language that is natural to
the congenitally deaf, and that therefore such children must acquire
this language as their vernacular before learning the English lan-
guage, and must be taught the meaning of the latter through its
means. To my mind such a statement consists of a succession of
fallacies, each one resting on the preceding. The proposition that
the sign language is the only language that is natural to congeni-
tally deaf children is like the proposition that the English language
is the only language that is natural to hearing children. It is nat-
ural only in the same sense that English is natural to an American
child. It is the language of the people by whom he is surrounded.
A congenitally deaf child who for the first time enters an insti-
GENERAL MEETING. 65
tution for the deaf and dumb finds the pupils and teachers em-
ploying a gesture language which he does not understand ; but in
time he comes to understand it, and learns by imitation to use it,
just as an American child in Germany comes in time to understand
and speak German.
Although congenitally deaf children, when they enter an institu-
tion, do not understand or use the sign language as there employed,
they each know and use a gesture language of some kind, which
they employ at home in communicating with their friends and rela-
tives. Hence it is argued that if the " sign language " employed in
our institutions is not the only one, a gesture language of some kind
is necessarily the vernacular of the congenitally deaf child. The
scope of the statement is thus widened, and the proposition we have
now to consider may be thus expressed : Gesture language, in the
wider sense, is the only form of language that is natural to those
who are congenitally deaf.
It is a matter of great importance to the 34,000 deaf-mutes of
this country, and to their friends and relatives, as well as to all
persons who are interested in the amelioration of the condition of
the deaf and dumb, that we examine this proposition with care and
decide whether it is a fallacy or not. To my mind it is a fallacy
based upon another concerning the nature of language itself, namely,
that there is such a thing as a natural language. Such an idea has
led to errors in the past, and will ever continue to do so. We have
all read of the monarch of ancient times, who is recorded to have
shut up a number of little children by themselves, and to have
given orders to their attendants to hold no communication with
them, so that he might observe what language they would naturally
speak as they grew up. It is recorded that the first word uttered
was a Greek word, from which it was argued that the Greek lan-
guage was the natural language of mankind.
In the seventeenth century the ingenious Van Helmont was im-
bued with the idea that the Hebrew language was of divine origin,
from which he argued that Hebrew was the natural language of
mankind, and that the shapes of the Hebrew letters had some nat-
ural relation to the sounds they represented ; that they pictured, in
fact, the positions of the vocal organs in forming the sounds. The
latter idea led him to employ the characters as a means of teaching
articulation to a deaf-mute ; but the former idea led him to teach
his deaf-mute Hebrew, instead of his native tongue.
66 PHILOSOPHICAL SOCIETY OF WASHINGTON.
When we examine the languages of the world that are naturally
acquired by hearing children, we fail to discover any natural con-
nection between the sounds of the words and the things they repre-
sent ; everything is arbitrary and conventional.
Origin and Mode of Growth of a Gesture Language.
Now, let us examine for a moment the nature of a gesture lan-
guage and the manner in which it comes into existence. You are,
we shall suppose, a farmer, and your little deaf boy comes run-
ning into the house in great excitement, anxious to tell you some-
thing he has observed. How does he do so?
We shall imagine a case. He commences by placing his hands
above his head, bowing low, and marching about the room, after
which he points out of the window.
You shake your head ; you have not the remotest idea what he
means.
His face assumes an anxious look, and down he goes upon his
hands and knees, and scrambles over the floor, touching the carpet
with his mouth from time to time, and then again points out of the
window.
Still you do not comprehend.
A look of perplexity crosses his face. What can he do to make
you understand ? At last his face lights up, as a new thought comes
into his mind, and he touches the bridge of his nose and again points
out of the window.
But, alas ! alas ! you cannot understand.
The little fellow is perplexed and troubled. At last, in despair,
he takes hold of your coat and pulls you out of the door, around
the corner, and you find your cow in the turnip patch.
Now you begin to understand what it was he meant to say ; he
had tried to picture the -cow, and to imitate its actions. The
hands held above the head had indicated the horns ; the scrambling
on the floor on his hands and knees had imitated the action of a
four-footed animal, and his mouth to the carpet meant the cow
eating the turnips.
But how about the bridge of his nose ?
You will probably observe that the cow to which he referred had
some white spot or other mark upon the nose, and the gesture of the
child had not indicated a cow in general, but your black cow
" Bessie," with the white spot on her nose, in particular.
GENERAL MEETING. 67
Having advanced thus far in the comprehension of his meaning,
do you think that the child will take the trouble to go through this
same pantomime the next time he wishes to tell you about your
cow ? No. He may commence such a pantomime, but before he
gets half through you understand what he means, and he never
completes it. A process of abbreviation commences, until finally a
touch on the bridge of his nose alone becomes the name of your
black cow " Bessie," and the simple holding of his hands above his
head conveys to your mind the idea of a cow in general.
By a natural process of abbreviation the child arrives at a sim-
ple gesture or sign for every object or thing in which he is inter-
ested.
But there are many thoughts he desires to express which are ab-
stract in their nature. How, for instance, can he indicate by any
sign the color of an object? Suppose, by way of illustration, that
he desired to communicate to you the idea that he had seen in the
road a cow that was perfectly white ?
I shall try to depict the conversation between yourself and your
deaf boy as it might actually have occurred.
The boy. The boy points to the road, touches his teeth, and holds
his hands above his head.
You gather from this a vague idea of some connection between
that road, the boy's teeth, and a cow.
Here is a problem : What did he mean ? It is pretty clear that
he had seen a cow in the road, but what connection had his teeth
with that ? Perhaps the cow's teeth were peculiar. You think you
had better get him to explain, so
—
The father. You touch your teeth with an interrogative and
puzzled look.
The boy. The boy responds by showing you his shirt sleeve and
pointing to the road.
Can he mean that there was any connection between his shirt
sleeve and the cow. To clear this point
—
The father. You touch his shirt sleeve and raise your hands
above your head with a look of interrogation.
The boy. The boy nods vigorously, raises his hands above his
head, and makes his sign for " snow," followed by other signs for
objects that are white.
After he has presented a sufficient number of such signs, you per-
ceive that the one thing common to them all was their color—they
68 PHILOSOPHICAL SOCIETY OF WASHINGTON.
were white. And thus you gain the idea that the cow was white.
Do you suppose he goes through this process every time he desires
to communicate the idea of white? No; he remembers the object
which had conveyed to your mind the idea that that cow was white,
and the sign for this object is ever after used as an adjective, quali-
fying the object the whiteness of which he desires to indicate. Of
course you cannot predicate what this particular sign may be. I
have seen children who have conveyed the idea by touching their
teeth ; others who expressed it by an undulatory downward move-
ment of the hand, expressive of the way in which a snow-flake falls
to the ground.
It will thus be understood that a deaf child first commences to
express his ideas by pantomime, and that by a process of abbrevia-
tion pantomimic gestures come to be used in a conventional manner.
Pantomime is no more entitled to the name of language than a
picture is, although many ideas can be conveyed through its means.
In proportion as it becomes more conventional and arbitrary it be-
comes more and more worthy of the name of language.
The Sign-Language of Our Institutions.
Now, when the deaf children who lived with the Abbe de l'Epee
were first brought together, each of them used a gesture-language
he had invented for himself as a means of communicating with his
friends at home. Thus there were as many gesture-languages as
there were children. The only element common to these languages
was probably the pantomime from which they had all sprung. But
now what happened ? Association and the necessity of intercom-
munication led to the adoption of common signs. Each child pre-
sented his gestures to his fellows, and by a process of selection those
signs that appeared to the majority to be most fitting survived, and
were adopted by the whole ; and the synonymous signs, which were
not so well fitted, were either forgotten by disuse or used in a new
meaning to express other ideas.
I do not wonder at the interest displayed in this growth by the
Abbe de L'Epee and his contemporaries. To my mind it was the
most interesting and instructive spectacle that has ever been pre-
sented to the mind of man
—
the gradual evolution of an organized
language from simple pantomime.
When, in 1817, the first school for the deaf and dumb was opened
in America, the sign-language as used in the school of the Abbe de
GENERAL MEETING. *69
l'Epee (then under the charge of his successor, the Abbe Sicard)
was imported from France, and became the medium of instruction.
The teachers trained in this school naturally became the principals
of other institutions established upon its model, and thus the sign-
language has been diffused over the length and breadth of our land.
I heartily agree with all that experienced teachers of the deaf
have urged concerning the beauty and great interest of this gesture
language. It is indeed interesting to observe how pantomimic ges-
tures have been abbreviated to simple signs expressive of concrete
ideas ; how these have been compounded or have changed their
meaning to indicate abstract thoughts ; and how the sequence of
the sign-words has to a certain extent become obligatory, thus
forming a sort of gesture syntax or grammar.
The original stock or stocks from which our languages are derived
must have disappeared from earth ages before historic times ; but
in the gesture speech of the deaf we have a language whose history
can be traced ab origine, and it has appeared to me that this fact
should give it a unique and independent value. In the year 1878,
in a paper read before the Anthropological Society of London, I
advocated the study of the gesture language by men of science
;
for it seemed to me that the study of the mode in which the sign
language has arisen from pantomime might throw a flood of light
upon the origin and mode of growth of all languages.
You may ask why it is that, with my high appreciation of this
language as a language, I should advocate its entire abolition in
our institutions for the deaf.
I admit all that has been urged by experienced teachers con-
cerning the ease with which a deaf child acquires this language,
and its perfect adaptability for the purpose of developing his mind
;
but after all it is not the language of the millions of people among
whom his lot in life is cast. It is to them a foreign tongue, and
the more he becomes habituated to its use the more he becomes a
stranger in his own country.
This is not denied by teachers of the deaf and dumb, but the
argument is made, as I have stated above, that it is the only lan-
guage that is natural to congenitally deaf children, or that at all
events, some form of gesture language must necessarily be their
vernacular, and be employed to teach our English tongue.
70 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The Fallacy that a Gesture Language is the only form of Language
in which a Congenitally Deaf Child can Think.
Now what do we mean by a language being " natural" or not?
I cannot believe that in this 19th century any one really entertains
the fallacy that there is a natural language per se. So I presume
that that language is considered natural to a person in which he
thinks. Under this meaning the proposition assumes this shape :
The sign language taught in our institutions, or a gesture language
of some kind, is the only form of language in which a congenitally
deaf child can think ; that is, it is the only language of which the
elements can be associated directly with the ideas they express.
In this form the fallacy is easily exploded, for in the course of
the last one hundred years so many experiments have been made
in the education of the deaf that we now know with absolute cer-
tainty that deaf children can be taught to associate written words
directly with the ideas they represent ; and when they are taught
to spell these words by a manual alphabet, the movements of the
fingers become so natural a method of giving vent to their thoughts
that even in sleep their fingers move when they dream.
Not only has written English been made the vernacular of con-
genitally deaf children, but the same result has been achieved with
written French, German, Spanish, Dutch, and other languages.
Congenitally deaf children who have been taught articulation
move their mouths in their sleep and give utterance to words when
they dream.
Laura Bridgman, the blind deaf-mute, was taught by the late
Dr. Howe to gather ideas through the sense of touch. English
words printed in raised letters were presented to her sense of touch
in connection with the objects which they represented, and she
associated the impressions produced upon the ends of her fingers
with the objects themselves. The English language in a tangible
form became her vernacular.
All these facts assure us that any form of language may become
natural to a deaf child by usage, so long as it is presented to the
senses he possesses. There is only one way that language is natu-
rally acquired, and that is by usage and imitation. Any form of
language that can be clearly appreciated by the senses the deaf
child possesses, will become his vernacular if it is used by those
about him.
GENERAL MEETING. 71
Why the Deaf employ a Gesture Language.
A gesture language is employed by a deaf child at home, not
because it is the only language that is natural to one in his con-
dition, but because his friends neglect to use iu his presence any
other form of language that can be appreciated by his senses.
Speech is addressed to his ear ; but his ear is dead, and the motions
of the mouth cannot be fully interpreted without previous familiarity
with the language. On account, therefore, of the neglect of parents
and friends to present to his eye any clearly visible form of lan-
guage, the deaf child is forced to invent such a means of communi-
cation, which his friends then adopt by imitation. I venture to
express the opinion that no gesture language would be developed
at home by a deaf child If his parents and friends habitually em-
ployed, in his presence, the English language in a clearly visible
form. He would come to understand it by usage, and use it by
imitation.
An old writer, George Dalgarno, in 1680, expressed the opinion,
in which I fully concur, that " there might be successful addresses
made to a dumb child even in its cradle, risu cognoscere matrem, if
the mother or nurse had but as nimble a hand as usually they have
a tongue."
When deaf children enter an institution they find the other
pupils and the teachers using a form of gesture language which
they do not understand. For the first time in their lives they find
a language used by those about them that is addressed to the senses
they possess. After a longer or shorter time they discard the lan-
guage that they had themselves devised, and acquire, by imitation,
the sign language of the institution.
Harmful Results of the Sign Language.
After a few months residence in the institution, the children re-
turn to their friends in the holidays using easily and fluently a lan-
guage that is foreign to them, while of the English language they
know no more than the average school boy does of French or Ger-
man after the same period of instruction. The only language they
can employ in talking to their friends is the crude gesture language
of their own invention, which they had long before discarded at
school ; and they perpetually contrast the difficulty and slowness of
comprehension of their friends with the ease with which their school
fellows and teachers could understand what they mean. They have
72 PHILOSOPHICAL SOCIETY OF WASHINGTON.
learned by experience how sweet a thing it is to communicate freely
with other minds, and they are continually hampered and annoyed
by the difficulty they meet with in conversing with their own parents
and friends.
Can it be wondered at, therefore, that such a child soon tires of
home? He longs for the school play-ground, and the deaf com-
panions with whom he can converse so easily. Little by little the
ties of blood and relationship are weakened, and the institution be-
comes his home.
Nor are these all the harmful effects that are directly traceable
to the habitual use in school, as a means of communication, of a
language foreign to the mass of the people. Disastrous results are
traceable inwards in the operation of his mind, and outwards in his
relation to the external world in adult life. He has learned to
think in the gesture-language, and his most perfected English ex-
pressions are only translations of his sign speech.
As a general rule, when his education is completed, his knowl-
edge of the English language is like the knowledge of French or
German possessed by the average hearing child on leaving school.
He cannot read an ordinary book intelligently without frequent re-
course to a dictionary. He can understand a good deal of what he
sees in the newspapers, especially if it concerns what interests him
personally, and he can generally manage to make people under-
stand what he wishes by writing, but he writes in broken English,
as a foreigner would speak.
Let us consider for a moment the condition of a person whose
vernacular is different from that of the people by whom he is sur-
rounded. Place one of our American school boys just graduated
from school in the heart of Germany. He finds that his knowledge
of German is not sufficient to enable him to communicate freely
with the people. He thinks in English, and has to go through a
mental process of translation before he can understand what is said,
or can himself say what he means. Constant communication with
the people involves constant effort and a mental strain. Under
such circumstances what a pleasure it is for him to meet with a per-
son who can speak the English tongue. What a relief to be able
to converse freely once more in his own vernacular. Words arise
so spontaneously in the mind that the thought seems to evoke the
proper expression.
But mark the result: the more he associates with English-
GENERAL MEETING. 73
speaking people the less desire does he have to converse in German.
The practice of the English language prevents progress in the
aquisition of German. I have known of English people who have
lived for twenty years in Germany without acquiring the language.
If our American school boy desires to become familiar with the
German language, he must resolutely avoid the society of English-
speaking people. He then finds that the mental effort involved in
conversation becomes less and less, until, finally, he learns to think
in German, and his difficulties cease.
Now consider the case of a deaf boy just graduated from an
institution where the sign language has been employed as a means
of communication. His vernacular is different from that of the
people by whom he is surrounded. He thinks in the gesture lan-
guage and has to go through a mental process of translation before
he can understand what is said or written to him in English, and
before he can himself speak or write in English what he desires to
say. He finds himself in America, in the same condition as that
of the American boy in Germany. If he avoids association with
those who use the sign language, and courts the society of hearing
persons, the mental effort involved in conversation becomes less and
less, and finally he learns to think in English and his difficulties
cease.
But such a course involves great determination and perseverance
on the part of the deaf boy, and few, indeed, are those who succeed.
Not only do the other deaf-mutes in his locality have the same
vernacular as his own, but they were his school fellows, and they
have a common recollection of pleasant years of childhood spent
in each other's society. Can it be wondered at, therefore, that the
vast majority of the deaf graduates of our institutions keep up
acquaintance with one another in adult life ? The more they com-
municate with one another the less desire they have to associate
with hearing persons, and the practice of the gesture language
forms an obstacle to further progress in the acquisition of the
English language.
These two causes (a) previous exclusive acquaintance with one
another in the same school, and (b) a common knowledge of a form
of language specially adapted for the communication of the deaf
with the deaf, operate to attract together into the large cities large
numbers of deaf persons, who form a sort of deaf community or
society, having very little intercourse with the outside world.
74 PHILOSOPHICAL SOCIETY OF WASHINGTON.
They work at trades or businesses in these towus, and their
leisure hours are spent almost exclusively in each other's society.
Under such circumstances can we be surprised that the majority of
these deaf persons marry deaf persons, and that we have as
a result a small but necessarily increasing number of cases of
hereditary deafness due to this cause. Such unions do not gene-
rally result in the production of deaf offspring, because the deaf-
ness of the parents in a large proportion of cases is of accidental
origin, and accidental deafness is no more likely to be inherited
than the accidental loss of a limb. Still I would submit that the
constant selection of the deaf by the deaf in marriage is fraught
with danger to the community.
Why the English Language should be Substituted for the Sign
Language as a Vernacular.
If we examine the position in adult life of deaf children who
have been taught to speak, or who have acquired the English lan-
guage as a vernacular, whether in its written or spoken forms, we
find an entirely different set of tendencies coming into play, especi-
ally if these persons have not been forced in childhood to make the
acquaintance of large numbers of other deaf children, by social
imprisonment for years together in the same school or institution
apart from the hearing world.
Their vernacular use of the English language renders it easy for
them to communicate with hearing persons by writing, or by word
of mouth if they have been taught to articulate ; and hearing per-
sons can easily communicate with them by writing, or by word of
mouth if they have been taught the use of the eye as a substitute
for the ear. The restraints placed upon their intercourse with the
world by their lack of hearing leads them to seek the society of
books, and thus they tend to rise mentally to an ever higher and
higher plane. A cultivated mind delights in the society of edu-
cated people, and their knowledge of passing events derived from
newspapers forms an additional bond of union between them and
the hearing world.
If they have formed in childhood few deaf acquaintances, they
meet in after life hundreds of hearing persons for every deaf acquain-
tance, and if they marry, the chances are immensely in favor of
their marrying hearing persons.
There is nothing in the deaf-mute societies in the large cities to
GENERAL MEETING. 75
attract them, and much to repel them ; for the more highly edu-
cated deaf-mutes in these societies speak what is to them a foreign
language; while the greater number of the deaf-mutes to be found
there are so ignorant that self-respect forbids them from mingling
with them.
Thus the extent of their knowledge of the English language is
the main determining cause of the congregation or separation of
the deaf in adult life. A good vernacular knowledge of the Eng-
lish language operates to effect their absorption into society at
large, and to weaken the bonds that tend to bring them together
;
whereas, a poor knowledge of the language of the country they
live in causes them to be repelled by society and attracted by one
another ; and these attractive and repulsive tendencies are increased
and intensified if they have been taught at school a language for-
eign to society and specially adapted for intercommunication among
themselves. I say, then, let us banish the sign language from our
schools. Let the teachers be careful in their intercourse with their
pupils to use English and English alone. They can write, they can
speak by word of mouth, they can spell the English words by a
manual alphabet, and by any or all of these methods they can
teach English to their pupils as a native tongue.
Conclusion.
In conclusion allow me to say
:
1. That those whom we term " deaf-mutes " have no other natural
defect than that of hearing. They are simply persons who are
deaf from childhood and many of them are only " hard-of-hearing."
2. Deaf children are dumb, not on account of lack of hearing,
but of lack of instruction. No one teaches them to speak.
3. A gesture language is developed by a deaf child at home,
not because it is the only form of language that is natural to one
in his condition, but because his parents and friends neglect to use
the English language in his presence in a clearly visible form.
4. (a) The sign language of our institutions is an artificial and
conventional language derived from pantomime.
(6) So far from being natural either to deaf or hearing persons,
it is not understood by deaf children on their entrance to an insti-
tution. Nor do hearing persons become sufficiently familiar with
the language to be thoroughly qualified as teachers until after one
or more years' residence in an institution for the deaf and dumb.
76 PHILOSOPHICAL SOCIETY OF WASHINGTON.
(c) The practice of the sign language hinders the aquisition of
the English language.
(d) It makes deaf-mutes associate together in adult life, and
avoid the society of hearing people.
(e) It thus causes the intermarriage of deaf-mutes and the
propagation of their physical defect.
5. Written words can be associated directly with the ideas they
express, without the intervention of signs, and written English can
be taught to deaf children by usage so as to become their ver-
nacular.
6. A language can only be made vernacular by constant use as
a means of communication, without translation.
7. Deaf children who are familiar with the English language in
either its written or spoken forms can be taught to understand the
utterances of their friends by watching the mouth.
8. The requisites to the art of speech-reading are :
(a) An eye trained to distinguish quickly those movements of
the vocal organs that are visible (independently of the meaning of
what is uttered.)
(b) A knowledge of homophenes ; * that is, a knowledge of those
words that present the same appearance to the eye ; and
(c) Sufficient familiarity with the English language to enable
the speech-reader to judge by context which word of a homophe-
nous group is the word intended by the speaker.
If we look back upon the history of the education of the deaf,
we see progress hindered at every stage by fallacies. Let us strive,
by discussion and thought, to remove these fallacies from our minds
so that we may see the deaf child in the condition that nature has
given him to us. If we do this, I think we shall recognize the fact
that the afflictions of his life are mainly due to ourselves, and we
can remove them.
Nature has been kind to the deaf child, man cruel. Nature has
inflicted upon the deaf child but one defect—imperfect hearing ;
man's neglect has made him dumb and forced him to invent a
language which has separated him from the hearing world.
Let us, then, remove the afflictions that we ourselves have caused.
* This word was suggested to me some years ago by Mr. Homer, lately Prin-
cipal of the Providence (R. I.) School for Deaf-Mutes, and has now been per-
manently adopted.
GENERAL MEETING. 77
1. Let us teach deaf children to think in English, by using
English in their presence in a clearly visible form.
2. Let us teach them to speak by giving them instruction in the
use of their vocal organs.
3. Let us teach them the use of the eye as a substitute for the
ear in understanding the utterances of their friends.
4. Let us give them instruction in the ordinary branches of edu-
cation by means of the English language.
5. And last, but not least, let us banish the sign language from
our schools.
If it were our object to fit deaf children to live together in adult
life and hold communication with the outside world as we hold
communication with other nationalities than our own, then no bet-
ter plan could be devised than to assist the development of a special
language suitable for intercommunication among the deaf.
But if, on the other hand, it is our object to destroy the barriers
that separate them from the outside world and take away the isola-
tion of their lives, then I hold that our energies should be devoted
to the acquisition of the English language as a vernacular in its
spoken and written forms. With such an object in view we should
bring the deaf together as little as possible and only for the pur-
pose of instruction. After school hours we should separate the deaf
children from one another to prevent the development of a .special
language and scsftter them among hearing children and their friends
in the outside world.
The subject being presented to the Society for discussion, Mr.
E. M. Gallaudet spoke, in substance, as follows
:
I have listened with great interest to the remarks of Mr. Bell
this evening, and am ready to agree in many particulars with the
views he has so Avell presented.
I am, however, compelled to differ with him at several points
;
and as these involve matters of vital importance in the treatment
of the deaf, I will beg the indulgence of the Society for a short
time, while I attempt to show to what extent some of Mr. Bell's
views are erroneous.
In proving the generally received opinion that the vocal organs
of persons deaf from infancy are defective, to be a fallacy, Mr.
Bell declared that difficulties encountered by such persons in
acquiring speech are wholly external to themselves, and that all
78 PHILOSOPHICAL SOCIETY OP WASHINGTON.
persons so situated can, with proper instruction, be taught to speak
and to understand the motions of the lips of others.
That this is a grave error has been proved by the experience of
more than a century of oral teaching in Germany.
The late Moritz Hill, of Wessenfels, Prussia, a man of the widest
experience and highest standing among the oral teachers of Europe,
expressed to me the opinion a few years since that out of one hun-
dred deaf-mutes, including the semi-mute and semi-deaf, only
" eleven could converse readily with strangers on ordinary subjects"
on leaving school. Of course a much larger number would be able
to converse with their teachers, family, and intimate friends on
common-place subjects ; but it would be found that very many
could never attain to any ready command of speech.
The explanation of this lies in the fact that a child, deaf from
infancy, in order to succeed with speech and lip-reading must pos-
sess a certain quickness of vision, a power of perception, and a
control over the muscles of the vocal organs, by no means common
to all such children.
Mr. Bell's view has been held by many instructors with more
or less tenacity, and this fact is explained by a readiness on their
part to argue from the particular to the general. Having
attained marked success with certain individuals, they draw, in their
enthusiasm, the mistaken conclusion that success is possible in the
case of every other deaf child, overlooking the fact that many
things, besides the mere deafness of the child, may affect the result.
Experience has demonstrated that in attempting to teach the
deaf to speak, failure in many cases must be anticipated.
Mr. Bell is mistaken in supposing ignorance as to the mech-
anism of the vocal organs to be a prominent cause of failure to
impart speech to the deaf. It is no doubt true that among per-
sons unfamiliar with the training of the deaf, few have made the
mechanism of speech a study ; but in Germany, Italy, and France,
not to speak of our own country, many are to be found who may
be said to have mastered this subject. The results of their labors
have been made available to instructors of the deaf, and all the
best oral schools are profiting thereby.
Mr. Bell is also mistaken when he says that " in a majority of
our schools and institutions articulation and speech-reading are
taught to only a favored few, and in these schools no use of articu-
lation is made as a means of communication," and that " few, if
GENERAL MEETING. 79
any, attempts are made to teach articulation to those who have not
naturally spoken." In most of the larger institutions for the deaf
in this country, every pupil is afforded an opportunity to acquire
speech, and instruction in this is discontinued only when success
seems plainly unattainable.
It is a great error to suppose it to be true of a deaf person edu-
cated on what Mr. Bell calls the sign-method, that, " as a general
rule, when his education is completed, his knowledge of the English
language is like the knowledge of French or German possessed
by the average hearing child on leaving school," or to say that
" he cannot read an ordinary book intelligently without frequent
recourse to a dictionary." On the contrary, a majority of persons
thus educated have a good knowledge of their vernacular, are
able to use it readily as a means of communication with hear-
ing persons, and are able to read intelligently without frequent
recourse to the dictionary.
When Mr. Bell has become familiar with the peculiarities of
the deaf by personal contact with a large number of this class
of persons, I am confident he will not repeat his assertion that
" nature has inflicted upon the deaf child but one defect—imperfect
hearing." For he will then have discovered, what has long been
known to teachers of experience, that deaf children, in addition to
their principal disability, are often found to be lacking in mental
capacity, or in the imitative faculty, in the power of visual or tactile
perception, and in other respects; all of which deficiencies, though
they do not amount even to feeble-mindedness, much less to idiocy,
do operate against the attainment of success in speech, as well as
in other things which go to complete the education of such chil-
dren. .
Passing over several points of relatively small importance, in
regard to which I believe Mr. Bell's views to be subject to criti-
cism, I come to his characterization as a fallacy of the opinion
held by many " that the language of gestures is the only language
natural to the child born deaf or who has become deaf in infancy."
I think that in order to sustain his view that this is a fallacy
Professor Bell gives a strained and very unusual meaning to the
words " natural language." If, as he explains, a natural language
is any one that a child may happen to be first taught by those with
whom he is associated, then I should have no controversy with him.
But I understand a natural language to be one that is mainly spon-
taneous, and not at all one that is borne in upon a child from without.
80 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Moritz Hill, to whom I have already alluded, speaks of the lan-
guage of signs as " one of the two universally intelligible innate
forms of expression granted by God to mankind," the other being
speech. Now it is hardly necessary to urge that speech is the form
of expression natural to hearing persons, and I think a little re-
flection will satisfy most persons that with the deaf the language of
signs is the only truly natural mode of expressing their thoughts.
Mr. Bell urges that the use of signs in the education of the deaf
is a hinderance rather than a help, and that it would be better
to banish them altogether. To this view I must give my earnest
dissent.
I might, of course, cite the opinions of very many successful in-
structors of the deaf, who have followed only the sign method, to
sustain my position, but I prefer to call in again the testimony of
Moritz Hill, a man whose whole life was devoted to the instruction
of the deaf by the oral method. In an exhaustive work on the
education of the deaf,* Hill says, speaking of those who pretend
that in the " German method " every species of pantomimic language
is proscribed
:
" Such an idea must be attributed to malevolence or to unpardon-
able levity. This pretence is contrary to nature and repugnant to
the rules of educational science.
" If this system were put into execution the moral life, the in-
tellectual development of the deaf and dumb, would be inhumanly
hampered. It would be acting contrary to nature to forbid the
deaf-mute a means of expression employed by even hearing and
speaking persons. * * * It is nonsense to dream of depriving
him of this means until he is in a position to express himself orally.
* * * Even in teaching itself we cannot lay aside the lan-
guage of gestures (with the exception of that which consists in
artificial signs and in the manual alphabet—two elements proscribed
by the German school), the language which the deaf-mute brings
with him to school, and which ought to serve as a basis for his edu-
cation. To banish the language of natural signs from the school-
room and limit ourselves to articulation is like employing a gold
key which does not fit the lock of the door we would open aud
refusing to use the iron one made for it. * * * At the best, it
would be drilling the deaf-mute, but not moulding him intellectually
or morally."
* Der gegenwartige Zustand des Taubstummen Bildungswesens in Deutsch-
land; von Hill, Inspector der Taubstummen Anstalt zu Wetssenfels; Ritter des
St. Olafs, &c. Weimar, H. Bohlau, 1 866.
GENERAL MEETING. 81
Hill then follows with thirteen carefully formulated reasons why
the use of signs is important and even indispensable in the educa-
tion of the deaf.
Mr. Bell is in error when he supposes that in the so-called sign-
schools verbal language is only imparted through the intervention
of the sign-language. In many well-ordered schools of this class,
language is taught without the use of signs, and in such schools
the language of signs is kept in its proper position of subordination.
It goes without saying that in schools for the deaf there may be an
injudicious and excessive use of signs. This is always to be guarded
against, and when it is, I am convinced that no harm, but great
good, results from the use of signs in teaching the deaf.
Furthermore, it is well known that the attempt to banish signs
from a school for the deaf rarely succeeds. Miss Sarah Porter, for
three years an instructor in the Clarke Institution at Northamp-
ton, Mass., an oral school in which most excellent results have been
attained, shows candor as well as judgment when she says, in a re-
cent article in the American Annals of the Deaf and Dumb, " Every
oral teacher knows that fighting signs is like fighting original sin.
Put deaf children together and they will make signs secretly if not
openly in their intercourse with each other."
It is not true as a matter of fact that the use of signs necessarily
prevents the deaf from acquiring an idiomatic use of verbal lan-
guage and from thinking in such language. Large numbers of
them who have never been taught orally have come into such a
use of verbal language, and while it is granted that many edu-
cated under the sign system do not use verbal language freely and
correctly, the same is found to be true of very many who have
been educated entirely in oral schools.
In one important particular the language of signs performs a
most valuable service for the deaf, and one of which nothing has
yet been found to take the place. Through signs large numbers of
deaf persons can be addressed, their minds and hearts being moved
as those of hearing persons are by public speaking in its various
forms.
Having seen the good effects on the deaf of the discreet use of
the sign-language through a period of many years, I am confident
that its banishment from all schools for the deaf would work great
injury to this class of persons intellectually, socially, and morally.
82 PHILOSOPHICAL SOCIETY OP WASHINGTON.
The Hon. Gardiner G. Hubbard being present, was invited by
the chair to participate in the discussion. He said he had been
connected with the Clark Institution for many years. The deaf
pupils in that school are taught entirely by articulation.
From recent inquiries which had been made to ascertain how
far the graduates had profited by instruction in articulation, it ap-
peared that in almost in every instance they could carry on conver-
sation with others sufficiently to engage in many kinds of business
from which they would have been excluded if they had only used
signs.
It was true, as Mr. Gallaudet said, the congenitally deaf were fre-
quenty able to articulate more distinctly than those who lost their
hearing at an early age, but this arises from the fact that the dis-
ease that caused the deafness affected the organs of articulation to
a greater or less degree ; but the congenitally deaf do not make as
rapid progress in their studies as those who had once spoken, for
these have a knowledge of language which the former could ob-
tain only by long protracted study.
Mr. Hubbard believed that the pupils at the Clark Institution
made at least as rapid progress in all their studies as those taught
by signs ; while, at the same time, they acquired the power of read-
ing from the lips and speaking, in which those taught by signs were
deficient.
When the first application was made to the Legislature of Mas-
sachusetts for the incorporation of the Clark Institution, Mr. Dud-
ley, of Northampton, chairman of the committee to whom the peti-
tion was referred, had a congenitally deaf child under instruction
at Hartford. The petitioners were opposed by the professors from
the asylum, as they believed an articulating school would retard
the education of the deaf, as it was impractical to teach the deaf
by articulation, that system having been tried and proved a failure,
and the new method was stigmatized as one of the visionary theories
of Dr. Howe, (the principal of the Perkins Institute for the Blind,
and the teacher of Laura Bridgeman, the blind deaf mute,) who
was associated with the petitioners in the hearing.
The application was rejected through the influence of these pro-
fessors and of Mr. Dudley, who ' knew, from experience with his
own child, that it was impossible to teach the congenitally deaf to
talk.'
Two years after, our application was renewed and with better
success.
GENERAL MEETING. 83
Mr. Hubbard in the meantime, with the aid of Miss Rogers, had
opened a small school where the deaf were taught to speak. This
school was visited and examined by the committee, and the progress
made was so great that Mr. Dudley became a warm convert, con-
vinced that the impossible was possible, and the application was
granted, although again opposed by the gentlemen from Hartford.
The school was opened at Northampton, and has been in operation
for nearly fifteen years, and teaching by articulation has ceased to
be a visionary theory.
Many of the warmest friends of the Institution now are, like Mr.
Gallaudet, connected with institutions where signs are used. In
almost every institution for the deaf classes are now taught to articu-
late, though articulation is not used as the instrument for instruc-
tion.
Mr. Gallaudet had taken exception to the remark of Mr. Bell, that
idiots were born dumb, and said that in every school for idiots there
were many feeble-minded children who could talk readily; but Mr.
Bell used the word idiot not as simply a feeble-minded person, but
according to its ordinary meaning, " a human being destitute of
reason or the ordinary intellectual powers of man."
It has always been the policy at Northampton to prevent, as far
as possible, marriages of deaf with deaf, for the records show that
the children of such intermarriages are often deaf; and even where
a congenitally deaf person marries a hearing person, the children
sometimes are deaf.
The tendency of the intermarriage of the deaf would be to raise
a deaf race in our midst.
About one in 1,500 of the population are deaf; but if these in-
termarriages should take place and a deaf race be created, the propor-
tion would rapidly increase. The object of all friends of the deaf
should be to prevent the deaf from congregating, and to induce
them to associate with hearing people. In bringing the deaf to-
gether in institutions, where they are taught by signs, the tendency
is to make the deaf deafer and the dumb more dumb.
It was originally intended to have only a family or small school
at Northampton, but it was soon found that signs could not be ex-
cluded from the play-ground, as the young children could not com-
municate in any other way. The plan was changed, the number of
pupils was largely increased, and a preparatory department estab-
lished, in which signs were tolerated on the play-ground. On
84 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the removal of the pupils to the higher departments, the use
of signs is forbidden, and they are rarely used on the play-ground
or between the pupils, either in or out of school hours.
In the later years of instruction they acquire great facility in
articulation and reading from the lips, though there is almost always
some difficulty for a stranger to understand them.
Mr. Gallaudet had referred to the International Convention of
deaf-mute teachers and their friends, at Milan, three years ago. Mr.
Hubbard was present at the convention held this year at Brussels,
and was there informed that a delegate had been sent from France
to attend the convention at Milan and investigate the method of in-
struction in Italy, where articulation was used, for the purpose of
deciding whether the instruction in the French schools should con-
tinue to be by signs, or instruction by articulation be substituted
for signs.
The preference of the delegate had been for signs, but on witness-
ing the results obtained in the Italian schools and hearing the dis-
cussion, he was led to advise that the instruction in the French
schools hereafter be by articulation, instead of signs, and such a
change has, Mr. Hubbard understands, been made in most of the
schools of France.
Mr. Hubbard learned from the reports at Brussels that almost all
the European schools were taught by articulation, and that this means
of instruction was being rapidly substituted for the sign language
in England as well as in France.
Mr. Bell, in reply to the remarks of Mr. Gallaudet, said
:
There are signs and signs. There is the same distinction between
pantomime and the sign-language that there is between a picture
and the Egyptian hieroglyphics.
Pictures are naturally understood by all the world, but it would
be illogical to argue from this that a picture-language, like that de-
veloped by the ancient Egyptians, must also be universally intelli-
gible. Pantomime is understood by all the world, but who among
us can understand the sign-language of the deaf and dumb without
much instruction and practice?
No one can deny that pantomime arid dramatic action can be
used, and with perfect propriety, to illustrate English expressions
so as actually to facilitate the acquisition of our language by the
deaf; but the abbreviated and conventionalized pantomime, known
GENERAL MEETING. 85
as the " sign-language," is used in place of the English language,
and becomes itself the vernacular of the deaf child.
Judging from the quotations given by Dr. Gallaudet, Moritz
Hill himself makes a clear distinction between pantomime and the
sign-language, retaining the former and proscribing the latter.
" Every species of pantomimic language is not proscribed," he
says. " Natural signs," or " signs employed by hearing and speak-
ing persons," are retained, while "artificial signs " are proscribed.
All the arguments that have been advanced regarding pantomime
and a pantomime language are equally applicable to pictures and
a picture-language. For instance, we may say that a picture-
language is more natural than any of the spoken languages of the
world, because pictures are naturally understood by all mankind.
We may even arrive, by a further process of generalization, at the
idea that picture-language, in the wider sense, really constitutes
the only form of language that is natural at all, for all the other
languages of the world appear to be entirely arbitrary and conven-
tional. If we pursue the parallel we shall arrive at the conclusion
that a picture-language of some kind must necessarily become the
vernacular of our pupils, through which the other more conventional
languages may be explained and taught.
It is immaterial whether such statements are fallacious or not, so
long as we do not apply them to educational purposes. But let us see
how they work in practice. The exhibition of a picture undoubtedly
adds interest to the fairy tale or story that we tell a child. It
illustrates the language we use, and it may be of invaluable
assistance to him in realizing our meaning. But is that any reason
why we should teach him Egyptian hieroglyphics ? Granting the
premises : Is the conclusion sound that we should therefore teach
him English by means of hieroglyphics ?
If such conclusions are illogical, then the fundamental ideas
upon which our whole system of education by signs is based are
also fallacious and unsound.
One word in conclusion regarding speech.
The main cause of the fallacies that fog our conception of the
condition of the deaf child is his lack of speech. A deaf person
who speaks is regarded by the public more as a foreigner than as a
deaf mute. Speech, however imperfect, breaks through the barriers
of prejudice that separate him from the world, and he is recognized
as one of ourselves.
86 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Gallaudet under-estimates the value of speech to a deaf
child. He seems to think that speech is of little or no use, unless
it is as perfect as our own. The fact is that the value of speech
to a deaf child must be measured by its intelligibility rather than
by its perfection.
It is astonishing how imperfect speech may be and yet be intelli-
gible. We may substitute a mere indefinite murmur of the voice for
all our vowel sounds, without loss of intelligibility. (Here Mr. Bell
spoke a few sentences in this way, and was perfectly understood.)
Here at once we get rid of the most difficult elements we are called
upon to teach. If now we examine the relative frequency of the con-
sonantal elements, we shall find that 75 per cent, of the consonants
we use are formed by the point of the tongue, and that the majority
of the remainder are formed by the lips. The consonants that are
difficult to teach are chiefly formed by the top or back part of
the tongue ; but, on account of their comparative rarity of occur-
rence, they may be very imperfectly articulated without loss of
intelligibility. Hence I see no reason why, in spite of the general
ignorance of teachers respecting the mechanism of speech, we
may not hope to teach all deaf children an intelligible pronuncia-
tion.
Let teachers appreciate the value of intelligible speech to a deaf
child, and they will make the attempt to give it to him. At the
present time, lack of appreciation operates to prevent the attempt
from being made upon a large scale. Skilled teachers of articula-
tion will become more numerous as the demand for their service
increases, and their ingenuity, intelligently applied, will increase
the perfection of the artificial speech obtained.
In the meantime, do not let us discard speech from the difficulty
of obtaining it in perfection. Do not let us be misled by the idea that
intelligible but defective speech is of no use, and must necessarily
be painful and disagreeable to all who hear it. Those who have
seen the tears of joy shed by a mother over the first utterances of
her deaf child will tell you a different tale. None but a parent can
fully appreciate how sweet and pleasant may be the imperfect articu-
lation of a deaf child.
240th Meeting. November 10, 1883.
The President in the chair.
Forty-eight members present.
GENERAL MEETING. 87
Announcement was made of the election to membership of
Ethelbert Carroll Morgan.
It was announced from the General Committee that invitation had
been extended to the members of the Anthropological and Biologi-
cal Societies to attend the meeting of December 8th, for the pur-
pose of listening to the annual address of the President.
Mr. Edwin Smith exhibited a
SEISMOGRAPHIC RECORD OBTAINED IN JAPAN,
describing the apparatus by which it was made, and giving a brief
account of the seismographic investigations of Professor J. A.
Ewing.
Remarks were made by Mr. Antisell.
Mr. C. E. Dutton made a communication, entitled
the volcanic problem stated.
[Abstract.]
It is sufficiently obvious that the volcano is a heat problem, or a
thermo-dynamic problem. All volcanic activity is attended with
manifestations of great energy. This energy is due to the elastic
force of considerable quantities of water occluded in red-hot or
yellow-hot lavas. The problem is to find a satisfactory explanation
of the origin of the heat, the origin of the occluded water, and their
modes of reaction.
In attempting this solution, various explanations have been con-
jectured. The first to be noticed, and the one which, in various
forms, has met with the most favor from geologists and physicists,
is that the source of heat is primordial
—
i. e., it is the remains of a
large amount of heat contained by the entire earth-mass in its sup-
posed primordial condition, according to the nebular hypothesis ;
that water has penetrated from above, either from the ocean or from
lakes ; and that the contact of cold water with the hot magmas within
the earth is a summary explanation of the phenomena. This view
is supported by the following considerations : 1st, the contact of
water with intensely hot bodies and the resulting generation of
great explosive force is matter of the commonest experience ; 2d,
the outer rocks and strata are known to be full of fissures, and the
ocean bottom and lake bottoms are, therefore, presumably very
leaky ; 3d, nearly all active volcanoes are situated either within, or
88 PHILOSOPHICAL SOCIETY OF WASHINGTON.
in the neighborhood of, large bodies of water ; 4th, volcanoes near
the sea often deliver salts which may reasonably be supposed to be
the same as those contained in the ocean ; 5th, the analogy of gey-
sers gives us a series of phenomena which seem to be, in many respects,
quite parallel, and which have been satisfactorily explained in a
similar way.
To this view of the origin and causation of volcanic activity there
are some objections. There is difficulty in understanding how water
obtains access to hot magmas. No doubt the rocks are full of
fissures, but we cannot, by any means, confidently infer that these
fissures extend sufficiently deep to afford free or even capillary pas-
sages to melted magmas beneath. We should more legitimately
infer that the heat increases gradually with the depth. At a depth
of a few miles the rocks presumably have a temperature which,
though high, is still below fusion, and at such temperatures it is well
known that all the siliceous or rocky materials we are acquainted
with are viscous. Remembering the immense statical pressure due
to a thickness of a single mile of rocks, all fissures at such depths
would be closed, as if the rocks were wax or butter.
2d. Although the contact of cold water with intensely hot masses
will surely produce a violent explosion, we are not at liberty to admit
offhand that cold water does obtain such contact in the volcanoes.
On the contrary, as it penetrates it takes up the heat of the rocks
through which it passes. But water is believed by all physicists to
have what is technically termed a critical temperature, i. e., a tem-
perature at which it can exist only in the form of vapor however
great the pressure, and this temperature is computed theoretically
to be about 772° F., which is far below that of melted rock. If
therefore, water could reach the liquid lavas below, it would reach
them only in the form of vapor. There is indeed no difficulty in
supposing that the vapor of water may, under great statical pres-
sure, be forced into the rocks, passing between inter-molecular spaces.
This is but one aspect of the phenomena of the diffusion and occlu-
sion of gases in solids, and we know that water-vapor in large quan-
tities is readily occluded by lava. But this is evidently no explan-
ation of the explosive action. It is in the broadest possible con-
trast with the gross conception of the sudden access of cold water
to hot bodies. The presumption is, under the process here sug-
gested, that the vapor of water might penetrate slowly into regions
of great heat until the hot magmas were saturated, and then the
GENERAL MEETING. 89
process would come to a standstill. But there would be no volcano
in this case, for the supposed condition is evidently statical and
stable. For the pressure which is supposed to force the vapor in is
that due to the hydrostatic pressure of a column of water. The
pressure which keeps it from blowing out is that due to an equally
high or even higher column of rock, the density of which is at least
two and a half times greater.
3d. The analogy of the geyser thus fails to become a true ho-
mology, or an epitome of the volcano. For the geyser is due to the
access of cold water to a cavity walled by hot rocks and its vapor-
ization ; the volcano, if due to the penetration of water, is due to pen-
etration in the form of vapor in the first instance ; and the difference
is radical.
4th. The proximity of volcanoes to large bodies of water does
not necessarily imply a logical and causal relation, and is not nec-
essarily the true law of distribution. Another and perhaps a more
rational law of distribution may be given. As a matter of fact all
active volcanoes are not situated near seas or lakes, though in truth
the exceptions are at the present time few, as for instance, Sangay,
in the eastern Cordilleras of Peru, and the volcanoes of Central
Asia. It seems as if Darwin had acutely divined the true associa-
tion, viz : that volcanoes are situated in areas which are undergoing
elevation. So far as we know this rule is without exception, but
there are many cases where the verification of the elevation is want-
ing. So far, however, as the test has hitherto been applied it has
approved the rule. This is especially conspicuous in the western
half of our own country when applied to the late Tertiary and Post
Tertiary volcanoes, and it is true, so far as known, of the Andes,
Java, Philippines, and Mediterranean, and I have recently been
able to verify it in the case of the Hawaiian volcanoes. It happens
that elevations, as well as subsidences, are much more frequent and
extensive near coast lines than in continental interiors, whence the
proximity of volcanoes to the sea becomes a secondary rather than
a primary relation. But elevations also occur in continental in-
teriors, though less frequently. And when they do occur, we find
associated phenomena of volcanism as abundant and forcible as in
littoral regions. This has been the case in the great Tertiary ele-
vation of the Rocky Mountains, of the Alps, and of the Himalayan
plateau. Darwin's law of the distribution of volcanoes is as thor-
oughly sustained by geological history as by modern instances;
10
90 PHILOSOPHICAL SOCIETY OF WASHINGTON.
while the other law, though largely predominant at the present
period, shows a few conspicuous failures at the present time, but a
very large number of them in times past.
Another hypothesis to account for volcanic energy supposes the
interior of the earth to consist of unoxidized elements, which grad-
ually become oxidized by the penetration of oxygen from the at-
mosphere.
The objections to this hypothesis are as follows : On the assump-
tion that the earth acquires no oxygen from space, the primitive
atmosphere would have been many thousand times greater than at
present ; but the geological record argues strongly in favor of an
atmosphere which may indeed have varied in quantity and compo-
sition, but nowhere near so greatly as the hypothesis implies. Any
such extravagant difference would have recorded itself legibly in
the strata. Furthermore, on this view, the end of all volcanic ac-
tivity is close at hand. Only three pounds of oxygen to the square
inch of terrestrial surface are left. A few hundred or thousand
centuries and the last volcanic beacon is extinguished, and with it
all organic life.
But suppose the earth gathers up oxygen in its march through
space. This may be true, but we can make any supposition on this
point which pleases our fancy and feel sure that no prudent scien-
tific man will dispute it.
A third hypothesis is that of the late Robert Mallet, which as-
sumes the earth to be contracting interiorly by a secular loss of prim-
itive heat. As the interior cools and shrinks, the external shell is
crushed and crumpled together, and this mechanical crushing is a
sufficient source of heat.
To this hypothesis there are many answers. The most direct one
is that the very facts which are relied upon to prove that there is
any interior cooling at all now going on also prove that the amount
hitherto has been excedingly small, and has been limited as yet to
a thin external shell, not exceeding 150 miles in thickness, while
the great interior is about as hot as ever ; but, by the terms of the
hypothesis, if the interior has not cooled there has been no interior
contraction. The hypothesis is refuted by taking its own premises
and pushing them to their inevitable conclusions.
There is a fourth hypothesis, which cuts the Gordian knot in-
stead of untying it. It assumes, as the result of causes unexplained,
heat is generated locally within the earth, and such local movements
GENERAL MEETING. 91
of heat are the cause of volcanism. This is an arbitrary postulate,
which, by its own terms, precludes discussion. Nevertheless it is
the one which I believe agrees best, and perhaps perfectly, with ob-
served facts. It undoubtedly sweeps away the difficulties which
encumber all other hypotheses, but unfortunately it is an appeal to
mystery, and therefore substitutes a single difficulty as great as, if
not greater, than all the other difficulties put together.
There is a fifth hypothesis, which takes account of the fact that
many bodies which are solid under great pressure are immediately
liquefied when the pressure is removed, heat being neither lost nor
gained. The removal of pressure by denudation of the surface
above the seat of lavas may thus determine volcanic action. The
reply to this is that volcanoes do not always, nor even generally,
occur where such denudation and consequent relief of pressure, are
in progress. The true law of the distribution of volcanoes appears
to be the one given by the late Charles Darwin, viz., that they occur
in areas which are undergoing elevation.
There are several broad facts, or categories of facts, which a true
theory of the volcano must cover, and which will be recited
briefly.
1. Lavas, in their subterranean seat, could not possibly have been
in a highly elastic explosive condition from the earliest epochs of
the earth's evolution, and only waiting a convenient season to break
forth. We have no alternative but to regard them as being inert
and inexplosive in their primitive condition, and as having acquired
explosive energy just before the epoch of eruption. To assume that
they have always been in the condition they present while pouring
forth, and that the opening of a fissure has been the accident which
determined the eruption, is reasoning in a circle. It is the energy
of the lavas which causes the fissure, and not the fissure which
causes the lavas to extrude. The lavas extrude themselves by vir-
tue of their acquired elastic force. The theory must explain how
materials which antecedently were inert, passive, incapable of erup-
tion, may become active, dynamical, eruptible.
2. Another broad fact, closely related to the foregoing, is the in-
termittent action of volcanoes. These vents do not discharge all
their available products at once, but by repeated spasms of activity,
separated by longer intervals of repose. If these fiery explosive
liquids had lain so long in the earth, chock-full of energy and only
awaiting the opening of a passage-way, how happens it that when
92 PHILOSOPHICAL SOCIETY OP WASHINGTON.
a vent is once opened they do not all rush forth 'at once, and con-
tinue to outpour until the reservoir is completely exhausted, and
why does not the vent thereafter close up forever ? In a word, why
should a volcano dole out its products in driblets, instead of send-
ing forth one stupendous belch, equal to all the driblets combined ?
The answer here proposed is that it is because lavas, in their primi-
tive condition, do not have sufficient potential energy, in the form
of elastic force, to break open the covering which keeps them in
;
but they gradually acquire that energy in a portion of the reser-
voirs at a time, and when a sufficient portion of them has acquired
it the covering is ruptured, and the whole of this energetic portion
is extravasated. The vent then closes, and the process is repeated
upon a second installment. The agency which thus progressively
develops this force is the missing factor, and when we discover it
we shall discover the secret of the volcano.
The third general fact to be taken account of is the enormous
quantity of heat given off by volcanoes through long periods of
time without any sign of exhaustion. The quantity of heat brought
up by the lavas themselves is but a fraction of the whole amount
dissipated. Kilauea wastes many times more heat by quiet radia-
tion from the surfaces of its lava lakes and by steaming and by
numberless modes of escape than by actual eruption of lavas.
Mauna Loa also dissipates the greater part of its heat in the same
way, and the same fact is wholly or partially true of all other active
or intermittent volcanoes. And yet for very long periods, for thou-
sands of centuries, these great volcanoes show no sign of heat-exhaus-
tion ; on the contrary, such indications as we have suggest the con-
clusion that the earth benegth them is hotter than before.
A fourth general fact is that volcanoes are located in areas which
have recently been or are now undergoing elevation.
All these facts suggest the action of some cause generating heat
within the earth. This cause, if such it be, is for the present wholly
mysterious and unknown.
Mr. Powell, referring to the relation between volcanic eruption
and elevation, said that the typical, secular sequence of geologic
events was, first, elevation, resulting in, second, degredation, accom-
panied by, third, extravasation, followed sooner or later by, fourth,
subsidence, resulting in, fifth, sedimentation. There are numerous
regions in which this circle of events has been recorded, and in
some places it has been repeated two or three times.
GENERAL MEETING. 93
Mr. F. W. Clarke suggested that the difficulty in the way of a
chemical explanation of volcanic phenomena was due to our ignor-
ance of chemical force under high pressures. Spring has lately
shown that chemical union could be brought about by pressure
alone. Hence, water coming in contact with molten rock matter
in the interior of the earth might be prevented from dissociating.
If, however, dissociation takes place, we may conceive that water
may play the following part in volcanic explosions. Gradually
filtering through the surface rocks to the hot lava, it would undergo
slow decomposition, and great quantities of mixed oxygen and hy-
drogen would thus slowly accumulate. Now let a process of cool-
ing begin. Soon the temperature at which oxygen and hydrogen
unite would be reached, and explosive union would occur. This
may account for volcanic explosions, at least in part. By such a
process, potential energy is gradually stored up, to be later, sud-
denly or instantaneously, released. This hypothesis does not ac-
count for volcanic heat, but presupposes its existence.
Mr. White, referring to Mr. Powell's remarks on the instability
of continental areas, said that the prevalent doctrine of the perma-
nence of oceans, and the gradual development of the continents?
was not sustained by paleontology. Continents were needed some-
where to develop the land plants and land mammals which ap-
peared during the emergence of the known continents.
Mr. Harkness pointed out that Mr. White was postulating un-
known continents to support the Darwinian hypothesis, to which
Mr. White assented.
Mr. Powell added, that in detailing the great cycle of geologic
events, he should have included metamorphism as a sixth term, re-
sulting from burial by sediment ; and Mr. Dutton remarked that
he had included this consideration in a paragraph contained in his
written manuscript, but not read.
Mr. McGee made a communication on
THE DRAINAGE SYSTEM AND THE DISTRIBUTION OF THE LOESS OF
EASTERN IOWA.
[Abstract.]
The most conspicuous geographic feature of eastern Iowa is
the remarkable parallelism among its water-ways. Yet the region
comprises two essentially distinct geologic tracts ; and the coincidence
94 PHILOSOPHICAL SOCIETY OF WASHINGTON.
in direction of drainage in these is fortuitous : 1. The Wisconsin
Driftless Region so far extends into the northeastern corner of Iowa
as to include all of the triangular area bounded on the southwest
by the elevated Niagara escarpment extending from the extreme
eastward projection of the state northwestwardly to the Minnesota
line, fifty miles west of the Mississippi. Within this tract, the drain-
age was originally determined by general surface slope and by rock-
structure, and the present topography, which is varied and pictu-
resque, was developed by sub-serial erosion. 2. Within the far more
extensive tract formed by the glacial drift and its derivatives, the
surface is a gently undulating plain, over which the general relief
is inconspicuous, and the local topography faintly defined though
singularly uniform and symmetric in character ; and here the par-
allelism in drainage is prevalent and characteristic. There are, in-
deed, both local and general exceptions to this parallelism, which
exemplify a variety of types of aberrant behavior of the streams
;
but while these impair the geographic symmetry of the drainage
system, they add much more largely to its geologic significance-
Putting together the instances of accordant, and neglecting the in-
stances of aberrant extension of water-lines, a normal direction oj
drainage for the whole of the drift-formed tract might be empiric-
ally determined ; which normal direction is represented by a sym-
metric series of slightly divergent and slightly curved lines, concave
to the northeastward, radiating from a point north of the state in
a general southeasterly direction, toward the Mississippi. Probably
nowhere else on the surface of the globe does so symmetric a normal
drainage system exist, and assuredly nowhere else does the sum of
directions of stream-flow over so considerable an area present so few
examples of departure from the normal.
The broader topographic features of eastern Iowa are dependant
upon geologic structure. The dip of the rocks is to the southwest,
and the outcrops of the several formations represented form suc-
cessive approximately parallel zones (trending northwest and south.
east), of which those of the Niagara and Hamilton are widest. Now
the Niagara rocks resisted well the planation of the pre-quaternary
eons, and their eastern margin is accordingly defined by a promi-
nent escarpment varying from 1,000 to 1,350 feet in altitude, from
which there is a steep northeasterly slope to the Mississippi, and a
gentle inclination, corresponding to the dip of the strata, in the op-
posite direction. The Hamilton rocks, on the other hand, have so
GEjSLERAL meeting. 95
yielded to erosion that their area is topographically represented
by a broad, shallow trough, of which the altitude is only from
600 to 1,000 feet, and of which the sides rise and culminate in the
Niagara escarpment on the east and in the Mississippi-Missouri
water-shed on the west. There is, however, a subordinate general
topographic feature which is independent of geologic structure. A
wide, gentle, indefinitely outlined depression extends directly across
the great eastward projection (the " Cromwell's Nose ") of Iowa and
diagonally across the Upper Silurian, Devonian, and Carboniferous
rocks alike, in the line of the general course of the Mississippi, from
near the' mouth of the Turkey to the mouth of the Iowa. It is
manifestly of great antiquity.
Thus, in its general topography, eastern Iowa is characterized,
primarily, by an elevated escarpment near its eastern border, by a
broad depression intersecting its western portion diagonally, and
by a general southwesterly slope extending over most of its area
;
and secondarily, by an indefinite ancient valley cutting off its eastern
pi'ojection. And its general drainage system is almost absolutely
independent of this general topography ; for not only do the prin-
cipal streams flow at right angles to the prevailing slope and cut
through the elevated escarpment when it lies in their way, but, with
the single exception of the Cedar, they preserve their courses directly
across the ancient valley.
In their relation to minor topographic features the rivers of
eastern Iowa conform to two diametrically opposite laws: 1. for
two-thirds or three-fourths of their combined length they flow in
the axes of the ill-defined, shallow valleys which characterize the
drift-plain ; and, 2, for the remaining portion of their courses they
flow in narrow gorges which they have excavated for themselves in
the axes of the elongated ridges that constitute the leading features
in the local topography of the region. Moreover, they have in
many instances, at the same time gone out of their direct courses,
and deserted valleys already prepared for them, to attain the anoma-
lous positions assumed under the second law of association. And let
it be noted that in every such case the gorges have demonstrably
been carved by the streams themselves through the quaternary and
older formations alike ; that the pre-existent valleys which they
avoided have not been appreciably eroded since the quaternary
;
and that there has been no localized orographic movement in the
region since long antecedent to the quaternary.
96 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The principal tributaries entering the rivers from the right simi-
larly conform to two antagonistic laws in their relation to topog-
raphy : 1. Most of them flow throughout their courses in directions
coincident with local and general slopes, and avoid elevations in
their vicinity ; and, 2. Many of them originate with directions ap-
proaching those normal to their localities, but curve more and more
to the left toward their mouths, until they flow directly against the
general slope, and enter the rivers at large angles ; and all such
streams have high north banks which they closely hug, and low
south banks which they avoid.
So the drainage system of eastern Iowa is essentially independent
of the more general topographic features, though affected by local
topography ; and the relations of the waterways to local topography
are largely anomalous, and without parallel elsewhere.
Though essentially continuous stratigraphically, and of unques-
tionable genetic unity, the loess of eastern Iowa is variable in many
characters, and may be separated into three geographic divisions;
viz: 1, the Driftless Region division; 2, the Riparian division;
and, 3, the Southern division. That of the first division forms the
surface throughout the Driftless Region, as it exists in Iowa, and
everywhere overlaps the eastern border of the drift ; it is generally
rather coarse, heterogeneous, and non-calcareous, and yields depau-
perate fossils of characteristic species ; it reposes upon or gradu-
ates into a thin stratum of water-worn erratic materials, which, in
turn, rests upon either the residuary clays of the Driftless Region
or the margin of the drift-sheet ; its western border is exceedingly
sinuous, affects the greatest altitudes, and invariably overlooks the
contiguous drift-plain ; and, in capping the elevated Niagara escarp-
ment, it forms the highest land within hundreds of miles, except in
northerly directions. The loess of the Riparian division occurs
chiefly in the elongated ridges so common and so intimately asso-
ciated with the waterways in eastern -central Iowa ; it is often fos-
siliferous, and its characters are generally typical ; it usually grad-
uates downward into stratified sands or gravels, which may or may
not merge into drift; and it invariably seeks the highest summits in
the region;—for the ridges in which the rivers have carved their
canons are always loess-topped ; wherever streams avoid low-lying
valleys for high-lying plateaus, the plateaus are of loess exteriorly;
and the high northern banks of the aberrant tributaries are gen-
erally loess-capped. The loess of the Southern division prevails
GENERAL MEETING. 97
over southeastern Iowa ; it abounds in characteristic fossils (which
may or may not be depauperate), in loess-kindchen, and in calcare-
ous tubes ; it is fine, homogeneous, and vertically cleft ; it generally
graduates into the subjacent drift so imperceptably that neither
geographic nor stratigraphic separation of the formations, by other
than a purely arbitrary line, is possible ; and it occurs indiscrimi-
nately at all levels.
So, in its distribution, the loess of eastern Iowa is intimately con-
nected with the Driftless Region, with the drainage, and with the
topographic configuration ; but in its disposition to seek the greatest
altitudes in the north, and to merge into the drift in the south, its
behavior is as anomalous as is that of the rivers of the same region.
Mr. Powell remarked that these peculiarities of drainage were
different from those observed in the drainage systems of mountain
regions and demanded a different explanation, which was not yet
forthcoming. It was probable, however, that not enough allowance
was made for the differential effects of general degradation subse-
quent to the determination of the drainage.
Mr. Gilbert, after defining antecedent and super-imposed drain-
age, said that Mr. McGee's description definitely negatived the hy-
pothesis of antecedent drainage, and rendered the hypothesis of
super-imposed drainage in the ordinary sense equally untenable.
The most plausible alternative is the hypothesis suggested by Mr.
McGee in one of his earlier papers, that the draiuage was super-
imposed by the ice-sheet, the distribution of loess having been de-
termined at the same time and by the same causes.
Mr. "White regretted that Mr. McGee's special investigations
did not include the portion of Iowa draining to the Missouri. The
details of drainage iu that region are equally interesting, and, in
his opinion, do not admit of the explanation mentioned by Mr.
Gilbert. The direction of the rivers diverges at right angles from
that of the Mississippi tributaries, and their valleys are excavated
from loess except along their upper courses.
Mr. Powell said that on the Illinois side of the Mississippi River
many of the features described in the paper are repeated. The loess
hills follow the river courses, and in the opposite directions over-
look plains. The explanation of the phenomena is problematic,
but the theory advocated by Mr. Gilbert does not appear sufficient.
98 philosophical society of washington.
241st Meeting. November 24, 1883.
Vice-President Billings in the Chair.
Fifty-three members and guests present.
It was announced by the Chair that the next meeting would be
held in the Lecture Hall of the National Museum, that the mem-
bers of the Anthropological and Biological Societies were invited
to be present, and that the members of all three societies were re-
quested to invite their friends.
Opportunity was afforded for the introduction of amendments to
the Constitution, but none were offered.
Mr. C. D. Walcott made a communication on
THE CAMBRIAN SYSTEM IN THE UNITED STATES AND CANADA.
[Abstract.]
Defining the Paleozoic period as has been done by Geikie in his
Text-Book of Geology, it will include all the older sedimentary for-
mations containing organic remains, up to the top of the Permian.
Upon the paleontologic evidence it may be divided into an " older
and newer division, the former (from the base of the Cambrian to
the top of the Silurian system) distinguished more especially by the
abundance of its graptolitic, trilobitic, and brachiopodous fauna,
and by the absence of vertebrate remains ; the latter (from the top
of the Silurian system to the top of the Permian system) by the
number and variety of its fishes and amphibians, the disappearance
of graptolites and trilobites, and the abundance of its cryptogamic
terrestrial flora." The two divisions may be still further subdivided
;
the upper into the Carboniferous and Devonian, the lower into the
Silurian above and the Cambrian beneath. It is the Cambrian
division we now have to consider.
Stratigraphically it is difficult to fix any definite upper limit to
the Cambrian system, owing to local causes having affected the con-
ditions of sedimentation and consequent extinction or continuance of
the fauna. Upon the evidence of the section in New York State on
the western side of Lake Champlain, the Potsdam sandstone closes
the period stratigraphically and paleontologically, the Calciferous
formation forming little more than a closing deposit of the Potsdam
and the large Chazy fauna appearing suddenly in the overlying lime-
stone is entirely distinct from that of the Potsdam. In central
GENERAL MEETING. 99
Nevada the section passes through limestones marked by the presence
of a typical Potsdam fauna and on up to one that has the general
facies of that of the Trenton Lower Silurian fauna. Midway of
these passage beds occur layers of rock that carry representatives
of both the Cambrian and Silurian faunas. Above this band the
Cambrian fauna gradually disappears, and below it soon predomi-
nates to the exclusion of the Silurian types. In this section we have
an illustration of the gradual extinction of an older fauna as a new
one is introduced, the sedimentation continuing and no physical dis-
turbance occurring to change the conditions necessary for the pres-
ence of animal life. It is the ideal section uniting the faunas of two
periods, and if we had the blanks filled in between all the groups,
as the blank between the Potsdam and Chazy in New York is filled
in by the Nevada section, the Paleozoic would be a record of con-
tinuous connected organic life from the base of the Cambrian to
the summit of the Permian.
It is convenient for stratigraphic geologic work to separate the
Paleozoic series into subdivisions, and, as this is almost necessarily
done on paleontologic evidence, I would separate the Cambrian as
one characterized by what Barrande has named the first fauna.*
Applying this to the Nevada section already mentioned, the line
between the Cambrian and Silurian would be drawn where the
types of the second fauna begin to predominate. With this defini-
tion of the Cambrian system, the strata referred to it in the United
States and Canada will be briefly noticed.
In the Grand Canon of the Colorado the top of the Cambrian is
the Tonto formation, a series of sandy calcareous strata 1,000 feet
in thickness. The contained fauna is closely allied to that of the
Potsdam sandstone and continues up to the summit of the forma-
tion, the overlying Devonian rocks resting directly above strata
containing Lingulepis, Iphidea, Conocephalites, Dlcellocephalus, etc.
The Tonto rests uncomfortably on strata that were extensively
eroded prior its deposition. This lower series comprises over 11,000
feet of unmetamorphosed shales, limestones, and sandstones, with
1,000 feet of interbedded lavas. It forms the Grand Canon and
Chu-ar' groups of Powell and is characterized by the presence of a
few fossils that enable us to refer it to the Cambrian but not to de-
fine its stratigraphic horizon. That is done on the evidence of the
position it occupies with reference to the Tonto.
*The paleontologic evidence and discussion will appear in a future paper.
100 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The relations of the Grand Caiion section are snown in the first
column of the page of sections.
The Potsdam sandstone in Wisconsin occupies the same relative
stratigraphic position as the Tonto formation, except that the break
above the Tonto and between it and the Devonian is filled in by
the Calciferous and other Silurian formations. As has already
been said, the faunas of the Potsdam and Tonto are very much the
same in general character. The Potsdam formation here overlies
unconformably a series of strata that are directly comparable with
the Grand Canon and Chu-ar' series. The Keweenawan series,
according to Chamberlin, has about 10,000 feet of sedimentary
strata distributed through 30,000 feet of eruptive rocks. In all
this great mass no decisive evidence of organic life has been dis-
covered, but knowing that the series is unconformably overlain by
the Potsdam formation and that it in turn rests unconformably on
the Archaean, as does the Grand Canon series, we feel justified in
correlating the Grand Caiion and Wisconsin sections and they are
uuited in the first column of the page of sections.
The upper part of the Nevada section has already been men-
tioned. Below the Potsdam horizon there occurs a distinct fauna,
characterized by a considerable development of the trilobitic genus
Olenellus, a genus that in the embryonic development of several of
its species proves that it is derived from the Paradoxides family
and is consequently of later date. This section is readily correlated
with that of the Georgian group of Vermont, as there we have the
Potsdam sandstone above the Olenellus horizon, and in the down-
ward section both stop at nearly the same relative horizon. The
position of the Georgian formation in Nevada and Vermont, in
relation to the Potsdam, leads to the view that it represents a por-
tion of the period of erosion between the Tonto formation and the
Grand Caiion series and also the Potsdam formation and the
Keweenawan series.
The upper portion of the Tennessee Cambrian, the Knox shale,
is correlated with the Potsdam sandstone, and so is the Knox sand-
stone. The Chilhowee sandstone and Ocoee conglomerate and
slates cannot be directly connected with the Georgian horizon,
since the paleontologic data are insufficient. From their position
beneath the Knox shale with its Potsdam fauna they are extended
downward past the Georgian and into the Paradoxidian or St. Johns
horizon. Their total thickness (Geology of Tennessee, pp. 158,
159) is nearly 15,000 feet.
GENERAL MEETING. 101
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102 PHILOSOPHICAL SOCIETY OF WASHINGTON.
There is still another group, the St. Johns or Acadian, that occu-
pies an horizon below the Georgian and may fill in a portion of the
period of erosion between the pre-Potsdam and Keweenawan and
the Tonto and Grand Canon series, or it may represent some of the
upper portions of the Grand Canon and Keweenawan series. In
the geologic sections it is placed beneath the Georgian and as above
or passing down into the lower groups. For the present both it
and the Paradoxidian argillites of Braintree must be left in doubt
with regard to their relations to the lower Cambrian of Wisconsin
and northern Arizona.
Of the Canadian survey sections, the one on the north side of the
Straits of Belle Isle is most interesting as it gives the Georgian
horizon, but unfortunately an interval often miles in width is occu-
pied by the straits before the section is again continued. In this
interval the Potsdam group is lost, but farther along the coast
there occurs, below limestones referred to the Calciferous horizon,
a mass of sandstone that may be assigned to the Potsdam forma-
tion
—
giving, in connection with the Olenellus or Georgian horizon,
a section not unlike that of Central Nevada.
No other section that has been determined in the British Provinces
throws much light on the stratigraphic succession of the Cambrian
rocks. At Point Levis a curious mingling of the Cambrian and
Silurian faunas has been said to occur, but this is rather to be at-
tributed to error in the interpretation of the stratigraphy in a much
disturbed area than to a break in the sequence of organic remains,
elsewhere so uniform. I prefer to accept the interpretation given
by M. Jules Marcou, who says (The Taconic and Lower Silurian
Pocks of Vermont and Canada, Proc. Bos. Soc. Nat. Hist., Vol.
VIII, p. 252, 1862,) that the primordial or Cambrian types are
associated together and occur in a belt of limestone that contains
no traces of the second or Silurian fauna.
The accompanying table of sections gives a general outline of the
Cambrian. Numerous local sections of the Potsdam series are not
mentioned, as they do not add materially to the general informa-
tion in regard to the system in its vertical range.
The geographic range is great, extending as it does from New-
foundland to Montana on the northern line, and thence south to
Nevada, Texas, and Alabama.
GENERAL MEETING. 103
Mr. John Jay Knox made a communication on
THE DISTRIBUTION OF THE SURPLUS MONEY OF THE UNITED STATES
AMONG THE STATES.
[Abstract.]
President Jackson, in his message to Congress in 1829, referred
to the difficulty in adjusting the tariff, so that the revenues of the
Government should be but slightly in excess of its expenditures.
He considered the appropriation of money for internal improve-
ments, by Congress, as unconstitutional, but suggested that, if the
anticipated surplus in the Treasury should be distributed among
the States, according to their ratio of representation, such improve-
ments could then be made by the States themselves. If necessary
it would be expedient to propose to the States an amendment to the
Constitution, authorizing such legislation.
In his message for the following year he again suggested the
same proposition.
The receipts from sales of public lands for the three years, 1834,
1835, and 1836, were $44,492,381—slightly less than the total re-
ceipts from this source for the thirty-eight years previous, from
1796 to 1834. On January 1, 1835, the country was virtually out
of debt, and the receipts of the Government largely exceeded the
previous estimates of the Secretary. The amount of surplus on
January 1, 1835, was $8,892,858, and at the same date in 1836
$26,749,803. On January 1, 1837, it amounted to more than forty-
two millions.
In 1834-5-6, the public money, which had heretofore been de-
posited in the Bank of the United States, was deposited in favorite
State banks by order of General Jackson. The deposit of the
revenues in these banks was followed by financial distress, and dur-
ing the year 1834, and previous thereto, propositions were made in
vhe public press for distribution of the surplus revenue among the
States as a measure of relief. These propositions were first in the
form of a distribution of the revenue from public land ; then a
a distribution of the lands themselves ; and finally a distribution
of the surplus. During the session of 1835, a select committee was
appointed in the Senate, which reported a resolution to amend the
Constitution so that the money remaining in the Treasury at the
end of each year, until the first of January, 1843, should annually
be distributed among the States and Territories. Both General
104 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Jackson and Secretary Woodbury were opposed to this proposition,
as the withdrawal of public moneys would deprive the State banks
of the deposits, and would be likely to increase the financial troubles.
A bill to distribute the surplus was, however, introduced in the-
Senate, and passed by a vote of 25 to 20. It was evident that this
bill could not pass the House, as a majority of its members con-
sidered the bill, in the form of a distribution, as unconstitutional.
The friends of the measure in the Senate determined to change its
form so as to remove the difficulty. A bill then pending in the
Senate was so amended as to change the proposition for distribu-
tion to a proposition for deposit with the States, and in this form it
passed the Senate, and subsequently the House by a large majority,
155 to 38.
This act of June 23, 1836, provided for the deposit with the
treasurers of the several States of 37 millions ($37,468,859) in four
instalments during the year 1837—the Secretary of the Treasury
to receive certificates of deposit therefor signed by competent au-
thority, in such form as he should prescribe, which certificates
should express the usual legal obligation, and pledge the faith of
the State for the safe keeping and repayment of the deposit, from
time to time, whenever the same should be required. The first three
installments were deposited. Before the last installment, payable
on the 1st day of October, was transferred, a series of financial dis-
asters culminated in the crisis of 1837, and there was no surplus to
deposit. Further legislation was deemed necessary in this emer-
gency, and an extra session of Congress was called by President
Van Buren. During this session, on September 11, 1837, a bill was
reported from the Finance Committee of the Senate, providing that
the transfer of the fourth installment should be indefinitely post-
poned. The opposition to this bill was persistent, and there was a
long debate, which was participated in by "Webster, Clay, Calhoun,
Buchanan, Benton, Silas Wright, Caleb Cushing, and others of the
Senate; and in the House by Adams, Fillmore and Sibley of New
York, Bell of Tennessee, Wise of Virginia, and many others.
A bill was finally passed, providing for the postponement of the
deposit of the fourth installment until January 1, 1839. It passed
the House by a vote of 119 to 117, and contained an amendment
proposed by Mr. Buchanan, providing that the deposits should not
be subject to the requisition of the Secretary of the Treasury, but
should remain until called for by Congress. On the 1st of Jan-
GENERAL MEETING. 105
uary, 1839, there were no funds in the Treasury available for the
payment of the fourth installment, and since that date there has
never been a surplus in the Treasury above the debts and estimated
expenditures of the Government.
The amount of the three installments was $28,101,645, and the
amount placed in the Treasury of each State has since been carried
among " unavailable funds of the general Treasury," as may be
seen by reference to the annual reports of the Treasurer of the
United States.
The fourth installment, amounting to $9,367,215, has never been
transferred or deposited, and recently the State of Virginia, through
the action of its Legislature, and the State of Arkansas, through
the action of its treasurer and one of its United States Senators,
has applied to the Secretary of the Treasury for the payment of
this last instalment.
It is generally believed that the moneys deposited by the Gov-
ernment with the different States were, for the most part, wasted or
employed in works of internal improvement which were unneces-
sary. The data for a full investigation of this subject are not at
hand, but it is known that the States of Massachusetts, Connecticut,
New York, New Jersey, Pennsylvania, Delaware, Maryland, North
Carolina, Illinois, Indiana, Kentucky, Ohio, and Missouri appro-
priated a considerable portion of the income from this fund to the
support of public schools ; and that in many of these States the
income from the whole fund has been from the commencement, and
still is, devoted to the education of the people.
A bill was introduced by Senator Logan, during the first session
of the last Congress, providing that the entire income derived from
the internal-revenue tax on the manufacture and sale of distilled
spirits shall be appropriated and expended for the education of all
children living in the United States, as shown by the census of 1880
and each succeeding census. The bill also provides that the States
shall be required, before receiving the benefits of the act, to make
school attendance obligatory upon all children between the ages of
seven and twelve years, for at least six months in each year.
Mr. Alvord inquired as to the present status of the Smithsonian
fund, amounting to about half a million of dollars, which was in-
vested in the bonds of the State of Arkansas.
Mr. Knox said that the Government has assumed the Arkansas
11
106 PHILOSOPHICAL SOCIETY OF WASHINGTON.
bonds formerly held by the Smithsonian Institution, and that the
Government also held quite a large amount of the bonds of the
States of Virginia and Arkansas in the Indian Trust Fund. If
legislation should be obtained authorizing the payment of the fourth
nstalmeut to these States, such legislation should provide that the
payment be made in the bonds now held by the Government.
Mr. Alvord said that the history of agricultural college grants
was not thus far very encouraging. It would have been better if
Congress had provided that the agricultural colleges should never
be united with other colleges. The union was apt to lead to con-
fusion and controversies, and lower the standard and prestige of
both. Witness the case of Dartmouth College. In this reference
Mr. Mussey concurred.
The Hon. Hugh McCullough, being invited by the Chair to
participate in the discussion, said that in Indiana the application of
the money deposited by the United States had occasioned a long de-
bate, which had resulted in its division. One half, by means of a
system of commissioners, was loaned to individuals on land and
mortgage ; the other half was put into stock of the State Bank,
with which the speaker was at that time connected. In a financial
crisis the first half was practically lost, probably less than one-
twentieth part being recovered ; but the loss was fortunately made
good by the bank stock, upou which dividends were regularly paid,
and by which the investment was eventually doubled. Since the
closing of the bank, this money has constituted the school fund of
Indiana.
Mr. R. D. Cutts made a communication on
THE ACTION OF THE INTERNATIONAL GEODETIC ASSOCIATION AS TO
AN INITIAL MERIDIAN AND UNIVERSAL TIME.
[Abstract.]
The International Geodetic Association of Europe, formed for
the purpose of connecting the systems of triangulation executed by
the different States of Europe, and hence for the measurement of
arcs, and for the discussion of all questions of science comprised
within the term Geodesy, has been in active existence for many
years. The meeting in 1882 was held at The Hague, and before
adjournment it was decided that the seventh conference should meet
at Rome, in October, 1883.
GENERAL MEETING. 107
Iii the meantime, all governments in diplomatic relations with
the United States were invited by the President, in accordance with
the act of Congress, August 3, 1883, to send delegates to Washing-
ton for the purpose of fixing upon a meridian proper to be em-
ployed as a common zero of longitude and standard of time, reck-
oning throughout the globe. More than twenty of these countries
had signified, before October last, their acceptance of the invitation,
but these did not include many of the principal governments of
Europe. The delay in forwarding their definitive replies was due to
their desire to have the advice, before committing themselves, of the
Eurpean Geodetic Association. Hence it was at the request of
many of these governments that the Association took up the subject
of the unification of longitudes, and of the introduction of a uni-
versal time.
So soon as it was decided to take such action, General Ibanez, of
Spain, the then President of the Association, addressed a letter to
the Superintendent of the Coast and Geodetic Survey, urging him
in strong terms to send a delegate to the meeting at Rome. So short
a notice was given, however, that the delegate selected had to start
at once, reaching Rome only on the morning of the first day's ses-
sion, October 15th.
After a full discussion of the different views presented, the fol-
lowing resolutions were almost unanimously passed on October 24th.
It must be borne in mind that they are merely of an advisory
character, sanctioned and urged, nevertheless, by the highest scien-
tific authority. It is the function of the convention to be held at
Washington next year to take official and decisive action on the
subject in all its details.
Resolutions of the International Geodetic Commission in relation to
the Unification of Longitudes and of Time.
The seventh general conference of the International Geodetic Asso-
ciation, held at Rome, and at which representatives of Great Britain,
together with the directors of the principal astronomical and nau-
tical almanacs, and a delegate from the Coast and Geodetic Survey
of the United States, have taken part, after having deliberated
upon the unification of longitude by the adoption of a single initial
meridian, and upon the unification of time by the adoption of a
universal hour, have agreed upon the following resolutions
:
108 PHILOSOPHICAL SOCIETY OF WASHINGTON.
I. The unification of longitude and of time is desirable, as much
in the interest of science as in that of navigation, of commerce,
and of international communication. The scientific and practical
utility of this reform far outweighs the sacrifice of labor and the
difficulties of adaptation which it would entail. It should, there-
fore, be recommended to the Governments of all the States in-
terested, to be organized and confirmed by an International Conven-
tion, to the end that hereafter one and the same system of longitudes
shall be employed in all the institutes and geodetic bureaus, for
the general geographic and hydrographic charts, as well as in the
astronomical and nautical almanacs, with the exception of those
made to preserve a local meridian, as, for instance, the almanacs for
transits, or those which are needed to indicate the local time, such
as the establishment of the port, &c.
II. Notwithstanding the great advantages which the general in-
troduction of the decimal division of a quarter of the circle in the
expressions of the geographical and geodetic co-ordinates, and in
the corresponding time expressions, is destined to realize for the
sciences aud their applications, it is proper, through considerations
eminently practical, to pass it by in considering the great measure
of unification proposed in the first resolution.
However, with a view to satisfying, at the same time, very serious
scientific considerations, the Conference recommends, on this occa-
sion, the extension by the multiplication and perfection of the nec-
essary tables, of the application of the decimal division of the quad-
rant, at least, for the great operations of numerical calculations, for
which it presents incontestable advantages, even if it is wished to
preserve the old sexagesimal division for observations, for charts,
navigation, &c.
III. The Conference proposes to the Governments to select for the
initial meridian that of Greenwich, defined by a point midway be-
tween the two pillars of the meridian instrument of the Observa-
tory of Greenwich, for the reason that that meridian fulfils, as a
point of departure for longitudes, all the conditions demanded by
science ; and because being at present the best known of all, it
presents the greatest probability of being generally accepted.
IV. It is advisable to count all longitudes, starting from the
meridian of Greenwich, in the direction from west to east only.
V. The Conference recognizes for certain scientific wants and for
the internal service in the chief administrations of routes of com-
GENERAL MEETING. 109
munication, such as the railroads, steamship lines, telegraphic and
post routes, the utility of adopting a universal time, along with
local or national time, which will necessarily continue to be em-
ployed in civil life.
VI. The Conference recommends, as the point of departure of
universal time and of cosmopolitan date, the mean noon of Green-
wich which coincides with the instant of midnight, or with the
commencement of the civil day, under the meridian situated 12
hours or 180 degrees from Greenwich.
It is agreed to count the universal time from h to 24h .
VII. It is desirable that the States which, for the purpose of
adopting the unification of longitudes and of time, find it necessary
to change their meridians, should introduce the new system of lon-
gitudes and of hours as soon as possible.
It is equally advisable that the new system should be introduced
without delay in teaching.
VIII. The Conference hopes that if the entire world should agree
upon the unification of longitudes and of time by accepting the
meridian of Greenwich as the point of departure, Great Britian will
find in this fact an additional motive to make, on its part, a new step
in favor of the unification of weights and measures, by acceding to
the Convention du Mitre of the 20th May, 1875.
IX. These resolutions will be brought to the knowledge of the
Governments and recommended to their favorable consideration,
with the expression of a hope that an International Convention,
confirming the unification of longitudes and of time, shall be
concluded as soon as possible, by means of a special conference,
such as the Government of the United States has proposed.
Mr. Hilgard said that while the report of the Association did
not conform in some of its details to the desires and interests of this
country, nevertheless our principal object had been gained by the
endorsement of the Association for the International Conference on
the subject of standard time, to be held in Washington.
The selection of the meridian of Greenwich as the starting point
for longitudes, was more convenient for us than for Europeans
;
Europeans alone are liable to the confusion arising from the
numerical identity of meridians east and west of Greenwich. It
will be impossible, however, for us to agree to the rule which counts
all longitudes from west to east.
110 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Elliott opposed the establishment of noon as the initial
hour of the clay. It seemed to be proposed in the interest of astron-
omers, who work at night, and would not be submitted to by the
people at large.
He exhibited a map showing a grouping of the railroads of the
country under the recently adopted time schedule.
Mr. Cutts said that the resolutions of the Geodetic Association
do not appertain to civil time. The " universal time " they advo-
cate is for the use only of astronomers and great transportation
corporations.
Other remarks were made by Mr. Newcomb.
242d Meeting. December 8, 1883.
By permission of the Secretary of the Smithsonian Institution,
the Society occupied for the evening the Lecture Hall of the
National Museum.
The President called Vice-President Mallery to the Chair.
There were present about three hundred members and guests.
By invitation, the Presidents of the Biological and Anthropo-
logical Societies occupied seats on the platform.
The President of the Society, Mr. J. W. Powell, delivered the
annual address, taking for his subject
THE THREE METHODS OF EVOLUTION.
[The address is printed on pages xxvh-lh, ante.~]
The Chair invited the members of the Society and their friends
to remain for a period after adjournment, for the purpose of social
intercourse.
The Society then adjourned.
GENERAL MEETING. Ill
243d meeting. December 22, 1883.
the thirteenth annual meeting.
The President in the chair.
Thirty-four members present.
The minutes of the 226th, 241st, and 242d meetings were read.
The Chair announced the death, since the last meeting, of
General R. L). Cutts.
The Chair announced the election to membership of Messrs.
Robert Simpson Woodward, Daniel Elmer Salmon, and John
Mills Browne.
The Secretary's report on the membership of the Society was
read. During the year the Society received seventeen new mem-
bers, lost eight by death, and lost three by resignation.
The Treasurer not being present, the Chair appointed Mr. Henry
Farquhar Treasurer pro tempore.
The officers for the ensuing year were then elected by ballot. (The
list is printed on page XV.)
On motion of Mr. Jenkins, the vote for President was made
unanimous.
The Chair appointed Messrs. C. A. White, S. Newcomb, and H. C.
Yarrow a committee to audit the annual report of the Treasurer.
The Society then adjourned.

BULLETIN
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON,
MATHEMATICAL SECTION.
"3

STANDING RULES
OF THE
MATHEMATICAL SECTION.
Adopted March 24, 1883.
1. The object of this Section is the consideration and discussion
of papers relating to pure or applied mathematics.
2. The special officers of the Section shall be a Chairman and a
Secretary, who shall be elected at the first meeting of the Section
in each year, and discharge the duties usually attaching to those
offices.
3. To bring a paper regularly before the Section it must be sub-
mitted to the Standing Committee on Communications for the
stated meetings of the Society, with the statement that it is for the
Mathematical Section.
4. Meetings shall be called by the Standing Committee on Com-
munications whenever the extent or importance of the papers sub-
mitted and approved appear to justify it.
5. All members of the Philosophical Society who wish to do so
may take part in the meetings of this Section.
6. To every member who shall have notified the Secretary of
the General Committee of his desire to receive them, announcements
of the meetings of the Section shall be sent by mail.
7. The Section shall have power to adopt such rules of pro-
cedure as it may find expedient.
115
LIST OF MEMBERS
WHO RECEIVE ANNOUNCEMENT OF MEETINGS OF THE
MATHEMATICAL SECTION.
Abbe, C.
Alvord, B.
Avery, R. S.
Babcock, O. E.
Baker, M.
Bates, H. H.
Billings, J. S.
Burgess, E. S.
Christie, A. S.
Coffin, J. H. C.
DeLand, T. L.
Doolittle, M. H.
Eastman, J. R.
Elliott, E. B.
Farquhar, H.
Flint, A. S.
Gilbert, G. K.
Newcomb, S.
Gore, J. H.
Green, B. R.
Hall, A.
Harkness, W.
Hazen, H. A.
HlLGARD, J. E.
Hill, G. W.
King, A. F. A.
KUMMELL, C. H.
Lefavour, E. B.
Peirce, C. S.
Ritter, W. F. M'K.
Smiley, C. W.
Taylor, W. B.
Upton, W. W.
Walling, H. F.
Winlock, W. C.
116
INAUGURAL ADDRESS
OF THE
CHAIRMAN OF THE MATHEMATICAL SECTION,
By Asaph Hall.
Gentlemen of the Mathematical Section:
I thank you for the honor you have conferred on me by my
election as Chairman of this Section, and the best return that I can
make is to do my utmost to render our meetings as interesting and
successful as possible.
Although my duties have been such that I have not been able to
take a very active part in the proceedings of the Philosophical So-
ciety, it is easy to understand how a need has been felt for a more
full and frequent discussion of mathematical questions. Mathe-
matics has indeed been called the queen of the sciences, but the
rigor and dryness of its methods make it distasteful to many.
The fact seems to be that as any branch of knowledge advances
and finally is reduced to law, it loses in a large degree its attractive-
ness and popularity. Then, it is only with the indefinite outlines
and the obscure boundaries of this science that most people like to
deal ; and this may be natural and right, since nearly all advance-
ment originates in speculation and doubt, which lead to investiga-
tion, and which, by a variety of motives, spur men on to labor.
But the science of mathematics, though old, is yet young and vigo-
rous. We have now six journals of the highest rank, which are
devoted almost exclusively to pure mathematics—two in Germany,
two in France, one in England, and, I am glad to say, one in our
own country. These journals are devoted to the discussion of the
highest conceptions of space and number, treating chiefly of the
laws and forms of analytical expressions, and generally they touch
lightly on any practical application of the science. Such discus-
sions prepare the way, however, for better and more general prac-
tical methods, and in our own country they have, I think, another
value. For one, I can hardly accept the doctrine, advocated in
some quarters, that the American scientific man of the future should
117
118 PHILOSOPHICAL SOCIETY OF WASHINGTON.
be distinguished by his facility in getting a patent on his discovery,
in forming joint stock companies and watering stock, and in sud-
denly becoming rich at the expense of his fellow-men. Such a
career may be a natural result of our present system of sociology,
but it does not seem to be in harmony with scientific thought and
research, and our social need is for men of a different character.
Far nobler is the life of one who devotes himself to the study of
the most abstract forms of science ; winning for us, if haply he
may, another forward step up the hill of knowledge.
But when we come to the field of applied mathematics we soon
learn how necessary are the studies of the pure mathematician.
Nearly all the researches in natural philosophy, where the action of
forces is concerned, require the formation and solution of differen-
tial equations, and hence the theory of such equations becomes
important, and in some cases almost essential, for the advancement
of physical investigations. It is not, of course, to be supposed that
experiment and observation are to be done away with or neglected,
or that mere skill in differentiating, integrating, and solving equa-
tions can supply the place of correct thinking. In fact, we may be
sure that Leibnitz was mistaken when he declared that the inven-
tion of the differential calculus had made known that royal road to
knowledge for which the king had inquired in vain of Euclid. But
still it remains true that this calculus forms the most powerful
engine we have for the solution of questions in natural philosophy.
It enables us to adopt the old maxim, " divide et i?npera." If we
can reduce the problem to its elements, and can form its true differ-
ential equation, the rest of the work is purely mathematical. Un-
fortunately, the differential equations that occur in the problems of
nature are very different from those given in our text-books, and
their exact solution is in most cases impossible. Here we must rely
chiefly on that happy device of the variation of constants, by means
of which the solution of simpler forms is extended to the more
complex.
One of the great advantages of putting a question in a mathemati-
cal form is the precision with which it can be stated. If we are right,
the truth of our assertion will be the sooner acknowledged, and if
we are wrong, our error can be the more easily detected. Fre-
quently it has seemed to me that disputes would be avoided in the
meetings of our scientific societies if men would take the trouble to
put their assertion into a formula and write it on the blackboard
;
MATHEMATICAL SECTION. 119
and certainly there would be a clearness and meaning that are so
often wanting. Thus, if any one asserts that when a planet comes
to its perihelion it ought to fall into the sun, the law of gravitation
being true, he is not worth listening to unless he will put his asser-
tion into a formula ; and when he is able to do this he will probably
find out his own error. There will be so much gain by simply re-
ducing the problem to its elements and giving it a correct form.
Again, where scientific statements may be true, there will be a gain
in giviug them, when possible, a mathematical expression. Thus,
when we are told that the fixed star 1830 Groombridge is running
away, disobedient to the law of gravitation, how much better it
would be if we could see on the blackboard the mathematical proof
of this assertion, so that we could judge for ourselves on what
assumption it is based. The subject of impulsive forces is one that
we hear disputes about in our own society, and it seems to be a fair
field for a mathematical exposition. How often do we see such
phrases as " energy," " potential energy," " kinetic energy," " con-
servation of energy," " work," " virial," &c. Could not some one
of our members give us a clear account of these terms, show us how
they are connected with the general equations of mechanics, what
new ideas they contain, and on what limitations they may be based ?
As the application of mathematics is extended, sounding phrases
are sure to come into use, and it is well to test them and know what
they mean.
In the discussions of this Section, while all are invited to be
critical, I trust that we shall all be kind and good tempered. We
come together for discussion and mutual improvement, and while
error is not to be spared we must be charitable to each other's faults.

BULLETIN
MATHEMATICAL SECTION,
A communication signed by Mr. J. E. Hilgard and nineteen
other members of the Philosophical Society, asking that a Section
in Mathematical Science be formed, as provided in Paragraph 6 of
the Standing Rules of the Society, was presented to the General
Committee at its regular meeting January 27, 1883. The propo-
sition was agreed to, and Mr. Hilgard was empowered to call a
special meeting for the purpose of organizing such a section ; the
call being extended to all members of the Society.
1st Preliminary Meeting. February 17, 1883.
Twelve members met in the library of the Army Medical Mu-
seum, in answer to the first call.
Mr. Hilgard not being present, Mr. E. B. Elliott was called
to the Chair.
An informal discussion followed, which brought out a unanimous
sentiment in favor of forming the Section.
With some differences of opinion as to details, it was agreed to
postpone formal action, and the meeting adjourned subject to call.
2d Preliminary Meeting. March 5, 1883.
Mr. Hilgard in the Chair.
Fifteen members present.
A plan of organization was adopted, and referred to the Gene-
ral Committee of the Society for consideration.
12 121
122" PHILOSOPHICAL SOCIETY OF WASHINGTON.
1st Regular Meeting. ' March 29, 1883.
Fourteen members present.
In the absence of Mr. Hilgard, who had presided over the
meeting for organization, Mr. G. W. Hill was called to the Chair.
The standing rules for the government of the Section, as adopted
at the last meeting of the General Committee of the Society, were
read.
The Section then proceeded to elect officers for the year 1883.
On motion of Mr. Winlock the rules of the Society at its An-
nual Meeting were followed.
Mr. Asaph Hall was chosen Chairman and Mr. H. Farquhar
Secretary.
A letter from Mr. Marcus Baker, dated Los Angeles, Cal., was
read by Mr. Christie. It expressed a strong interest in the Sec-
tion, recommending that it should be conducted as nearly as possi-
ble on the plan devised by the late Prof. Henry for the Society
itself, by which business and science are kept apart. A free use of
pencil and paper at the meetings, and seats around a table, were
further suggested. The letter closed by advocating the foundation
of a new mathematical journal.
Mr. Christie then made a communication on
A QUASI GENERAL DIFFERENTIATION.
The paper was discussed by Messrs. Kummell, Elliott, Hill,
and Doolittle. The author reserves it from publication to await
further research.
A resolution was passed, requesting the committee in charge of
the matter to call meetings of the Section on Wednesday evenings.
2d Meeting. April 11, 1883.
The Chairman, Mr. Hall, presided.
Present, ten members and two invited guests.
It was announced that the Editor of " Science " would publish
brief reports of the meetings of the Section.
MATHEMATICAL SECTION. 123
The Chairman read an inaugural address, [given in full on pp.
117 to 119 ante.]
Mr. C. H. Kummell then began a paper on
ALIGNMENT CURVES,
which was not finished at the time of adjournment.
3d Meeting. April 26, 1883.
The Chairman presided.
Present, sixteen members and one invited guest.
Mr. Kummell completed his paper, begun at the second meet-
ing, on
ALIGNMENT CURVES ON ANY SURFACE, WITH SPECIAL APPLICATION
TO THE ELLIPSOID.
[Abstract.]
The attempt to put a number of points in line on a curved sur-
face whose normals are supposed to be given (abstraction is made
of deviations of the plumb-line and lateral refraction) gives rise to
various curves, which I call alignment curves. There are two
classes—alignment curves with two given termini and those with a
starting point only. There are three distinct curves of the first
class, viz. : 1. The normal section, if the surveyor directs his assist-
ant to place staffs in line from one end of the line. 2. A curve
described if the surveyor would align a point near him, then move
up to this point, thence align another point, etc., until the terminus
is reached. This process is that used in chaining, or more roughly
by a pedestrian going towards a point, and is characterized by
requiring only foresights. I call it proorthode (xpo, 6p0u$, 6do?)*
3. A curve resulting if a backsight is also taken. This curve is
therefore defined by the condition that the normal plane at any
point of it which passes through one end also passes through the
other. I call it diorthode {did, 6p0d$, 636$), because it may be con-
* This and other names of curves were coined by my friend, Mr. Wm. R.
Gait, of Norfolk, Va.
124' PHILOSOPHICAL SOCIETY OF WASHINGTON.
sidered straight all through at any of its points. This curve may
be considered the ideal curve of a primary base line. Various
names have been given to it when on the terrestrial spheroid. Dr.
Bremiker, who appears to have first considered it (in his Studien
ueber hoehere Geodsesie, 1869), proposed the name " Feldlinie"
;
that is, field line. He thinks it should be adopted as the geodetic
line, because both linear and angular measurements conform to it.
Clarke, Zacharise, and Helmert have also mentioned it, the latter,
however, only in a note, where he remarks that it deserves no con-
sideration in geodesy.
To the second class belong two curves : 1. A curve described as
follows: The surveyor at the starting point takes his directions
from a staff at short distance and directs his assistant to place
a staff in the prolongation. Repeating this operation from the
first staff, from the second staff, etc., he describes a curve which
is well known to be the shortest curve between any of its points.
It is usually called the geodetic line. However, since this name
would apply at least equally well to the three curves already con-
sidered, I propose the name brachisthode (fipd^t<rrug). The proper-
ties of this curve need not be considered here, such mathematicians
as Gauss, Hansen, Bessel, and others, having perfected its theory.
Helmert, in his " Hoehere Geodsesie," makes this curve the basis of
nearly all geodetic computations. The brachisthodic process on a
plane evidently results in a straight line, and on a sphere in a great
circle. If, on these surfaces, it is in starting directed to a distant
point, that point will be reached (disregarding errors of observation).
Not so on other curved surfaces; there, in general, the first element
of the brachisthode is not in direction to any of its points at a finite
distance. 2. The loxodrome being a curve which has a constant
inclination to a given direction, may, perhaps, be mentioned as be-
longing to this class.
The general equations of the two-end curves on any surface may
be developed as follows
:
Let the equation of the surface be
:
u=f(x,y, z)=0 (1)
then if (?, rj, is any point in the normal at the surface point
(x, y, z), we have its equations
:
£ — x rj — y Z — z
. = J. i= (2)
du\ fdu\ fdws/ ( f^\
\Tx) \dy) \dj)
MATHEMATICAL SECTION. 125
and the equation of a normal plane at the surface point (x, y, z)
and passing through (x2 , y2 , z2), (not necessarily a surface point, but
considered so here), is
:
^[<^>®-<^&]D^©-(*-'>®]
-[<^®-<<-'>(g)][<^®^-<>(*)]
= [Cy8 — V) ($ — X) — {x2 — x)(rj— y)-] (^£j
+ to -•)(*-*)- (ft -3D (C- *)](^)
+ [(^ _ x) (c - .) - fc - .) (? - *)] (^) (3)
If in this we replace the surface point (x, y, z) by the surface
point (xv yv zx) and (?, ^, CJ by the surface point (re, y, z) we obtain
:
= [(&— ^) (« - »,) — 0»8— a,) (g/- &)]^J
+ [(^2— *Q 0/ - !/i) — (2/2 — Vx) (« — 2i)J (^)
+ EO-2-*!) (-*)-(v-«0 (*-«i)](^) (4)
which, if combined with the equation of the surface, gives the nor-
mal section at (xv ylt zx) through (x2 , y2 , z2).
If, however, we replace in (3) (<?, 17, C) by the surface point
(x, y, z) we obtain
:
— [(ft— y) (fli— »)—fo - «) (2/j— ?/)] [£)
+ K«i - 2) (2/1 - 2/) - (2/2 - y) Oh - *)] (^)
+ to, - «) fc - ) - fc ~ 2) & - «)] (^) (5)
and this, combined with the equation of the surface, gives the dior-
thodic curve.
As we move along the diorthode, (5) may be considered a plane
which turns about the chord (1, 2) as an axis, so as to be always
normal to the surface. It follows that the normals at any point of
the diorthode are constrained to pass through the chord. They will
thus generate a ruled surface, whose equation is not (5) however.
126 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The equation of this ruled surface is obtained by eliminating x, y, z
from (1), (2), and (5). It is important to remark that the dior-
thode does not consist of parts which are diorthodes with respect to
their termini, otherwise the normals would at the same time pass
through two chords from the same point and the curve would be a
plane curve. Dr. Bremiker had erroneously supposed that the
diorthode was touched by the normal planes. This is only the case
at the termini. He has been criticized by Dr. Bruns of Pulkowa
and by Helmert, but neither critic has shown the existence of a curve
possessing this property, namely, the proorthode, in which the nor-
mal plane at any of its points passes through the consecutive point
and the forward terminus, but not in general through the starting
point. If then in (5) we replace (xlt yv zt) by (x + dx, y + dy,
z
-f- dz) we have
:
= [(&— y) dx — 2— *) dy] \j£)
+ [.{z2— z)dy—(y2 —y)dz][J^j
+ [C»2— *) dz — (z2— z) dx] (j^j
+[<*->(SO -<*-)(sH*
By means of the equation of the surface (1) and its differential
equation
any one of the variables with its differential can be eliminated.
The resulting differential equation being integrated so as to contain
the starting point (x
Y , yv zx ), will be the equation of a projection of
the proorthode on a coordinate plane.
The proorthode being differently related to its ends, will be dif-
ferent forward and backward, while the diorthode is the same for-
ward and backward.
MATHEMATICAL SECTION. 127
The following diagram will illustrate the relative course of these
curves
:
normal section
diorthode
prodrthode
brachisthode
Any surface of the second degree may be represented by
w=0
\ a J ^ p ^ q
(8)
The origin is taken at one of its real vertices, so that (a, 0, 0) is
its centre. The equation of the diorthode is then by (5), if we
write x2 — x 1 = A.r; y2 — yt = by ; z2 — z1 = A z,
= [(&- V) Oft - *) - Oft- «) (2/i - 2/)] Y
+ [(ft - 2) (y, — y) — (fc— !/) (ft - 2)] —
^~
+ r>3 - *) (ft - ^) - (ft ~ s) Oft - *)] J
= (ft <ft -yx x2 -\- ybx - x*y) —
+ (ft Vi — h y% + sAy - !/A2 ) -^r
+ (ar2 Zj — x1 z2 + a-Az — zAa;) P
= A*(|-}) F + Ay(7"j) B+A2 (F-a)p
+ (ft ft — ft ft)
xy
+ (x2 zx — xx z2 + pbz) — + (y,2 xt — yx x2 — qby)— (9)
The equations of the chord (1, 2) may be written
:
%—*
= ft
— y = ft
— g
(10n
ft— z y1 —yz1 — z J
Every point of the chord, therefore, satisfies (9), and since that
128 PHILOSOPHICAL SOCIETY OF WASHINGTON.
represents a surface of the second degree, it musl be a hyperboloid
of one sheet, for this and its varieties are the only ruled surfaces of
that order. In the general form (9) it has a center in finite space.
It is then the elliptic hyperboloid ; but if a = j> (or a = q or p = q),
it has its center at an infinite distance, and it is a parabolic hyperbo-
loid. In this case the base surface becomes
:
fe=£±J?+i_. (U)
a ' q
y
which is a surface of revolution of the second degree.
If a=^)= q, then (9) becomes a plane and the base surface a
sphere. (9) is evidently satisfied by the center (a, 0, 0), therefore
the intersecting surface always passes through the center of the
base surface.
I consider now the ellipsoid :
= J + F+7-! <12>
We have then the intersecting surface of the diorthode
:
x v
o = Oss/i— «i % + z*y— v* z) tf + (X zi— xv z-i + x*z —•***) p-
+ (2/2 xi —yr x-i+ y*x — xAy) ~# 0- 3)
Let (0, yx , 3X) be the point where the chord (1, 1) pierces the yz - plane
Oy,0,zy) " " " '« " ex- "
(x
z,yz,0)
" " " " - xy -
then we can easily verify the relations
:
X2 Vl Xl Vi
. _
X2 g l ^'l g2 Q^ \
(14v)
(14.)
#x — Aa;
MATHEMATICAL SECTION. 129
(13) will take either of the following equivalent forms :
= Az (y, - «bY) J + Ax (zx - fic2z) -jjr + Ay (xy - r»^f (131)
= Ay
y
- «» Jr + a3 O, - /3>)|- + a* (yx - rb2y)£ (1311)
The following relations will be much referred to
:
_
&. . 5l
_
£ _. 5- _£ + & n 6)Ay T A3 A3 ~ AX Ax ~ Ay K J
Xy— y* y. 2 v y, — v, zx xz
x? Vx zj — z, yz zz *z — *,
** ~ *z~yx — yz J
= Xy \k 3x + V* Zs Xz (18)
Replacing in these Ax, Ay, Az
; yx , g , xz ; 3X , ay , yz
hy ^->¥>1? '><> l3 *> r* > <> l3*> r» (19)
wehave:0=^ + §;=5+^=^ + ^ (16';
z
9
.
2
— r* k /? 2 . rf— «ba «c2 ra2
/V V /V — <2 ' rb2 ~"/? 2 ~ra2 -/*a
«.* - £' A2
(17 1)a
c ra <v — n
o = ,Vrb
2
«
c
2 + «b2 ^
2
ra
2 (is 1)
and these relations also will be found correct.
Because in the equation of the diorthodic surface the terras in
x2
, y
2
,
3s are wanting, there must be lines, perpendicular to the co-
ordinate planes, lying wholly in the surface. To determine those
perpendicular to the xy - plane, I place = the term in (13 1 ) de-
pendent on 3 and that in (13u) independent of z, or
= - yAx'f + ^rOy-r»
- - p-iy ?/+ (p - «) by (16) and (161 ;/a Jx V a '
= Ay2y %; -f A3 (x,- i^x) |
- h x + (f1* - *)
»
b>' ^16 ) aud (161)
130 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Substituting the value of y from the first into the second equation
we have
:
= ^x
rb
2
y* *
,
(x
7
- x
z) x + (^ - *) QjJ - a) by (17,) and (17/;
^
2
-r,
2 /_^y ,%z\ , *
Corresponding to the first value we have
/a /a 'a
»
~?7*"~?7
—
k— -*• hy (17i)
and corresponding to the second :
Denoting these constants by #
c ,
a;b , yo, ya , respectively, we have
then the equations of a pair of generatrices of the hyperboloid (13)
perpendicular to the xy - plane
:
x= 2^=xc ; y = fi=y (20,)/a I b
Similarly the pair of generatrices perpendicular to the 3/2 - plane:
2/= jh= y, ; -
z
f: =^ (20,
1
)
and that perpendicular to the zx • plane :
Z X
z= fi = z* ; * = f2 = xb (20y)
2 = ^
= z
* >
x = 7* = * (20,
1
)
o 'a
Now the second line of each pair intersects the chord, as may be
proved thus: The equations of the chord (1, 2) are any two of the
following three equations
:
£-+£_! = (21.)X -Ty
x
^
MATHEMATICAL SECTION. 131
—+——1 = (21)
f +^_l = (21,)
Now ^+¥~ 1=sh+h~ x = < + ^2 - <K = °
•"y js ' a b
and (21 x) or (21 ) can always be satisfied for some value of z;
therefore (20^) intersects the chord. In the same manner it may
be proved that (20^) and (20^) intersect the chord. It follows,
then, that (20
z), (20x), and (20y) cannot intersect the chord, and
hence belong to the same system of generation.
The equations of a pair of lines intersecting in a given point of
the hyperboloid and belonging to different systems of generation
can be easily found by the condition that one of them must inter-
sect (20) and the other (201 ). I omit this, but give a remarkable
symmetrical form of the equation of the hyperboloid :
0-(»-*J(y-yJ(»-0-(*-0(y-lO(«-0 (22)
= *(&*.—&O + 2/(za s b- 2b<> + 2 <X*/ — XcVj
— xy (z
a
— z„) — yz (a-b — xc ) — zx (y — yj, because xb yc za= xc y^
by (18) and (181 ).
It is immediately evident that this equation is satisfied by equa-
tions (20). It is not uninteresting to prove that it also satisfies (21),
or that it contains the chord, since it shows the remarkable plia-
bility of these forms by virtue of the relations (16), (17), (18),
(161), (17 1 ), (18
1
).
The points (x
c , yc , za), (.<r , ye , zb), (#„, yc , «„)• Ob > V* ZJ> 0*b> V*> ZJ>
(x
c , ya , za) form a warped hexagon, which lies wholly in the hyper-
boloid, and its sides may be considered six intersecting edges of a
characteristic parallelopipedon. These edges ai*e
:
^ = y<X-*c); £ = -2-(?/ -2/a); C=yOa —sb) (23)
and the co-ordinates of its center are
:
x
„
=
~2 Ob + *e) ; yo = ~2 & + 20 3 zo=Y ^ + *») (24)
and these must be those of the center of the hyperboloid also.
Transferring the origin of co-ordinates to this center, we have
the equation of the hyperboloid regarding (23) :
= (x- A) (y -B)(z-C)- (z+ A) (y + B) (*+ C) (25)
132 PHILOSOPHICAL SOCIETY OF WASHINGTON.
From this equation we soon find by familiar processes the
lengths and directions of the principal axes.
As to the question, Which of the alignment curves should be
used in geodesy? I observe that between two intervisible points on
the terrestrial spheroid the difference between the course of these
curves is so extremely minute that they are practically identical
;
we can use then that method of tracing which is most convenient.
For the distance of non-intervisible stations I consider the brachis-
thode the geodetic line as heretofore, because 1st, the diorthode be-
comes impracticable ; and 2d, it cannot be divided into portions
which are themselves diorthodes. As Assistant Wm. Eimbeck, of
the United States Coast and Geodetic Survey, suggested to me, the
diorthode proper cannot even be traced between very distant
stations, which are intervisible only from very elevated positions,
such as high peaks or the usual wooden structures. This led me to
consider a new class of alignment curves—the apparent horizon
alignment curves. The a. h. pro-orthode would be the locus of all
points for which the tangent cuts the normal at the forward end
;
while the a. h. diorthode is a curve, at any point of which a tangent
to the surface, which passes through the normal at one end, also
passes through that at the other end. The equation (3) being
adapted to these changed conditions will furnish also the equations
of these curves ; and I have thus found that the a. h. diorthode on
an ellipsoid has an intersecting surface of the fourth order.
Messrs. Harkness and Doolittle made remarks on this paper.
Mr. Asaph Hall then made a communication on
THE DETERMINATION OF THE MASS OF A PLANET FROM OBSERVA-
TIONS OF TWO SATELLITES.
[Abstract.]
M. Struve recommends that the position angle and distance of one
satellite from another satellite be measured, instead of referring the
place of each to the center of the primary planet ; and a series of
such measurements on satellites of Jupiter has been begun under
his direction at Pulkowa. These observations are found to occupy
one-third the time, and are considered two or three times as accurate
as those where the planet is used. The most important advantage
of the new method is its freedom from the unknown constant errors
attending the old, due to the great difference in size and bright-
MATHEMATICAL SECTION. 133
ness of the objects measured. The price to be paid for this ad-
vantage is a greatly increased complexity in the computation ; for
the elements of both orbits now enter into each equation of con-
dition, and there are therefore twelve normal equations instead
of six to solve. The comparative difficulty may be estimated by
the number of auxiliary quantities that must be computed in the
solution of n equations, namely
:
•g-»(»-f 1) + 5),
which amounts to 77 for n = 6, and to 442 for n = 12 ; a value
nearly six times as great. But it is worth while to bear in mind
that the twelve equations, by giving the elements and mean distance
of each satellite, give two values of the planet's mass.
Mr. Harkness called attention to the advantage of substituting
an accidental error, be it even a large one, for an unknown constant
error.
Mr. Taylor criticised the designations usually given to the
apsides of satellites orbits as being particular when they should be
general. He suggested the terms peri-apsis and apo-apsis, or aphapsis.
Remarks were also made by Messrs. Kummell and Hill.
Before adjournment the Chairman replied to some questions as
to the new object glass for the Imperial Observatory at Pulkowa;
and gave a short explanation of the difficulty of calculating the
true anomaly in elliptic orbits.
4th Meeting. May 9, 1883.
The Chairman presided.
Present : twelve members and one guest.
The report of a committee appointed by the General Committee
of the Society to consider matters pertaining to Sections was read.
Mr. Doolittle read a paper entitled
INFINITE AND INFINITESIMAL QUANTITIES.
[Abstract.]
An infinitesimal may be defined as the result of infinite division
;
134 PHILOSOPHICAL SOCIETY OF WASHINGTON.
but the term infinite division probably does not represent the same
conception to all mathematicians. If we suppose a quantity divided
into a number of parts, and each of these parts subdivided, and
similar subdivisions to go on forever, each requiring finite time, we
have a conception to which the name infinite division may be given
with some appropriateness, but which might better be called eternal
division. Such division never reaches a result. But if we suppose
the time of each subdivision to be proportional to the magnitude of
each part, the entire process is completed in finite time, although
no limit can be given to the number of subdivisions. If a point
be supposed to have passed with constant velocity over a given
distance, there was a time when it had passed over half the distance
;
afterward a time when the remaining distance was one-fourth of the
original distance ; the number of such successive halvings is cer-
tainly unlimited ; and the result is that there is no remaining dis-
tance. This is division infinite but not eternal, and the result seems
to be zero.
As a point is defined to be position without magnitude, so may an
infinitesimal be defined to be quantitative relation without magnitude.
The terms infinitesimal, differential, nothing, and zero, are not
synonyms. They have the same logical denotation but differ in
connotation. Mathematicians usually speak of " the value " or
" the true value " of a vanishing fraction, as though any quantity
whatever were not a true value. The term serial value is proposed
as conducive to clearness of thought. A differential coefficient is
the serial value of a vanishing fraction ; and a differential or infi-
nitesimal may be further defined as zero in serial relation to con-
tinuously diminishing quantity.
The term infinitesimal is however frequently employed like other
terms to denote the symbol of its exact signification. We speak of
drawing and erasing lines, meaning the visible symbols of Euclidean
lines. Even in our purely mental processes we give the name
points to the imagined small volumes that symbolize positions with-
out magnitude. In like manner the term infinitesimal is employed
to denote the imagined small quantity in approximate relation that
symbolizes a relation which becomes exact only when magnitude
disappears.
A line is infinite relatively to a point, but infinitesimal, i. e., zero,
relatively to a surface or volume. Every quantity is finite rela-
tively to other quantities of its own order—zero relatively to orders
MATHEMATICAL SECTION. 135
above and infinite relatively to orders below. A volume is inte-
grated from surfaces, a surface from lines, and a Hue from points.
Each integral is infinite relatively to the magnitudes from which
it is integrated. As momentum is integrated from motion-genera-
ting force, it is infinite relatively thereto. Momentum may also be
dissipated by infinitesimal decrements ; and it is possible that mo-
mentum is always thus dissipated and re-integrated whenever
motion is communicated from one body to another; but the prin-
ciples of mathematics are equally consistent with the hypothesis
that actual contact sometimes occurs, in which case motion is di-
rectly, and instantaneously transmitted without dissipation or re-
integration. Granting that infinitesimal time requires infinite force,
momentum satisfies that condition.
This paper gave rise to considerable discussion, in which Messrs.
Taylor, Hill, Kummell, and Lefavour maintained the legiti-
macy of the notion of infinitesimals as real elements out of which
quantity is built up ; Messrs. Elliott, Doolittle, and Farquhar
took the opposite ground, preferring the Newtonian view of the
Calculus; while Mr. Christie, while preferring the infinitesimal
method, maintained that no evaluation of continuous quantity, in
terms of units as it must necessarily be, could ever be precise or
entirely satisfactory, to however small a compass the uncertainty be
reduced. Mr. Christie also pointed out some paradoxes to which
the usual definitions of curves and tangents appeared to lead.
Mr. Elliott then exhibited some tables to serve as a perpetual
calendar, and gave a full explanation how by means of them the
day of the week corresponding to that of the month for any year,
New or Old Style, B. C. or A. D., could be found.
5th Meeting. May 23, 1883.
The Chairman presided.
Twenty members and guests present.
The appointment of the committee called for under the new
Standing Rule relating to papers read before Sections of the
Society was considered. Mr. Taylor moved that the committee
consist of the Chairman and Secretary and a third member to be
136 PHILOSOPHICAL SOCIETY OF WASHINGTON.
appointed by the Chair. After some discussion by Messrs.
Harkness and Elliott it was so ordered, with the additional
provision that this appointment be made for each paper separately.
Mr. G. W. Hill made a communication on
PLANETARY PERTURBATIONS OF THE MOON,
which was yet unfinished when he yielded the floor to Mr. G. K.
Gilbert, who made a communication on
GRAPHIC TABLES FOR COMPUTING ALTITUDES FROM BAROMETRIC
DATA.
This paper will appear in the Bulletins of the U. S. Geological
Survey.
6th Meeting. June 6, 1883.
The Chairman presided.
Present, sixteen members and guests.
Mr. G. W. Hill concluded his paper on
CERTAIN POSSIBLE ABBREVIATIONS IN THE COMPUTATION OF THE
LONG-PERIOD PERTURBATIONS OF THE MOON'S MOTION
DUE TO THE DIRECT ACTION OF THE PLANETS.
[Abstract.]
Hansen has characterized the calculation of these inequalities as
extremely difficult. However, it seems to me that if the shortest
methods are followed there is no ground for such an assertion. The
work may be divided into two portions independent of each other.
In one the object is to develop, in periodic series, certain functions
of the moon's coordinates, which in number do not exceed five.
This portion is the same whatever planet may be considered to act,
and hence may be done once for all. In the other portion we seek
the coefficients of certain terms in the periodic development of
certain functions, five also in number, which involve the coordinates
of the earth and planet only. And this part of the work is very
similar to that in which the perturbations of the earth by the
planet in question are the things sought. And as the multiples of
the mean motions of these two bodies, which enter into the expres-
MATHEMATICAL SECTION. 137
sion of the argument of the inequalities under consideration, are
necessarily quite large, approximate values of the coefficients may
be obtained by semi-convergent series similar to the well-known
theorem of Stirling. This matter was first elaborated by Cauchy,*
but in the method as left by him we are directed to compute special
values of the successive derivatives of the functions to be developed.
Now it unfortunately happens that these functions are enormously
complicated by successive differentiation, so that it is almost impos-
sible to write at length their second derivatives. Manifestly then,
it would be a great saving of labor to substitute for the computation
of special values of these derivatives a computation of a certain
number of special values of the original function, distributed in
such a way that the maximum advantage may be obtained. This
modification has given rise to an elegant piece of analysis.
It will be noticed that in this method it is necessary to substitute
in the formulae, from the outset, the numerical values of the elements
of the orbits of the earth and planet. There seems to be no objec-
tion to this on the practical side, as for the computation of the
inequalities sought no partial derivatives of R, with respect to
these elements, are required.
The paper is printed in fall in the American Journal of Mathe-
matics, Vol. VI.
Mr. E. B. Elliott made a communication on
UNITS OF FORCE AND ENERGY, INCLUDING ELECTRIC UNITS.
Seventh Meeting. November 21, 1883.
The Chairman presided.
Thirteen members present.
* Memoire sur les approximations des fonctions de tres-grands nombres, and
Rapport sur un Memoire de M. Le Verrier, qui a pour objet la determination
d'une grande inegalite du moyen mouvement de la planete Pallas. Comptes
Rendus de l'Academie des Sciences de Paris. Tom. XX, pp. 691-726, 767-786,
825-847.
13
138 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. C. H. Kummell read a communication erftitled
THE THEORY OP ERRORS PRACTICALLY TESTED BY TARGET-
SHOOTING.
[Abstract.]
Sir John Herschel treats a special case in which shots of equal
probability are in circles. According to Liagre's theory target
shooting is compounded of two distinct operations, viz., sighting
and leveling, each of which is liable to errors, independently fol-
lowing the ordinary linear law of error. Some reasons for the in-
dependence of these operations are that for sighting the direction
of the wind, which does not affect the leveling, must be regarded;
and that, on the other hand, leveling only is affected by the range.
The consequences of Liagre's theory will now be developed.
Let x = error of sighting and e
x
its mean error;
y = error of leveling and ey its mean error ;
then it follows that
dx — jTHi
—7= e x = probability to hit anywhere at distance x from
sighting axis. (l
x)
r
£
y = probability to hit anywhere at distance y from
leveling axis. (ly)
x- y
dxdy — £7"=? — 2e 2
.
o e y = probability to hit the point (x,y). (2)
» y
This probability is the same for any point on the ellipse:
X V^ T^
73 + fl- -5 , where s
2
=
-j ft," + e/) (3)
x "y
This I shall call, then, an equal probability ellipse; its semi-axes
are
:
£„
— r and — r (4)
and r = mean semi-diameter (which is equal to its conjugate).
Assume x
T
= — and yr =— y (5)
1 y
MATHEMATICAL SECTION. 139
then every point on the equal probability ellipse (3) corresponds
to a point (x
x , yt) on the circle : x* + y* = r
2
, (6)
which is the reduced equal probability circle.
Counting directions from the right of the x - axis, let
a = direction of (x, y) (7)
a
T
= " " (x
T,yJ, or reduced direction of (x,y) (8)
then tan a = ~ = -y yr -r- - xT = -
7
- tan «_
also 2 = -r cos a
e r
y = — r sin at
I
(9)
(10J
(10
y)
whence dx = — cos ar dr — —r sin a da£ r £ r r
£
.
£
dy = — sin a
x
dr
-f-^r cos a2cfar
Transforming, then, (2) to the new variables, r and a,, we must
replace
:
j j u exe,rdrdadx dy by -^-^ -r
and thus obtain
rdrda, — zs
2*e3
i3 the reduced point.
2£2 _= probability to hit a point of which (r, a
r)
(11)
Fig. 1 exhibits 24 shots of equal probability, on an equal proba-
bility ellipse, and their reduced positions evenly distributed over
the reduced circle.
140 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The probability to hit anywhere on the. perfmeter of an equal
probability ellipse of mean semi-diameter, r, is found by integrating
(11), with respect to at , through a circumference. It is
rtfr e -5 (12)
Let n
T
= number of shots on area of equal probability ellipse of
semi-diameter r, and n= total number ; then
1h.= C.
n J
lr
e
- i^==1 _ e ^ or ^ZL!ir = e-i Q3)
_^
Letr = /»; if »r= J»,then J = e 2f».; pss ev/2l2 (14)
The ellipse
:
£+'j?-2U (15)
£
is then an even chance ellipse, which is hit or missed with equal
probability. Eliminating e between (13) and 14), we obtain
:
(17)
/ log 2
\n — nj
These formulae agree with Herschel's in form, and have, also, the
same signification, in case the precisions of sighting and leveling are
equal, for in that case the ellipses (3) and (15) become circles and
r, p their radii, respectively. Herschel employs these formulae for
determining the skill of a marksman, which he defines to be =
—
,
P
from the number of shots that have fallen on a circle of radius r.
Correspondingly, we should have to count the shots that have
fallen on an equal probability ellipse, the axes of which have the
unknown ratio -£-, which, as yet, we have no method of finding
;
therefore formulae (14) and (17) cannot be employed in their gen-
eral signification. If, nevertheless, we count the shots on a circle
of radius r and compute a value for p and e, we shall come as near
to their true values as the problem requires, especially if the precis-
ions of sighting and leveling are not very different. This can be
MATHEMATICAL SECTION. 141
shown analytically by proving that the probability of hitting the
area of the circle
x
2
-j- if = r
2
differs from that of hitting the equal probability ellipse
x- y2 r
7^+72=72"
x y
by terras of the fourth order, with respect to the difference between
the mean errors of sighting and leveling.
In computing p by (17) the radius (or mean semi-diameter) r is
left arbitrary; it is, however, not at all indifferent; for if we take
it very small or very large it will give very unreliable values of p.
There must then be a certain magnitude of r giving the most re-
*
liable value of p, and it is that which makes P
r
= —& 2£i a
It2
maximum. This gives the condition : = ——
~r .". r = e
Thus the most favorable value of r for determining p is the
mean error e and the ellipse —2 + —t = 1 (18)
is the ellipse of the most probable shot.
Placing r = e in (13), we have
1
VL=2h
==e —T= 0.60653....
n
.'. n
e
= \1 - e '~~^)n= 0.39347
. . . n = 0.4n nearly (19)
The most probable shot is, therefore, the distance of the (0.4/i)th
shot from the center nearly ; also the mean of the (0.4n + w)th,
and the (0.4n — ra)th shot should, if m is not too large, give a fair
value of the most probable shot.
Solving (13) for e, we have also
\k (20)
From the definition of e
x and sy it is obvious that
142 PHILOSOPHICAL SOCIETY OF WASHINGTON.
which formulae afford a comparison between the precisions of
sighting and leveling. We have then
— >©* •-">/*+ * (22)
This formula, although laborious for practical use, is the most
rigorous measure of skill in shooting, and there is no need of other
formulae except when shots are lost. In that case it requires an
important modification, whereby it loses in rigor if the number of
lost shots is considerable. Assuming the precisions of sighting
and leveling equal, then the reduced distance r in (12) will be the
actual distance s of a shot ; and if the target is circular, of limiting
radius R, we have
_& /
_
R2\ )
= n 1 - R2e & + 2e 2 ( 1 - e * ] I
Now by (13) nR
=sn ( 1~ e 2E*
J
n
therefore ry^ R=%lR ?-U - nAx*
n
and ^ M *+(*-**)" (23)
This formula reverts, of course, to (22), if n = n and it makes
the most probable sum of the squares of the lost shots
[S2f = Jl(n - n \&
and since (
n ~~ n
r ) R2 is tne smallest
possible actual value of
this quantity ; this expression for it is quite plausible.
The targets used by the National Rifle Association are rectan-
gular. (At long range they are 12 feet wide and 6 feet high).
MATHEMATICAL SECTION. 143
Let a (= 6 feet) be the limiting value of x and b (= 3 feet) that
for y, then we have, if nab is the number of hitting shots
b y
*
/ r/r
——
- 9 f —p
-^-=. e 2V = -7= rff e > and
a o
similarly Pfb , is tabulated in Chauvenet's Method of Least Squares
(Table IX, appendix, to the argument t), and is therefore known.*
"We have further
:
x2 b
1*]**-% C tfJ^ e 2e"T -J3U
1 J
'
£x\/2TT J ^yV217
— a —b
2e 2
e y
-*\-[£i' "^ + *f el/ 2,r J J £*\/ 2n
— a —
a
J
= nex
si\(P*8 -*aP'0 (25x)
c/p^ 2 — a
Here P^
a
denotes ,, a = -7=-= e and can also be taken from
Chauvenet's table, being 100 X difference. Similarly,
ryf* = nt *Pt& {PK _ kFk) (25y)
By virtue of (24) we have also
[>
2
]
%
ab
i
—
-m ^
nAl — Kpt)
V = -T m (25/)
and these formulae may be used to compute sx and ey by an obvious
approximative process. They show that ex
2 > L Jl ' as it should
144 PHILOSOPHICAL SOCIETY OF WASHINGTON.
be ; but it may, or rather must, happen sometimes that the most
n n
probable increase of the sum of x2 and tf or [re2] + [y2] consistent
W
ab
_
_
«.b
with (25') is < (n — wab ) b2,b being the smaller limit. Such a re-
sult cannot be accepted, being contradictory to the fact that there
are n — ?iab shots at a greater distance than b. The following
method gives plausible results in that case. Assume
0/) = n (6<a) (25/0
as first approximate value in (25/), and if sy<C/sy ) adopt (s ) as
final value of £
y
: but if £
yX-y), then proceed in approximating to
ey by (25/). The solution of (25/) gives, as heretofore, the best
value of sx . Among the target records of the international shoot-
ing match of 1874, at Creedmoor, there are 9 with lost shots, 5 of
which give too small an increase of sum of squares, and this means
that from the record of the hitting shots it would not appear prob-
able that so many shots were lost.
Instead of the squares, we may, however, employ first powers of
distances ; and I shall develop the requisite formulae for a circular
target and equal precisions.
We have [a\ A = nj s !£ e ^
= »( - Be -53 + =\t PtR
J
. (» - ng^R+w^Plg by (13)
[.!* + (»-»,) ^
If nR— n, this becomes e =
—
•*/^- (27)
The quantity r -13 -t ^- (28)
MATHEMATICAL SECTION. 145
which may be called the average shot, has been recently introduced
by the United States Ordnance Department, under the name
" radius of the circle of shots," in place of the extremely defective
quantity, the mean absolute deviation, the insufficiency of which
was pointed out by Henry Metcalfe, Captain of Ordnance, in the
Report of the Chief of Ordnance of 1882. Thus the adopted
method of discussion of the precision of firearms, as used by that
department, is in agreement with Liagre's theory, only the shots
are not referred to the true center, but to the " center of shots,"
viz. : their center of gravity.
We have, now, the following three quantities, each of which may
be used as a measure of precision, sighting and leveling being
equally good.
1, the even chance shot, p.
2, the most probable shot, s, (or mean error of sighting and lev-
eling).
3, the average shot, r , also called radius of the circle of shots
;
and they are related to each other as follows
:
The preceding formulae I regard as complete, for practical discus-
sion of target records, provided there is no evidence for a constant
vitiating cause. If, for example, during a shooting match the wind
is blowing constantly in the same direction, the effect of this might
be partially revealed by computing for the whole match the quan-
tity
:
*. =
—
.
(30)n v J
If the sign of this quantity is consistent with the observed direc-
tion of the wind, it might, perhaps, be proper to refer the shots to
a new center, to the right or left of the true center, by this quan-
tity. In that case we have, however,
hbr" (31)
In leveling there may be a somewhat constant individual habit
of holding too high or too low, which, however, ought not to be
eliminated in a fair discussion of a match, although it would be of
interest to compute the quantity
Jo n
for each marksman and for a whole team.
146 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Much less proper, it would seem to me, to regard the position of
the axes unknown, and to compute their most probable position. If
center and axes are to be determined, x' y' denote the co-ordinates
of a shot from a random origin and position of axes, and w the
angle of turning the latter into their most probable direction ; then
the most probable co-ordinates of a shot are
:
x= x + x' cos w -j- y
1
sin w ; y — y + yf cos w — x' sin w.
Imposing the conditions of a minimum for [V] and [t/2], we find
x = - — (O'] cos w + [y] sin wj ;
y = —— {bl cos w - [sT] sin w)
(33)
tan 2iv =
W]--M[!/]
[*'2l-^Y-bn + ~WY
(34)
These formulse have, however, their proper place in the theory of
Andne's " Fehler-ellipse."
Fig. 2 exhibits an ideal distribution of 45 shots. Each ring con-
tains 6 shots, leaving 3 shots between the outer ring and infinity.
The dotted circle is that of the most probable shot, and the dashed
one that of the even chance shot.
It&2.
The following table refers to the combined target record of the
Irish team at 800 yards range, in the international shooting match
of 1874. at Creedmoor :
MATHEMATICAL SECTION. 147
Irish Team at 800 yards: e = 1.3095//.; 90 shots, 88 hits.
Leveling limit
Radii
148 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Target of j)istol shots at 50 yards range: e = 0.167 jft. ; 50 shots,
no misses.
Radii.
mathematical section. 149
Eighth Meeting. December 5, 1883.
The Chairman presided.
Fourteen members and guests present.
Mr. Alvord discussed
A special case in maxima and minima,
the problem being to find the radius of the sphere that will displace
the maximum quantity of liquid from a conical wine glass full of
water.
The differential co-efficient, when put equal to zero, is in the form
of two factors. Equating each to zero, one gives the radius of the
maximum sought; the other gives a still larger radius, which proves
to be the radius of the sphere just tangent to the centre of the base
of the cone, and to the sides of the cone, extended upwards. This
gives the minimum displacement equal to zero. Calling a the
radius of the base, b the height, and c the slant height of the cone,
theradius of the sphere producing maximum displacement equals
, —\7o—
T
—\ J the radius corresponding to minimum displace-
. ab
ment equals
^ e — a.
When the radius is still greater, the sphere does not reach the
surface of the liquid, but displaces an imaginary quantity of the
same. An analytical expression for this case was sought in vain
;
the result above is simple, and no square root of a negative
quantity appears. By some de.vice in the mode of investigation,
this imaginary case might appear, as in the question to obtain the
radical axis of two circles, discussed by Salmon.
Mr. Kummell suggested that the close relation between the
circle z2 + y
1 = R2 and the equilateral hyperbola x2 — y2= R2 , each
of which could be regarded as an imaginary branch of the other,
might help us to understand many of such difficulties. He showed
that the radical axis of two circles not intersecting was the com-
mon chord of two equilateral hyperbolas whose major axes were
those diameters of the circles which lie in the same straight line.
Mr. Elliott read a communication on
A FINANCIAL PROBLEM,
in which he gave formulae for calculating the advantage of in-
150 PHILOSOPHICAL SOCIETY OF WASHINGTON.
vestment in United States Government bonds, at six or at four per
cent., and making use of the banking privileges thus available,
over investment at a higher rate without such privileges. The
restrictions caused by the high premium on Government bonds, the
bank tax, and the necessary specie reserve were all allowed for.
This paper was discussed by Messrs. HaPvKNESS, De Land,
Smiley, and others.
Mr. H. Farquhar presented the following
FORM OF LEAST-SQUARE COMPUTATION.
Suppose four unknown constants, A, B, C and D, are to be cal-
culated from equations of condition of the form
aA + bB + cC + dD = y.
Arrange columns in order (l)a2
,
(2)ab, (3)ae, (4) ad, (5) ay,
(6) b\ (7) be, (8) bd, (9) by, (10) c\ (11) cd, (12) cy, (13) d\ (14) dy
Add up first five columns and place under (2) to (5) the quotients
of their sums divided by -(1).
v(2") v(2) 2(2')
Put the product -^jC 2(2) under (6), j^j^(3) under (7),^ i"(4)
vf2i v(3*) ~(3")
under(8),^2-(5)under(9),tvr^^(3) under (10),j^J(4) under
(11), wj-^ 2(5) under (12),^ ^(4) under (13), and ^f 2(5) under
(14), reversing the sign in every case.
Then add up (6) to (9), placing under the sums of (7) to (9)
their quotients divided by -'(6).
I'd) 2'(7)
Put the product ^ 2'(7) under (10), ygC 2(8) under (11),
|^U'(9) under (12, f^^(8) under (13), and |^^(9) under
(14), reversing each sign.
r'(ll) , ^(12)
Add (10) to (12), putting quotients Wnm and 2%0) un
the sums.
win 2'(11)]
Put the product^^'(ll) under (13) and yrfrffiW) ™-
der (14), reversing the signs.
MATHEMATICAL SECTION. 151
I'"(14)
Add (13) and (14) ; when iprhm = D.
-"(12) -"(ll)
Then, under (12), enter v"(i;n —
,
y/,
-j^ D = C.
^(9) -V8) -'(7)
Next, under (9), enter v^q — yr~Q\ D — ^Tg^ = B-
2"(5)
-(4) -(3) -(2)
Lastly, under (5), enter WT\— vyT\D — vTpvC — WT\^ ==J^
Notes.—[1] The sign of summation is distinguished by an ad-
ditional stroke for every additional quantity introduced under the
column added up.
[2] These additional quantities, under the columns of squares,
(6), (10), and (13), will evidently all be negative.
[3] This form may be extended to any number of unknown
quantities, by insertion of ae, etc., between (4) and (5), be, etc.,
between (8) and (9), and so on. Modifications where there is a
smaller number of unknown constants, and where one of them has
the coefficient always unity, will be obvious.
[4] One of the quantities a, b, etc., will, in many computations,
be zero when another one is significant, and vice-versa ; as when one
unknown quantity changes in the course of a series of observations.
In this case we may save some columns by arranging our equation
thus : a
x
A
x
+ a* A2 + b B + etc. == y (where av a2 — 0, always).
Here two sums are found under columns (1) to (5), two quotients
under (2) to (5), and two additional quantities placed under each of
the other columns before they are summed up. The remainder of
the work then proceeds as before, except that the last step will be
duplicate.
[5] It will be found advisable always to make -a, Sb, etc., as
nearly zero as possible, so that the products will be smaller and
there will be less danger of error.
[6] The computation is to be checked by applying A, B, etc.,
and finding the residuals of y. Then 2 (a Ay), I {a a6), etc., should
all be zero.
[7] Where but two unknown quantities are to be found, one of
them with the constant coefficient unity (as A -j- b B = y), other
methods will usually be preferable. Two of these will be given.
I. If the values of b are symmetrical, so that b = ft ± b\, ft ± b\,
P rh &'3) etc., here all that is necessary to find B is to subtract the
152 PHILOSOPHICAL SOCIETY OF WASHINGTON!
value of y for every — U from that for /?
-f b', to multiply the
remainders by V, to find 2 (b'&y) and divide it by 2 2 (&"), when
the quotient will be B. If A should be wanted also—as is very
often not the case—then ly must also be found, and A =— — ,SB
n '
where n equals the number of equations.
II. In all cases we may obtain the required values by taking the
difference of b and of y from the mean of the column, multiplying
the residual by the former difference, thus forming columns of
( ~b\ 2 / Ib\ ( Iy\
v n) aud V ~ l^J \y ~ ~n) adding these and dividing
the second sum by the first. That is,
B=
J {(6
-^-f)} ;wheuA^_^B , •
Ninth Meeting. December 19, 1883.
The Chairman presided.
Sixteen members and guests present.
Mr. H. Farquhar furnished a
NOTE ON THE PROBLEM DISCUSSED BY MR. ALVORD,
in which he showed that the volume of a spherical segment of
height h,xh2 (R — q"^)> being real for all values of h, both positive
and negative, was to be interpreted for /i<^0 or Ii^>2R as the vol-
ume of the segment of the equilateral hyperboloid of two sheets
whose axes equal R; this volume being taken with a negative sign.
It was positive for negative values of h, since it must become zero
when h = by negative increments ; hence the minimum of the
function when A = in such problems as the one discussed.
Mr. Doolittle read a communication on
THE REJECTION OF DOUBTFUL OBSERVATIONS.
[Abstract.]
For the purposes of this discussion we may divide errors into
MATHEMATICAL SECTION. 153
two 'grand classes, and name them, from their consequences, instruc-
tive errors and uninstructive errors. The latter class includes blun-
ders in recording, pointing on wrong objects, &c. The former con-
sists of errors that indicate error in other observations.
I once tried the experiment of dropping a short straight piece of
wire five hundred times upon a sheet of ruled paper and counting
the number of intersections of the wire with a ruled line. When
the end of the wire touched or nearly touched a line, and inter-
section was doubtful, I counted it as half an intersection. I re-
corded the number of intersections in groups of fifty trials, as fol-
lows : 23, 26, 28.5, 24, 31.5, 28, 27, 14, 25, 28.5. These numbers
may be regarded as observations from which may be deduced the
probable ratio of the length of the wire to the distance between
two consecutive lines ; and it seems impossible to account for the
remarkable smallness of the eighth number by any supposition of
uninstructive error. It is almost certain that a ratio deduced from
it alone is largely in error ; but it indicates that the other nine
observations are somewhat in error, and that its error is needed to
counterbalance theirs. If we retain it, and regard the mean of all
as the most probable truth, we infer that this observation is 11.55
units in error. If we reject it, and take the mean of the other nine
as the most probable truth, we infer that this observation is 12 5-6
units in error. It should be remembered that the rejection of an
observation does not sweep from existence the fact of its occurrence;
but merely increases its already large estimate of error. Because
an error of 11.55 units is so large as to be very improbable, shall
we therefore infer that an error of 12 5-6 units is more probable?
It seems very clear to me that the larger an instructive error is
the more instructive it is, and the more important is it that the
observation containing it should not be rejected. The mean of all
the ten above-described observations being regarded as the most
probable truth, any one of the other nine could be better spared
than the eighth. On the other hand, the larger an uninstructive
error is, the more important it is that the observation should be
rejected. Whenever an observation is intelligently rejected, there
is a comparison of two antecedent probabilities, viz. : that of the
occurrence of an instructive error of the magnitude involved and
that of the occurrence of an uninstructive error of the same mag-
nitude. When an error is evidently so large that it cannot possibly
belong to the instructive class, the antecedent probability of such
14
154 PHILOSOPHICAL SOCIETY OF WASHINGTON.
an instructive error is ; the antecedent probability of an unin-
structive error is always greater than ; and the observation should
certainly be rejected. But since the theory of least squares allows
no limit whatever to the possible magnitude of instructive errors,
such rejection involves the admission that the method of least
squares is not applicable to the case. When an observation involves
a merely suspicious error, which is neither so large that iustructive-
ness is impossible nor so small as to pass without question, it would
seem reasonable that the observation should be weighted according
to the relative magnitudes of the two antecedent probabilities
which I have mentioned ; but this can never be determined with
any approach to mathematical precision.
In order to make this matter clear, let us suppose for example
that ninety-nine observations of equal weight and known to be free
from uninstructive error are separately written on as many cards
;
that the number 25 is arbitrarily written on a similar card ; that
these hundred cards are thoroughly shuffled ; and that ten cards
being then drawn at random, the following numbers appear on
them : 15, 18, 14, 25, 17, 16, 15, 18, 16, 17. Let it be required to
determine from these data, according to the theory of least squares,
the probability that the number 25 on the fourth card drawn is the
record of an observation. Here the antecedent probability of an
uninstructive error is by hypothesis equal to 1-10.
I commence by assuming a value of the required probability,
and weight the doubtful observation accordingly. I then proceed
in the ordinary method and determine an approximation to the
antecedent probability of the occurrence of a genuine observation
giving the value 25 by integrating —— j e dt between the
limits corresponding to 24.5 and 25.5, since the observations are
taken to the nearest unit. This integral is the antecedent proba-
bility of an instructive error of the given magnitude, tainted with
the incorrectness of the assumption with which I began. Call this
integral -p. Then
,
is the resulting required probability. If
it agrees with my original assumption, the problem is solved. If it
does not agree, I have data for a better assumption according to the
well-known method of trial and error. After a few repetitions of
the process, as I have found by experiment, an assumption can be
made that will be verified by agreement with the result.
MATHEMATICAL SECTION. 155
In practical problems the antecedent probability of blunders and
other uninstructive errors is never known, and is only matter of
exceedingly vague conjecture. Perhaps if a very large number of
observations were examined, and the proportion of evidently unin-
structive errors ascertained, a somewhat intelligent estimate might
be made of the proportion of those that exist but are not evident
;
and data of some little value might be gathered toward a scientific
method of weighting. But I have no faith that the result would
be any where near worth the labor. At present, the best that a
computer can do is to reject entirely, or retain entirely, or assign
a simple weight, such as h, i, or I, in sheer desperation, and with
the feeling that his judgment is nearly or quite worthless. It would
be utter folly to assign weights upon a centesimal scale ; and it
would also be utter folly to conjecture au antecedent probability
and proceed accordiug to the method just set forth.
It is well known that the method of least squares gives very un-
trustworthy information in regard to the antecedent probability of
large instructive errors. In regard to the other antecedent proba-
bility required for an intelligent solution of the problem, it gives
no information whatever. So far as I can understand Prof.
Peirce's method of arriving at a criterion, he takes two probabili-
ties, both functions of probabilities of instructive error, and balances
them against each other. This procedure reminds me of what
sometimes happens in war, when two detachments of the same
army meet in the dark and fire into each other, each supposing the
other to belong to the common enemy. Prof. Peirce also seems to
me to violate the fundamental principle of the science of probabili-
ties, that probabilities must be independent in order that their
product shall equal concurrent probability.
If a computer resorts to the criterion when he feels that his own
judgment is worthless, and only then, the criterion is harmless
since it is of no importance whether a decision is made by a worth.
less judgment or a worthless criterion.
In the discussion that followed, Mr. A. Hall gave a brief account
of the literature of the criteria which have been proposed for the
rejection of doubtful observations. In addition to the criterion
proposed by Prof. Peirce, which had been discussed by Mr. Doolit-
tle, that of Mr. E. J. Stone was mentioned ; and also the proofs
of a criterion given by Chauvenet and Watson. The advocacy of
of Peirce's criterion by Gould, Winlock, Bache, Coffin, and Schott
156 PHILOSOPHICAL SOCIETY OF WASHINGTON.
was noticed, and also its criticism by Airy, Stdne, and Glaisher,
together with Glaisher's approval of De Morgan's method of
treating observations. In conclusion, Mr. Hall said :
The general result of what has been done in this matter appears
to be as as follows
:
Every one can devise a criterion that suits himself, but it will not
please other people.
Now there seems to be a good reason underlying this. The
attempt to establish an arbitrary and general criterion for the dis-
cussion and rejection of observations is an attempt to eliminate
from this work the knowledge and judgment of the investigator.
Such an attempt ought to fail, and it certainly will fail at length,
no matter by what personal influence it may be supported. It is
true that no proof has been given of the principle of the arith-
metical mean for a finite number of observations, such as the prac-
tical cases that always come before us ; but we assume this principle
as leading to the most probable result. When we depart from this
principle, it must be done, I think, for reasons that are peculiar to
each case, and there can be no better guide than the judgment of
the investigator. It may be said that if the criteria that have
been proposed be carefully managed they will do little harm, since
the result of the arithmetical mean will be altered very little ; and
in fact this is their chief recommendation. But by diminishing
the value of the real probable error the criteria give to the observ-
ations a fictitious accuracy and a weight they do not deserve.
The paper was also discussed by Messrs. Hill, Elliott, Far-
quhar, Woodward, and others, including Mr. James Main, a
visitor—all agreeing, on essential points, with Mr. Doolittle's view.
Mr. R. S. Woodward then discussed
THE SPECIAL TREATMENT OF CERTAIN FORMS OF
OBSERVATION-EQUATIONS.
[Abstract. ]
In a set of observation-equations whose type is
x -}- (t — t ) y — n = v with weight p,
in which t is an arbitrary constant, the same for each equation,
and in which the residuals, v, are supposed to arise solely from
errors in the observed quantities, n, it will be best to make
•
~ [rf
MATHEMATICAL SECTION. 157
This value of t makes the co-efficient of y in the first normal
equation and the co-efficient of x in the second normal equation,
zero, and hence gives directly
[p(t-t )n]
The weight of this value of x is a maximum ; i. e., the value of
x corresponding to i = j—=, has a greater weight than the value of
x correspondiDg to any other value of t .
The probable error of the function x
-f p-y is given by the simple
formula.
_______
A'. + A'
in which s^ and s
y
are the probable errors of x and y, respectively.
The investigation shows that, when several standards of length
are to be intercompared two and two, in order to obtain the length
of some one of them, it will be conducive to accuracy to have the
mean temperatures of the several sets of comparisons equal.
Remarks were made upon this communication by Mr. Kummell.
Mr. Alex. S. Christie made a communication on
CONTACT OF PLANE CURVES.*
[Abstract.]
Let = /(», y), (1), = <p(x, y), (2), and y = <f>(x), (3) be the
equations of plane curves. Transferring the origin to (I, >?), where
V = «K*)i writing /, <p for/l^, rj), p(£, v ), respectively, and ita for
1 8*f 1 fry
H!^'^ for^!^' wehave
from (l), =|°(££_. ? (^ ), (l^from (2),
+ ^J-f&c. (3')
* Throughout this paper, 5, for lack of sorts, is put for round d, and denotes
partial differentiation.
158 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Writing (3') in the form y= xwx + x2w2 + x3w3 + &c. (3")
V + 2
and assuming yv = xv(y ) -\- x (v2) -\- &c. (4)
Where (v ~) obviously equals tv^, and (vj, (v2), &c, are functions
V 1 fly V 1
of ?, 5j to be determined, we have, from (4), vy -^ = x v(yo)
+ af. v + 1. (yx) -L. / + \* + 2. (v.) + &c. (5)
from (3"), J[— of . 1 w, + a1 . 2 w2 + z2 . 3w3 + &c. (6)
from (3", 5), * tf>
.fx= ti> ( (v„) ,Wl) + * ((»>n+0O . .+1 . to,)
+ x
V
( (v6)vw3 + (v,) . v -f- 1 . w2 + (v2) . v + 2 . M>i) + &c.
from (4, 6), ty» . ^ = x*(y ) vw, + a ^(v > . 2w2 + (vx> . lwj j
+ re " ( (O v . 3w3 + (v,) v . 2w2 + (v8) m . lwj + &c.
•.• = (O . v - . v? + (vx) . — 1 . wl
= (O . 2v - . r«3 + 00 . v- 1 . w2 + (va) . - 2 . w1
= (O . 3v - . w4+ (»0 . 2v - 1 . w3 + 2) . y-2 . w,
+ (v3) . - 3 . w1 '
= <>o) • mv — . tvm + x+ 0,) . (m — 1) v — 1 . wm
+ (v2) . (« - 2)v - 2 . u^-H-CO . (» - 3).-3 . wm _,
+ ••• + Om) • — m . wx
MATHEMATICAL SECTION. 159
O © O
o o o
©
X
J w l © ©
O II
I I
^ CO
-a
©
160 PHILOSOPHICAL SOCIETY OF WASHINGTON.
which determines the coefficients in (4). (*) Putting u
t3
for
1 f+s
rl, si, d?6rt
r, we have j t~v ~ (xTut) = x" ( (v ) uQV)+x ((v ) ux„V'., Ofj Q
v+ 2
+ Oi) wo") + x ( (vo) u%v + Oi) uxv + (ya) uQV) + &c, and this in
(1') gives an equation of the form
= a? A + xl A, + x2 A 2 + a? A3 + &c. (8)
viz: = a? [(0 ) uj + xl [(0 ) m10 + (0,) u00 + (1 ) «oi]
+ as8 [(0 ) w20 + (00 m10 + (02) «w+ (1 ) wu + (l x)%+ (2 )O
+ «" [(0 ) «30+ (Ox) Mso+ (02 ) uw+ (03) iCo,, + (1 ) un+ (1, ) «u
+ (1 2 ) m01 + (2 ) u12 + (2X ) «02 + (3 ) w03] + &c. (8')
for the abscissae of points common to (1) and (3). Similarly for
the abscissae of points common to (2) and (3) we get an equation
of the form
= x° B + xl B
x
+ x2 B.2 + x
z B.
s + &c. (9)
viz : = x° [(0 ) t>00] + rf [(0 ) v10 + (0L) vm + (1 ) t>01] + &c. (9')
Let (2) contain at least p parameters, enabling us to pass (2)
through jo of the intersections of (1) with (3). When this is done
we have the equation = x° (A — BQ) + x 1 (A x— Bx) + x2 (A 2—B2)
-f &c. (10) true for the p values of x corresponding to the p points
common to (1), (2), (3). Let the p common points move to the
origin, (10) must have p roots equal zero, that is, = A —
B
,
= A
1
-B
1,0 = A.i -B2,...0= A p - 1 -Bp -
}
(11)
If we suppose (3) the parabolic representative of (1), x in (8)
becomes indeterminate, and hence besides = A we have also
= Av = A2, &c.
that is, = /, with
= d$~T~ did,]
1 &f
— -v
2 <J|2
1 &f
dtj 82 f , 1 d2rj df
+ L(<kV2! \d$)
d=<T^ri^ 2
1 dr, <ff
+
<?f 1 dr, d2 r, d2f
df2^+ 2 \d=) 'V
1 d2n <T'f , 1 d
3
rj8f
+ S!l/7i3 (12)
5*V^ 2!
&c. &c. &c.
* Putting x = I in (3
//
) and (4), we obtain the multinomial theorem in the form
(w, -\- w2 + wa + &c.)" == (v ) + fo) + (v2) + &c.
MATHEMATICAL SECTION. 161
drj (Prj d3
^
equations fully determining -rz , -yz? . j^ , &c., m terms or the
partial derivatives of /.
Again, suppose (3) the parabolic representative of (2), then
s«s B , with = Bv = B2 , &c, and consequently by (11) = A ,
with = Av = A 2 , . . . 0~Ap — 1 , or the first p— 1 of the
equations (12) are satisfied indifferently whether the -rz , p,...
dp~ l r, , .
i^p _i therein contained be derived from (1) or (2) ; that is, we
have arrived at Lagrange's conditions for contact of the (p — 1)
order, as a consequence of p - punctual contact ; and it follows at
once that the distance between two curves in the neighborhood
of a p - tuple common point is of the pth order when the distance
along the curves from the p • tuple point is of the 1st order.*
Note.
The abstracts of communications to the Mathematical Section
have each been examined by a special committee, consisting of the
Chairman, the Secretary, and a third member appointed by the
Chairman. These third members were as follows
:
Title. Author. Third Member.
Alignment Curves on any Surface C. H. Kummell. A. S. Christie.
The Mass of a Planet from Observa-
tions of two Satellites A. Hall. W. B. Taylor.
Infinites and Infinitesimals M. H. Doolittle. G. W. Hill.
Planetary Perturbations of the Moon_.G. W. Hill. E. B. Elliott.
The Law of Error practically tested
by Target-Shooting C. H. Kummell. A. S. Christie.
Form of Least-Square Computation H. Farquhar. R. S. Woodward.
Rejection of Doubtful Observations M. H. Doolittle. W. C. Winlock.
Special Treatment of certain forms of
Observation-Equations R. S. Woodward. W. C. Winlock.
Contact of Plane Curves A. S. Christie. C. H. Kummell.
* This paper will be continued.
CORRIGENDA.
Vol. V, p. 86, line 2. For " abused " read absurd.
« ' « " 7. For " east " read earth.
16:
INDEX.
Abbe, Cleveland: communication on Deter-
mining the temperature of the air 24
: report as Treasurer xxii
Address of the Chairman of the Mathemat-
ical Section 117
President xxv
Action of the International Geodetic Asso-
ciation as to an initial meridian and uni-
versal time 10G
Activital evolution xlvii
Agricultural college grants 100
Ague, The conservative function of 5
Air, Determining the temperature of the, 24, 46, 47
Alaska, Glaciation in 33
—, Humidity of 36
Alignment curves on any surface, with
special application to the ellipsoid 123
Alvord, Benjamin: communication on a
special case in maxima and minima 149
: remarks on agricultural college grants 106
glaciation in Alaska 35
Smithsonian funds invested in
Arkansas bonds 105
Analogues in zoo-geography 41
Announcement of death of B. F. Sands 41
C. H. Crane 41
Elisha Foote 48
Josiah Curtis 41
L. D. Gale 48
R. D. Cutts Ill
election to membership of Albert
Williams, Jr 14
CD. Walcott 48
D. E. Salmon Ill
E. C. Morgan 87
E. S. Burgess 28
H. F. Walling 14
J. H. Renshawe 14
J. M. Browne Ill
J. O. Skinner 36
R. S. Woodward 14
S/F. Emmons 33
S. H. Bodfish 28
T. C. Chamberlin 36
Thomas Russell 10
W. C. Kerr 33
W. T. Sampson 36
filling of vacant offices 41
invitation to Anthropological and Bio-
logical Societies 87, 98
Page.
Announcement of new rules concerning pa-
pers read before sections 38
organization of Mathematical Section.. 28
summer vacation 39
Anthropic evolutiou xlvii
Antisell, Thomas: inquiry concerning Ha-
waiian Islands 14
: remarks on meteorologic stations 47
: report of Auditing Committee 5
Aphapsis 133
Appalachian region, Geology of 31
Arithmetic, Binary 3,38
Arkansas bonds 105
Articulation by the corfgenitally deaf... 76, 78, 84
Astronomy (see Mars, Perturbation, Saturn,
Venus.)
Attraction xxviii, xxxii, xxxix
Auditing Committee, Appointment of. Ill
, Report of 5
Baker, Marcus : letter to Mathematical Sec-
tion 122
Balfour memorial fund 5
Bates, H. H. : communication on the nature
of matter 5
Beaches, Ancient, of the Hawaiian Islands.. 13
Bede, : cited on the miraculous cure of
dumbness 54
Bell, A. G. : communication on Fallacies con-
cerning the deaf, and the influence of
such fallacies in preventing the amelio-
ration of their condition 48, 84
: remarks on determining the tem-
perature of the air 47
Bibliography of medallic medical history ... 40
Billings, J. S. : remarks on the prevention of
malarial diseases 10
Binary arithmetic 3, 38
Biotic evolution xlv
Black bulb thermometer 25
Black drop, The, a spurious phenomenon 23
Bodfish, S. H., Election to membership of.... 28
Brachisthode, The 124
Browne, J. M., Election to membership of..... Ill
Bulletin of the General Meeting 1
Mathematical Section 113
— , Rules for the publication of the xiii
Bulwer, John: cited on the instruction of
deaf-mutes 54
Burgess, E. S., Election to membership of.. 28
163
164 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Burnett, S. M.: communication on Refraction
in the principal meridians of a triaxial
ellipsoid ; regular astigmatism and cylin-
drical lenses 4
The character of the focal
lines in astigmatism 45
Calendar, Perpetual 135
Cambrian system, The, in the United States
and Canada 98
Cape Hatteras, Geology of. 28
Certain possible abbreviations in the com-
putation of the long-period perturbations
of the moon's motion due to the direct
action of the planets 136
Chamberlin.T. C, Election to membershipof, 36
Character of the focal lines in astigmatism.. 45
Chemistry (See Explosive Eruption, Specific
Gravity.)
Chickering, J. W. : communication on The
thermal belts of North Carolina 11
Christie, A. S. : communication on A quasi
general differentiation 122
Contact of plane curves 157
: remarks on infinitesimals 135
Clarke, F. W.: remarks on volcanic ex-
plosions 93
Climate, Response of, to variations in solar
radiation 10
Coal, Origin of 28
Committee, Auditing, Appointment of. Ill
, Report of 5
—, General, Constitution and duties of the., vii
ix, x, xi
, Members of the xiv, xv
— on Communications, Constitution and
duties of the xii
, Members of the xiv, xv
Publications, Constitution and duties
of the xii, xiii
, Members of the xiv, xv
Committees on Mathematical Papers 135, 161
Computation, Least-square 150
— of lunar perturbations 136
Constitution vii
Contact of plane curves 157
Correlation of Cambrian groups 98
Corrigenda 162
Crane, C. H., Death of xiv, 41
Criteria for the rejection of observations 155
Crova's hygrometer 36
Cultivation of the eucalyptus on the Roman
Campagna 36
Curtis, Josiah, Death of 41
Curves, Alignment 123
—, Contact of 157
Cutts, R. D. : communication on The action
of the International Geodetic Association
Page,
as to an initial meridian and universal
time 106
, Death of Ill
Dalgarno, George : cited on communication
with mutes 71
Dall, W. H., Announcement by 5
: communication on glaciation in
Alaska 33
: remarks on glaciers and solar heat, 11
Darwin's theory of the distribution of vol-
canoes 89,91
Deaf, Fallacies concerning the 48
Donudation and volcanism 91
Deposition of ore by replacement 32
Determination of the mass of a planet from
observations of two satellites 132
specific gravity of solids by the
common hydrometer 26
Determining the temperature of the air, 24, 46, 47
Differentials defined 134
Differentiation, A quasi general 122
Diorthode, The 123
Dismal Swamp 28,30
Distribution of the surplus money of the
United States among the States 103
volcanoes 87
Doolittle, M. H.: communication on Infinite
and infinitesimal quantities 133
Substance, matter, motion, and
force 14
The rejection of doubtful ob-
servations 152
: remarks on binary arithmetic 39
Doubtful observations, Rejection of 152
Drainage, system, The, and the distribution
of the loess in eastern Iowa 93
Dreams in their relation with psychology.... 37
Driftless region, Loess of the 96
Dumbness, Fallacies concerning 49,78
Dunes of North Carolina 29
Dutton, C. E.: communication entitled The
volcanic problem stated 87
on the Geology of the Hawaiian
Islands 13
: exhibition of views of the Hawaiian
Islands 10
: remarks on determining the tem-
perature of the air 48
Ennis' hypothesis 45
the separation of minerals by
density 27
Dynamic hypothesis, The, controverted xxx
Easter, Formulas for the computation of. 15
Eastman, J. R.: communication on The Flor-
ida expedition for observation of the
transit of Venus 21
INDEX. 165
Page.
Education of deaf mutes 77, 82, 86
Elevation and subsidence 31,92
— in Alaska 35
— in the Hawaiian Islands 13
Elliott, E. B.: communication entitled Form-
ulas for the computation of Easter 15
A financial problem 149
on Units of force and energy, in-
eluding electric units 137
: exhibition of perpetual calendar 135
: remarks on infinitesimals 135
the metric system 4
unification of time 110
Ellipsoid, Alignment curves on the 123
Emmons, S. F.: communication on Ore dep-
osition by replacement 32
,
Election to membership of. 33
Errors, Theory of 138
Eruption of lava 87
Evolution defined xlii
—, The three methods of. xxvii
Experiments in binary arithmetic 3,38
Explosive eruption discussed '..... 93
Exposure of thermometers 24, 46
Fallacies concerning the deaf, and the influ-
ence of such fallacies in preventing the
amelioration of their condition 48
Fan structure of mountains 31
Farquhar, Edward : communication on
Dreams in their relation with psychol-
ogy 37
—, Henry: communication on Experiments
in binary arithmetic 3
A form of least-square computa-
tion 150
Further experiments in binary
arithmetic 38
: election as Secretary of Mathematical
Section 122
: remarks on infinitesimals 135
Fault near Harper's Ferry 30
Ferrel's temperature formula 25
Finance (See Distribution).
Financial problem, A 149
Fletcher, Robert: communication on Recent
experiments on serpent venom 38
Florida expedition for observation of the
transit of Venus 21
Foote, Elisha, Death of 48
Force xxviii, xxxiii
Form of least-square computation 150
Formulas for the computation of Easter 15
Fossil leaves, Method of preservation of 30
Frozen soil of the arctic regions 34, 35
Further experiments in binary arithmetic... 38
Gale, L. D., Death of 48
Page.
Gallaudet, E. M. : remarks on fallacies con-
cerning the deaf. 77
Geikie, Archibald : cited on the division of
Paleozoic time 98
General committee (See Committee).
— Meeting, Bulletin of the 1
Geodesy (See Alignment).
Geodetic line, The 124
Geology of Hatteras and the neighboring
coast 28
the Hawaiian Islands 13
— (see also Cambrian, Drainage, Fault, Glaci-
ation, Ore, Volcanic).
Gesture language of the deaf.. 63, 66, 71, 75, 79, 84
Gilbert, G. K.: communication on Graphic
tables for computing altitudes from bar-
ometric data 136
The response of terrestrial
climate to secular variations in solar
radiation 10
: remarks on the drainage system of
eastern Iowa 97
Gill, T. N.: communication on Analogues in
zoo-geography 41
Ichthyological results of the
voyage of the Albatross 48
Glaciation and solar heat 10
— in Alaska 33
Glaciers classified 33
Graphic tables for computing altitudes from
barometric data 136
Gravitation, Explanations of. xxxii
Hall, Asaph: address as Chairman of the
Mathematical Section 117
: communication on The determination
of the mass of a planet from observations
of two satellites 132
: election as Chairman of the Mathe-
matical Section 122
— —: remarks on criteria for the rejection
of doubtful observations 155
Harkness, William: communication on The
monochromatic aberration of the human
eye in aphakia 4
: remarks on accidental and constant
errors 133
determining the temperature of
the air 26
hygrometric observations 36
the postulation of continents to
support hypotheses
Harper's Ferry, Fault near 30
Hatteras, Geology of Cape 28
Hawaiian Islands, Geology of the 13
, Views of the 10
Hazen, H. A.: communication on Hygromet-
ric observations 36
166 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Hazen, H. A. : communication on Thermo-
meter exposure 46,47
Hilgard, J. E.: organization of the Mathe-
matical Section 121
: remarks on the unification of longi-
tudes and time 1°9 I
Hill, G. W.: communication on Certain possi-
ble abbreviations in the computation of
the long-period perturbations of the
moon's motion due to the direct action
of the planets 136
: remarks on infinitesimals 135
—, Moritz: cited on natural language 80
the education of deaf mutes 78
value of sign language to the
deaf 8°. 85
Homophenes 57 > 76
Hough, F. B.: communication on the culti-
vation of the Eucalyptus on the Roman
Campagna 36
Hubbard, G. G.: remarks on fallacies con-
cerning the deaf. - 82
Humidity observations 36
— of Alaska 36
Hydrometer determination of the specific
gravity of solids 26
Hygrometer observations 36
Hypothesis, Utility ot, in science xxxiii
Ichthyological results of the voyage of the
Albatross 48
Idiots, Dumbness of 50, 83
Illinois, Loess hills of 97
Inaugural address of the Chairman of the
Mathematical Section 117
Infinite and infinitesimal quantities 133
Initial meridian, Universal 106
Intermarriage of deaf mutes 74, 76,83
Intermittence of volcanoes 91
International Geodetic Association 100
Invitation to Anthropological and Biological
Societies 8?
Iowa, Loess of eastern 93
Kerr, W. C: communication On the geology
of Hatteras and the neighboring coast .. 28
, Election to membership of. 33
Kinematic hypothesis, The xxviii
King, A. F. A. : communication on The pre-
vention of malarial diseases, illustrating,
inter alia, the conservative function of
ague.
Knox, J. J.: communication on The distri-
bution of the surplus money of the
United States among the States 103
Kotzebue Sound ice cliffs 34
Kummell, C. H.: communication on Align-
Page
ment curves on any gurface, with spec-
ial application to the ellipsoid 123
The theory of errors practi-
cally tested by target shooting 138
: remarks on consequences of the re-
lation of the circle to the equilateral hy-
perbola 149
infinitesimals 135
refinement in the determina-
tion of the temperature of the air 26
Lavas of the Hawaiian Islands 13
Lee, William : communication entitled
Sketches from medallic medical history 39
Leadville ore deposits 32
Least-square computation 150
l.efavour, E. B. : remarks on infinitesimals... 135
Liagre's theory 139
List of members xvi
Loess of eastern Iowa 93
Longitudes, Unification of 106
McCullough, Hugh : remarks on money de-
posited by the United States with the
State of Indiana 106
McDowell, Silas : cited on thermal belts of
North Carolina 11,12
McGee, W J : communication on The drain-
age system and the distribution of the
loess of eastern Iowa 93
Malarial diseases, Prevention of. 5
Mallery, Garrick: election as Vice-president 41
Mallet's theory of volcanism 90
Marriage of deaf mutes 74,76,83
Mass of planets, Determination of 132
Mathematical Section, Address by Chair-
man of the 117
, Bulletin of the 113,121
, Committee of the 135, 161
, Members of the 116
, Officers of the 122
.Organization of the 28, 121
, Rules of 115, 135
Mathematics (see Arithmetic, Formulas, Math-
ematical Section.)
Matter, Combination of xxxv
Maxima and minima 149
Medallic medical history 39
Melanosis, Malarial 7
Members, List of xvi
— of the Mathematical Section 116
Meridian, Universal initial 106
Metamorphic deposits 32
Metamorphism and subsidence 93
Meteorology (see Climate, Humidity, Hygro-
meter, Temperature, Thermal, Thermome-
ter.)
INDEX. 167
Page.
Metric system discussed 4
Minerals, Separation of, by density 26
Modes of motion xxxviii
Moon's motion, Pertubations of the 13G
Morgan, E. C, Election to membership of ... 87
Mosquito, Inoculation by the 7
Motion, Modes of xxxviii, xli
Munroe, C. E. : communication on the De-
termination of the specific gravity of
solids by the common hydrometer 26
Mutes, Fallacies concerning 49,78
Natural language 64, 70, 75, 79
Nature, The, of matter 5
Nebular hypothesis and volcanic eruption... 87
not discredited by Saturnian and Mar-
tial periods 45
North Carolina, Geology of 28
, Thermal belts of 11
Notation, New arithmetic 3, 38
Note on the rings of Saturn 41
Observation-equations 156
Observations, Rejection of doubtful 152
Officers of the Mathematical Section 28, 122
Society xiv, xv
Ore deposition by replacement 32
Peat beds of North Carolina 28
Periapsis 183
Periods, Saturnian 43
Perpetual Calendar 135
Pertubations, Lunar 136
Physical evolution xliii
Picture language 84
Porter, Sarah : cited on the use of signs by
deaf-mute children 81
Powell, J. W. : address as President xxv
: remarks on the drainage system
of eastern Iowa 97
loess of western Illinois 97
volcanic eruption 92, 93
President's annual address xxv
Prevention of malarial disease 5
Proorthode, The 123
Quasi general differentiation, A 122
Recent experiments on serpent venom 38
Rejection of doubtful observations 152
Renshawe, J. H., Election to membership of, 14
Replacement in ore deposition 32
Report of the Treasurer xxi
— of Auditing Committee 5
Response, The, of terrestrial climate to va-
riations in solar radiation 10
Page.
Riley, C. V., Election of, as member of the
General Committee 41
Rings of Saturn 41
Rules for the publication of the Bulletin xiii
—
,
New, on papers read before sections 38
—
,
Standing, of the General Committee xii
Mathematical Section 115
Society ix
Russell, Thomas, Election to membership of, 10
Salmon, D. E., Election to membership of.... Ill
Sampson, W. T., Election to membership of, 36
Sands, B. F., Death of 41
Saturn's rings 41
"Science" to report the scientific proceed-
ings of the Society 5,122
Seismographic record obtained in Japan 38
Shelters for thermometers 4G
Sibscota, George : cited on the cause ofdumb-
ness 49
Sign language of the deaf 63, 66, 71, 75, 79, 84
Sketches from medallic medical history 39
Skinner, J. O., Election to membership of.... 36
Smith, Edwin : communication on a Seismo-
graphic record obtained in Japan 87
Smithsonian investment 105
Solar radiation in its relation to climate 10
Sound velocity as a measure of air tempera-
ture 47
Speech and thought 53, 81
— reading by the eye 56, 60, 70, 76, 78, 84
Special case, A, in maxima and minima 149
— treatment of certain forms of observation-
equations 156
Specific gravities, Determination of. 26
Standard time 106
Standing rules (See Bules).
Substance, matter, motion, and force 14
Surplus money, Distribution of 103
Survival of the fittest, not the law of an-
thropic evolution xlvii, lii
Taylor, W. B. : communication entitled Note
on the rings of Saturn 41
: remarks on binary arithmetic 4
designation of apsides 133
infinitesimals 135
thermometrie observation 47
Target shooting 139
Temperature of the air 24, 46, 47
The theory of errors practically tested by
target shooting 133
The thermal belts of North Carolina 11
Thermometer exposure 24, 26
Thought and speech 53, 81
Three methods, The, of evolution xxvii
Topographical indications of a fault near
Harper's Ferry 30
168 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Transit of Venus 21
Treasurer's annual report xxii
— accounts for 1882, Report of Auditing
Committee on the 5
Unification of longitudes and time 106
Units of force and energy, including electric
units 137
Universal time 106
Velocity of sound as a measure of air tem-
perature 47
Venus, Transit of 21
Volcanic problem, The, stated 87
Walcott, C. D. : communication on The Cam-
brian system in the United States and
Page
Canada * 98
, Election to membership of 48
Walling, H. P.: communication on Topo-
graphical indications of a fault near Har-
per's Ferry 30
, Election to membership of 14
Ward, L. F. : remarks on Dismal Swamp 30
Water, a factor in volcanic eruption 87
White, C. A. : remarks on the drainage sys-
tems of Iowa 97
instability of continents.... 93
Williams, Albert, Jr., Election to member-
ship of. 14
Woodward, R. S. : communication on the
Special treatment of certain forms of ob-
servation-equations 156
, Election to membership of. Ill
BULLETIN
PHILOSOPHICAL SOCIETY
WASHINGTON.
VOL. VII.
Containing the Minutes of the Society and of the Mathematical
Section for the year 1884.
PUBLISHED BY THE CO-OPERATION OF THE SMITHSONIAN INSTITUTION.
15
WASHINGTON
1885.

CONTENTS
Page.
Constitution
.
vn
Standing Rules of the Society ix
Standing Rules of the General Committee XII
Rules for the Publication of the Bulletin xrn
Officers elected December, 1883 xiv
Officers elected December, 1884 xv
List of Members, corrected to December 31, 1884 xvi
Calendar xxir
Annual Report of the Secretaries xxin
Annual Report of the Treasurer xxiv
Annual Address of the President, J. C. Welling xxix
Bulletin of the General Meeting 1
The Rochester (Minnesota) tornado, J. R. Eastman 3
Recent advances in our knowledge of the limpets, W. H. Dall. 4
The existing glaciers of the High Sierra of California, I. C.
Russell 5
The mica mines of North Carolina, W. C. Kerr 9
Recent advances in economic entomology, C. V. Riley 10
Why the eyes of animals shine in the dark, S. M. Burnett 13
Some eccentricities of ocean currents, A. B. Johnson 14
The periodic law of chemical elements, F. W. Clarke 15
The sun-glows, H. A. Hazen 17
The application of physical methods to intellectual science, R.
D. Mussey 18.
Deposits of volcanic dust in the Great Basin, I. C. Russell 18
Some physical and economic features of the upper Missouri sys-
tem, Lester F. Ward 20
The diversion of water courses by the rotation of the earth, G.
K. Gilbert 21
The relations between northers and magnetic disturbances at
Havana, G. E. Curtis, {Titleonly) 25
Composite photography applied to craniology, J. S. Billings.
_
25
Fisheries exhibitions, G. B. Goode, (Titleonly) 26
Music and the chemical elements, M. H. Doolittle 26, 27
Review of the theoretical discussion in Prof. P. G. Tait's " En-
cyclopaedia Britannica" article on mechanics, H. Farquhar. 29
A new meteorite, J. R. Eastman 32
Certain appendages of the mollusca, W. H. Dall, (Title only). 32
III
IV CONTENTS.
The volcanic sand which fell at Unalashka, October 20, 1883,
and some considerations concerning its composition, J. S.
Diller 33
The methods of modern petrography, G. H. Williams' 36
"What is a glacier? [Symposium) 37
The physical basis of phenomena, H. H. Bates 40
The strata exposed in the east shaft of the water-works exten-
, sion, T. Robinson 69
Plan for the subject bibliography of North American geologic
literature, G K. Gilbert and J. W. Powell 71
Are there separate centres for light- form- and color-percep-
tion? S.M.Burnett 72
"Was the earthquake of September 19th felt in the District of
Columbia? T. Robinson 73
Natural naturalists, "Washington Matthews 73
Resolutions on the death of Dr. "Woodward 75
The volcanoes and lava fields of New Mexico, C. E. Dutton __ 76
Electric lighting, E. B. Elliott, {Title only) 80
Thermometer exposure, H. A. Hazen 80
Presentation of the annual address 81
Annual Meeting 81
Bulletin of the Mathematical Section 83
Standing Rules of the Section 85
Officers of the Section 86
Curves similar to their evolutes, C. H. Kummell 87
The problem of the knight's tour, G. K. Gilbert 88
Empirical formula? for the diminution of amplitude of a freely-
oscillating pendulum, H. Farquhar 89
A concrete jiroblem in hydrostatics, G. K. Gilbert 92
The formula? for computing the position of a satellite, A. Hall- 93
A formula for the length of a seconds-pendulum, G. "W. Hill,
(Title only) 101
A form of the multinomial theorem, A. S. Christie, (Title only). 101
Discussion of a concrete problem in hydrostatics proposed by
Mr. G. K. Gilbert, R. S. Woodward, (Title only) 101
The quadric transformation of elliptic integrals, combined with
the algorithm of the arithmetico-geometric mean, C. H.
Kummell 101,102
A case of discontinuity in elliptic orbits, W. B. Taylor 122
The verification of predictions, M. H. Doolittle 122
Memorial to Gen. Alvord 127
Committees on mathematical communications 129
Index 131
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
CONSTITUTION, RULES,
OFFICERS AND MEMBERS,
AND RKPORTS OF
SECRETARIES AND TREASURER.

CONSTITUTION
THE PHILOSOPHICAL SOCIETY OF WASHINGTON.
Article I. The name of this Society shall be The Philosophi-
cal Society of Washington.
Article II. The officers of the Society shall be a President,
four Vice-Presidents, a Treasurer, and two Secretaries.
Article III. There shall be a General Committee, consisting of
the officers of the Society and nine other members.
Article IV. The officers of the Society and the other members
of the General Committee shall be elected annually by ballot ; they
shall hold office until their successors are elected, and shall have
power to fill vacancies.
Article V. It shall be the duty of the General Committee to
make rules for the government of the Society, and to transact all
its business.
Article VI. This constitution shall not be amended except by
a three-fourths vote of those present at an annual meeting for the
election of officers, and after notice of the proposed change shall
have been given in writing at a stated meeting of the Society at
least four vjeeks previously.
vii

STANDING RULES
FOR THE GOVERNMENT OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The Stated Meetings of the Society shall be held at 8 o'clock
p. M. on every alternate Saturday ; the place of meeting to be
designated by the General Committee.
2. Notice of the time and place of meeting shall be sent to each
member by one of the Secretaries.
When necessary, Special Meetings may be called by the President.
3. The Annual Meeting for the election of officers shall be the
last stated meeting in the month of December.
The order of proceedings (which shall- be announced by the
Chair) shall be as follows :
First, the reading of the minutes of the last Annual Meeting.
Second, the presentation of the annual reports of the Secretaries,
including the announcement of the names of members elected since
the last annual meeting.
Third, the presentation of the annual report of the Treasurer.
Fourth, the announcement of the names of members who, having
complied with Section 13 of the Standing Rules, are entitled to vote
on the election of officers.
Fifth, the election of President.
Sixth, the election of four Vice-Presidents.
Seventh, the election of Treasurer.
Eighth, the election of two Secretaries.
Ninth, the election of nine members of the General Committee.
Tenth, the consideration of Amendments to the Constitution of
the Society, if any such shall have been proposed in accordance
with Article VI of the Constitution.
Eleventh, the reading of the rough minutes of the meeting.
ix
X PHILOSOPHICAL SOCIETY OF WASHINGTON.
4. Elections of officers are to be held as follows : '
In each case nominations shall be made by means of an informal
ballot, the result of which shall be announced by the Secretary
;
after which the first formal ballot sliall be taken.
In the ballot for Vice-Presidents, Secretaries, and Members of the
General Committee, each voter shall write on oue ballot as many
names as there are officers to be elected, viz., four on the first ballot
for Vice-Presidents, two on the first for Secretaries, and nine on the
first for Members of the General Committee ; and on each subse-
quent ballot as many names as there are persons yet to be elected
;
and those persons who receive a majority of the votes cast shall be
declared elected.
If in any case the informal ballot result in giving a majority for
any one, it may be declared formal by a majority vote.
5. The Stated Meetings, with the exception of the annual meet-
ing, shall be devoted to the consideration and discussion of scientific
subjects.
The Stated Meeting next preceding the Annual Meeting shall
be set apart for the delivery of the President's Annual Address.
6. Sections representing special branches of science may be
formed by the General Committee upon the written recommenda-
tion of twenty members of the Society.
7. Persons interested in science, who arc not residents of the Dis-
trict of Columbia, may be present at any meeting of the Society,
except the annual meeting, upon invitation of a member.
8. Similar invitations to residents of the District of Columbia,
not members of the Society, must be submitted through one of the
Secretaries to the General Committee for approval.
9. Invitations to attend during three months the meetings of the
Society and participate in the discussion of papers, may, by a vote
of nine members of the General Committee, be issued to persons
nominated by two members.
10. Communications intended for publication under the auspices
of the Society shall be submitted in writing to the General Com-
mittee for approval.
STANDING KTJLES. XI
11. Any paper read before a Section may be repeated, either
entire or by abstract, before a general meeting of the Society, if
such repetition is recommended by the General Committee of the
Society.
12. New members may be proposed in writing by three members
of the Society for election by the General Committee ; but no per-
son shall be admitted to the privileges of membership unless he
signifies his acceptance thereof in writing within two months after
notification of his election.
13. Each member shall pay annually to the Treasurer the sum
of five dollars, and no member whose dues are unpaid shall vote at
the annual meeting for the election of officers, or be entitled to a
copy of the Bulletin.
In the absence of the Treasurer, the Secretary is authorized to
receive the dues of members.
The names of those two years in arrears shall be dropped from
the list of members.
Notice of resignation of membership shall be given in writing to
the General Committee through the President or one of the Secre-
taries.
14. The fiscal year shall terminate with the Annual Meeting.
15. Members who are absent from the district of Columbia for
more than twelve months may be excused from payment of the
annual assessments. They can, however, resume their membership
by giving notice to the President of their wish to do so.
16. Any member not in arrears may, by the payment of one
hundred dollars at any one time, become a life member, and be
relieved from all further annual dues and other assessments.
All moneys received in payment of life membership shall be
invested as portions of a permanent fund, which shall be directed
solely to the furtherance of such special scientific work as may be
ordered by the General Committee.
STANDING RULES
OF THE
GENERAL COMMITTEE OF THE PHILOSOPHICAL
SOCIETY OF WASHINGTON.
1. The President, Vice-Presidents, and Secretaries of the Society
shall hold like offices in the General Committee.
2. The President shall have power to call special meetings of the
Committee, and to appoint Sub-Committees.
3. The Sub-Committees shall prepare business for the General
Committee, and perform such other duties as may be entrusted to
them.
4. There shall be two Standing Sub-Committees ; one on Com-
munications for the Stated Meetings of the Society, and another on
Publications.
5. The General Committee shall meet at half-past seven o'clock
on the evening of each Stated Meeting, and by adjournment at
other times.
6. For all purposes except for the amendment of the Standing
Rules of the Committee or of the Society, and the election of mem-
bers, six members of the Committee shall constitute a quorum.
7. The names of proposed new members recommended in con-
formity with Section 11 of the Standing Rules of the Society, may
be presented at any meeting of the General Committee, but shall
lie over for at least four weeks before final action, and the concur-
rence of twelve members of the Committee shall be necessary to
election.
The Secretary of the General Committee shall keep a chronologi-
cal register of the elections and acceptances of members.
8. These Standing Rules, and those for the government of the
Society, shall be modified only with the consent of a majority of
the members of the General Committee.
xii
IE^TTXjIES
FOR THE
PUBLICATION OF THE BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The President's annual address shall be published in full.
2. The annual reports of the Secretaries and of the Treasurer
shall be published in full.
3. When directed by the General Committee, any communication
may be published in full.
4. Abstracts of papers and remarks on the same will be pub-
lished, when presented to the Secretary by the author in writing
within two weeks of the evening of their delivery, and approved hj
the Committee on Publications. Brief abstracts prepared by one
of the Secretaries aud approved by the Committee on Publications
may also be published.
5. If the author of any paper read before a Section of the
Society desires its publication, either in full or by abstract, it shall
be referred to a committee to be appointed as the Section may
determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the Secretary of the Section, together with any
action of the Section taken thereon.
6. Communications which have been published elsewhere, so as
to be generally accessible, will appear in the Bulletin by title only,
but with a reference to the place of publication, if made known in
season to the Committee on Publications.
xiii
OFFICERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 22, 1883.
President J. C. WELLING.
Vice-Presidents J. S. Billings. Garrick Mallerv.
J. E. Hilgard. Asaph Hall.
Treasurer-* Cleveland Abbe.
Secretaries Henry Farquhar. G. K. Gilbert.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates. E. B. Elliott.
W. H. Dall. Robert Fletcher;
C. E. Dutton. William Harkness.
J. R. Eastman. J. J. Knox.
*
C. V. Riley.
STANDING COMMITTEES.
On Communications :
J. S. Billings, Chairman. Henry Farquhar. G. K. Gilbest.
On Publications :
G. K. Gilbert, Chairman. Cleveland Abbe. Henry Farquhar.
S. F BAIRDf
* Mr. Knox resigned May 10, 1884, and the General Committee elected Mr. F. W. Clark
to the vacancy.
+ As Secretary of the Smithsonian Institution.
XIV
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 20, 1884.
President ASAPH HALL.
Vice-Presidents J. S. Billings. GARRICK MALLERY.
William Harkness. J. E. Hilgard.
Treasurer Robert Fletcher.
Secretaries G. K. Gilhert. Henry Farquhar.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
Marcus Baker.
F. W. Clarke.
C. E. Dutton.
E. B. Elliott.
H. H. Bates.
W. H. Dall.
J. R. Eastman.
H. M. Paul.
C. V. Riley.
STANDING COMMITTEES.
On Commnuications :
J. S. Billings, Chairman. G. K. Gilbert. Henry Farquhar.
On Publications :
G. K. Gilbert, Chairman. Robert Fletcher. Henry Farquhar.
S. F. Baird.*
As Secretary of the Smithsonian Institution.
LIST OF MEMBERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
Corrected to December 20, 1884.
The names of founders are printed in Small Capitals.
(d) indicates deceased.
(a) indicates absent from the District of Columbia and excused from payment of dues
until announcing his return,
(r) indicates resigned.
NAME. P. O. Address and Residence. Date orAdmission.
Abbe, Cleveland
Abert, Sylvanus Thayer.
Adams, Henry
Aldis, Asa Owen
Allen, James
Alvord, Benjamin (d)
Antisell, Thomas
Avery, Robert Stanton...,
Army Signal Office. 2017 I St. N. W.
1724 Penn. Ave. N. W
1G07 H St. N. W
1765 AIis 6*. Ay©
Army Signal Office'.'" 'l907 i's't'.N.'w.'.
Patent Office. 1311 QSt. N. W
Coast and Geodetic Survey Office.
320 A St. S. E.
Babcock, Orville Elias (d).
Bailey, Theodoras (d)
Baird, Spencer Fullerton.
Baker, Frank..
Baker, Marcus.
Bancroft, George
Barnard, William Stebbins.
Barnes, Joseph K. (d)
Bates, Henry Hobart
Bean, Tarleton Hoffman
Beardslee, Lester Anthony (a).
Bell, Alexander Graham
Bell, Chichester Alexander
Ben£t, Stephen Vincent
Smithsonian Institution. 1445 Mass.
Ave. N. W.
326 C St. N. W
Coast and Geodetic Survey Office.
1205 Rhode Island Ave.
1023 II St, N. W., or Newport, R. I
.i (Agricultural Department. 917 N. Y.
Ave. N. W., or Canton, 111.
Bessels, Emil
Billings, John Shaw.
Birney, William
Birnie, Rogers (a)
Blair, Henry Wayne (d)..
Bodfish, Sumner Homer..
Boutelle, Charles Otis
Bowles, Francis Tiffany.
Brown, Stimson Joseph .
Browne, John Mills
Patent Office. The Portland
National Museum. 1411 R. I. Ave
Captain IT. S. N., Navy Department...
Scott Circle. 1500 R. I. Ave
1221 Conn. Ave
Ordnance Office, War Department,
1717 I St. N. W.
Smithsonian Institution. 1444 N St.
N. W.
Surg. Genl's Office, U. S. A. 3027 N
St, N. W.
450 Louisiana Ave. 1901 Harewood
Ave., Le Droit Park.
Cold Spring, Putnam Co., N. Y
Burchard, Horatio Chapin
Geological Survey. G05 F St. N. W....
Coast and Geodetic Survey Office.
1513 20th St. N. W.
18f!3 Jefferson Place
Naval Observatory. 2133 K St. N.W..
Medical Director, U. S. N. The Port-
land.
Director of the Mint. Riggs House..
XVI
1871
1875
1881
1873
1882
1872.
1871
1879
1871
1873
1871
1881
1876
1875
18S4
1871
1871
1884
1875
1879
1881
1S71
1875
1871
1879
1876
1884
1883,
1884,
1884,
1884.
1883,
Oct. 29
Jan. 30
Feb. 5
Mn r. 1
Feb. 25
Mar. 23
Mar. 13
Oct. 11
June 9
Mar. 1
Mar. 13
May 14
Mar. 11
Jan. 16
Mar. i
Mar. 13
Nov. 4
Apr. 26
Feb. 27
Mar. 29
Oct. 8
Mar. 13
Jan. 16
Mar. 13
Mar. 29
Mar. 11
Fob. 2
Mar. 24
Feb. 16
Mar. 29
Apr. 12
Nov. 24
1879, May 10
LIST OF MEMBERS. XVII
NAME. P. 0. Address and Residence. Date ofAdmission.
Burgess, Edward Sandford.
Burnett, Swan Moses
Busey, Samuel Clagett
Capron, Horace
Case, Augustus Ludlow (n).
Casey, Thomas Lincoln
High School. 810 12th St. N. W-
1215 I St. N. W
1525 I St. N. W
Caziarc, Louis Vasmer(a)
Chase, Salmon Portland (d)
Chamberlin, Thomas Crowder.
Chickering, John White, .Tr
Christie, Alexander Smyth
Clapp, William Henry (a).
Clark, Edward
The Portland
Bristol, R. I
Col. Corps of Engineers. 1419 K St.
N. W.
War Department
Clark, Ezra Westcote..
Clarke, Frank Wigglesworth
Coffin, John Huntington Crane.
Collins, Frederick (d)
Comstock, John Henry (a)
Coues, Elliott
Craig, Benjamin Faneuil (d)
Craig, Robert
Craig, Thomas (a)
Crane, Charles Henry (d)
Curtis, George Edward
Curtis, Josiah (d)
Cutts, Richard Dominicus (d) ....
Dall, William Healey ....
Davis, Charles Henry (d).
Davis, Charles Henry
Geological Survey
Deaf Mute College, Kendall Green...
Coast and Geodetic Survey Office.
G2S Mass. Ave. N. W.
Ft. Davis, Tex. 1416 Corcoran St.
Washington.
Architect's Office, Capitol. 417 4th
St. N. W.
Revenue Marine Bureau, Treasury
Department. Wood ley Road.
Geological Survey. 1425 Q St. N. W..
1901 I St. N. W
... ...
Cornell University, Ithaca, N. Y
Smithsonian Inst. 1726 N. St. N. W.
Army Signal Office. 1008 I St. N. W..
Johns Hopkins Univ., Baltimore, Md.
Army Signal Office. 1416 Corcoran St.
Care Smithsonian Institution.
12th St. N. W.
Dean, Richard Grain (a) ,
De Caindry, William Augustin.,
De Land, Theodore Louis...
Dewey, Frederick Perkins.
Dewey, George (r)
Diller, Joseph Silas
,
Doolittle, Myrick Hascall ...
Navy Department. 1705 Rhode Island
Ave. N. W.
Naval Hospital, New York
Commissary General's Office. 924
19th St. N. W.
Treasury Da»t. 120 7th St. N. E
National Museum. 1007 G St. N. W....
Dorr, Frederic William (d)
Dun\voody,HenryHarrison Chase(a)
Dutton, Clarence Edward.
Dyer, Ai.f.xander B. (d)
Geological survey
Coast and Geodetic Survey Office.
1925 I St. N. W.
Army Signal Office. 3012 Dumbarton
St., Georgetown.
Geological Survey
Earll, Robert Edward
.
Eastman, John Robie..
Eaton, Amos Beebe (d).
Eat <:'ii, John
National Museum
,
Naval Observatory. 1823 I St. N. W.
Limbeck, William
Eldredge, Stewart (a)
Elliot, George Henry (r).
Elliott, Ezekiel Brown...
Emmons, Samuel Franklin.
Bureau of Education, Interior Dept.
712 East Capitol St.
Coast and Geodetic Survey Office
Yokohama, Japan
Endlich, Frederic. Miller (a)
.
Ewing, Charles (d).
Ewing, Hugh (a)....
Government Actuary, Treasury De-
partment. 1210 G St. N. W.
Geological Survey. 23 Lafayette
Place.
Smithsonian Institution. Lake Val-
ley, New Mexico.
Farquhar, Edward.
16 '
Lancaster, Ohio
Patent Office'Library. 1915 H St. N.W..
1883, Mar. 24
1S79, Mar. 29
1874, Jan. 17
1871, Mar. 13
1872, Nov. 16
1871, Mar. 13
1882, Feb. 25
1871, Mar. 13
1883, Mar. 24
1874, Apr 11
1880, Dec. 4
1882, Feb. 25
1877, Feb. 24
1882, M;r. 25
1874,
1871,
1879,
1880,
1874,
1871,
1873,
1879,
1871,
18S4,
1874,
1871,
Apr. 11
Mar. 13
Oct. 21
Feb. 14
Jan. 17
Mar. 13
Jan. 4
Nov. 22
Mar. 13
Jan. 5
Mar. 28
Apr. 29
1871, Mar. 13
1874, Jan. 17
1880, June 19
1872, Apr. 23
1881, Apr. 30
18S0, Dec. 18
1884, Apr. 25
1879, Feb. 15
1881, Mar. 1
1876, Feb. 12
1874, Jan. 17
1873, Dec. 20
1872, Jan. 27
1871, Mar. 13
1884, Apr. 26
1871, Mav 27
1871, Mar. 13
1874, May 8
1884, Feb. 2
IsTl, June 9
1871, Mar. 13
1871, Mar. 13
1883, Apr. 7
1873, Mar. 1
1874, Jan. 17
1874, Jan. 17
1876, Feb. 12
XVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
NAME.
Farquhar, Henry.
Ferrel, William ...
Fletcher, Robert..
Flint, Albert Stowell.
Flint, James Milton
Footk, Elisha (d)
Foster, John Gray (d)
French, Henry Flags (»')•
Fristoe, Edward T
Gale. Leonard Dunnell (d).
Gallaudet, Edward Miner..
Gannett, Henry
Gardiner, James Terry (a)
Garnett, Alexander Young P. (r)..
Gihon, Albert Leary
Gilbert, Grove Karl ,
Gill, Theodore Nicholas...
Godding, William Whitney.
Goode, George Brown
Goodfellow, Edward
Goodfellow, Henry (r)
Gore, James Howard
Graves, Edward Oziel (a)
Graves, Walter Hayden (a)
Greely, Adolphus Washington-
Green, Bernard Richardson
Green, Francis Mathews (a)
Greene, Benjamin Franklin (a)
Greene, Francis Vinton
Gregory, John^Milton.
Gunnell, Francis M
Hains, Peter Conover
Hall, Asaph
Hall, Asaph, jr
Hanscom, Isaiah (d)
Harkness, William
Hassler, Ferdinand Augustas (a)...
Hayden, Ferdinand Vandeveer (a).
Hazen, Henry Allen
Hazen, William Babcock..
Heap, David Porter
Henry, Joseph (d)
Henshaw, Henry Wetherbee.,
Hii.gard, Julius Erasmus ,
Hill, George William..
Hitchcock, Romyn
Holden, Edward Singleton (a)
Holmes, William Henry
Hough, Franklin Benjamin (a)
Howell, Edwin Eugene (a)
Humphreys, Andrew Atkinson (d)...
Jackson, Henry Arundel Lambe (a)
Jnmes, Owen (a)
Jeffers, William Nicolson (r)
Jenkins, Thornton Alexander
P. O. Address and Residence.
Coast and Geodetic Survey Office.
Brooks Station, D. C.
Arrnv Signal Office. 471 C St. N. W...
Surgeon Genl's Office, U. S. A. 1326
L St. N. W.
Naval Observatory. 1450 Chapin St.,
College Hill.
Navy Dept. U. S. S. Albatross
1434 N St. N. W.
Deaf Mute College, Kendall Green...
Geological Survey. 1881 Harewood
Ave., Le Droit Park.
State Survey, Albany, N. Y
Naval Hospital, 2019 Hillyer Place
N. W.
Geological Survey. 1424 Corcoran St..
Smithsonian Institution
Government Asylum for the Insane.
National Museum. 1620 Mass. Ave.
N. W.
Coast and Geodetic Survey Office
Columbian Univ. 1305 Q St. N. W..
Asst. Treasurer U. S
Denver, Colorado
Army Signal Office. 1909 I St
1738 N St. N. W
Navy Department
West Lebanon, N. H
District Commissioners' Office, 1915
G St. N. W.
15 Grant Place
Surgeon General, U. S. N. 600 20th
St. N. W.
Ijf24 Jefferson Place.
Naval Observatory.
Naval Observatory.
2715 N St. N. W..
2715 N St. N. W..
Naval Observatory. 1415 G St. N. W.
Santa Ana, Los Angeles Co.. Cal
Geological Survey. 1803 Arch St., Phil-
adelphia, Penn.
P. O. Box No. 427. 1416 Corcoran St...
Army Signal Office. 1601 K. St. N. W..
Light House Board,Treasury Depart-
ment. 1018 Rhode Island Ave.
Bureau of Ethnology, P. O. Box 585...
Coast and Geodetic Survey Office.
1709 Rhode Island Ave. N. W.
Nautical Almanac Office. 314 Ind.
Ave. N. W.
P. O. Box 630
Madison, Wisconsin
Geological Survey. 1100 O St. N. W...
Agricultural Dept. Lowville, N. Y
Rochester N. Y
War Department..
Scran ton, Pa
2115 Penn. Ave. N. W.
Date or
Admission.
1881, May 14
1872, Nov. 16
1873, Apr. 10
18S2, Mar. 25
1881, Mar. 19
1871, Mar. 13
1873, Jan. 18
1882, Mar. 25
1873, Mar. 29
1874, Jan. 17
1875, Feb. 27
1874, Apr. 11
1S74, Jan. 17
1878, Mar. 16
1880, Dec. 18
1873, June 7
1871, Mar. 13
1879, Mar. 29
1874. Jan. 31
1875,
1871,
1880,
1874,
1878,
1880,
1879,
1875,
1871,
1875,
Dec. 18
Nov. 4
Mar. 14
Apr. 11
May 25
June 19
Feb. 15
Nov. 9
Mar. 13
Apr. 10
1884, Mar. 29
1879, Feb. 1
1879, Feb. 15
1871, Mar. 13
1880. Dec. 20
1873, Dec. 20
1871, Mar. 13
1880, May 8
1871, Mar. 13
1882, Mar. 25
1881, Feb. 5
1884, Mar. 15
1871, Mar. 13
1874, Apr. 11
1871, Mar. 13
1879, Feb. 1
1884, Apr. 26
1873, June 21
1879, Mar. 29
1879, Mar. 29
1874, Jan. 31
1871, Mar. 13
1875, Jan. 30
1880, Jan. 3
1877, Feb. 24
1871, Mar. 13
LIST OF MEMBERS. XIX
NAME.
Johnson, Arnold Bulges..
Johnson, Joseph Taber...
Johnson, Willard Drake..
Johnston, William Waring..
Kampf, Ferdinand (d)
Kauffmann, Samuel Hays
Keith, Keuel
Kerr, Mark Brickell
Kerr, Washington Caruthers (a)
Kidder, Jerome Henry
Kilbourne, Charles Evans (a)
King, Albert Freeman Africanus..
King, Clarence (r)
Knox, John Jay (a)
Kummell, Charles Hugo
Lane, Jonathan Homer (d).
Lawrence, William
Lawyer, Winfield Peter.
Lee, William
Lefavour, Edward Brown.
Lincoln, Nathan Smith...
Lockwood, Henry H. (r).
Loomis, Eben Jenks
Lull, Edward Phelps (a)..
Lyford, Stephen Carr (r).
MacCauley, Henry Clay (a)
McGee, W J
McGuire, Frederick Bauders.
Mack, Oscar A. (d)
,
McMurtrie, William (a).
Maher, James Arrau
Mallery, Garrick
Marcou, John Belknap
Marvin, Joseph Badger (a)
Marvin, Archibald Robertson (d)..
Mason, Otis Tufton
Matthews, Washington
Meek, Fielding Bradford (d)
Meigs, Montgomery (a)
Meigs, Montgomery Cunningham...
Merrill, George Perkins
Milner, James William (d)
Morgan, Ethelbert Carroll
Morris, Martin Ferdinand (r)
Murdoch, John
Mussey, Reuben Delavan.
Myer, Albert J. (d)
Myers, William (a)
Newcomb, Simon
Nichols, Charles Henry (a).,
Nicholson, Walter Lamb
Nordhoff, < 'harles
,
Norris, Basil
,
Ogden, Herbert Gouverneur.
Osborne, John Walter
P. O. Address and Residence.
Light House Board, Treasury Dept.
501 Maple Ave., Le Droit Park.
926 17th St. N. W
Geological Survey. 501 Maple Ave.,
Le Droit Park.
1603 K St. N. W
1000 M St. N. W
2219 I St
Geological Survey. 812 21st St. N. W.
Raleigh, N. C
Smithsonian Inst. 1816 N St., N. W...
War Department
720 13th St. N. W
Nat. Bk. Republic, New York City...
Coast and Geodetic Survey Office.
608 Q St. N. W.
First Comptroller's Office, Treasury
Department. 1344 Vermont Ave.
Mint Bureau, Treasury Department.
1912 I St. N. W.
2111 Penn. Ave. N. W
Coast and Geodetic Survey Office.
905 O St. N. W.
1514 H St. N W
Nautical Almanac Office. 1413 Col-
lege Hill Terrace N. W.
74 Cedar St., Roxbury, Mass
P. O. Box 953, Minneapolis, Minn
Geological Survey. 1424 Corcoran St,
1306 F St. N. W. 614 E. St. N. W
Champaign, 111
Geological Survey. 21 E St. N. W..„.
Bureau of Ethnology, P. O. Box 585.
1323 N St. N. W.
Geological Survey
Internal Revenue Bureau
National Museum. 1305 Q St. N. W..
Surgeon General's Office, U. S. A
U. S. Engineer Office, Keokuk, Iowa.
1239 Vermont Ave. N. W
National Museum
918 E St. N. W.
Smithsonian Institution. 1441Chapin
St., College Hill.
P. O. Box 618. 508 5th St. N. W ,
War Department..
Navy Department
Bloomingdale, N. Y.
1322 I St. N. W
1731 KSt
1829 G St. N. W
Coast and Geodetic Survey Office.
1324 19th St. N. W.
212 Delaware Ave. N. E_
Date of
Admission.
1878, Jan. 19
1879, Mar. 29
1884, Feb. 16
1873, Jan. 21
Dec. 18
Feb. 16
Oct. 29
Feb. 16
Apr. 7
May 8
June 19
Jan. 16
May 10
May 8
Mar. 25
1875,
1884,
1871,
1884,
1883,
1880,
1880,
1875,
1879,
1874,
1882,
1871, Mar. 13
1884, Feb. 16
1881, Feb. 19
1874, Jan. 17
1882, Dec. 16
1871, May 27
1871, Oct. 29
1880, Feb. 14
1875, Dec. 4
1873, Jan. 18
1880, Jan. 3
1883, Nov. 10
1879, Feb. 15
1872, Jan. 27
1876, Feb. 26
1884, Feb. 16
1875, Jan. 30
1884,
1878,
1874,
1875,
1884.
1871,
1877,
1871,
1884,
1874,
1883,
1877,
1884,
Mar. 29
May 25
Jan. 31
Jan. 30
June 7
Mar. 13
Mar. 24
Mar. 13
Apr. 26
Jan. 31
Oct. 13
Feb. 24
Apr. 26
1881, Dec. 3
1871, Mar. 13
1871, June 23
1871, Mar. 13
1872, May 4
1871, Mar. 13
1879, May 10
1884, Mar. 1
1784, Feb. 2
1878, Dec. 7
XX PHILOSOPHICAL SOCIETY OP WASHINGTON.
NAME. P. O. Address and Kesidejwe. Date of
Admission.
Otis, Geokge Alexander (d).
Parke, John Grubc
Parker, Peter..
Parry, Charles Christopher (a)..
Patterson, Carlile Pollock (a)....
Paul, Henry Martyn
Peale, Albert Charles
Engineer Kureau, War Department.
16 Lafayette Square.
2 Lafayette Square
Davenport, Iowa
Peale, Titian Ramsay (a)
Peirce, Benjamin (d)
Peirce, Charles Sanders (a)....
Pilling, James Constantine....
Poe, Orlando Metcalfe (a)
Poindexter, William Mundy..
Pope, Benjamin Franklin
Porter, David Dixon (r)
Powell, John Wesley
,
Prentiss, Daniel Webster
Pritchett, Henry Smith (a)..
Naval Observatory. 109 1st St. N. E..
Geological Survey. 1010 Mass. Ave.
N. W.
Philadelphia, Penn
Coast and Geodetic Survey Office
Geological Survey. 918 M St. N. W..
34 Congress St. West, Detroit, Mich..
701 15th St. N. W. 80fi 17th St. N. W.
Surgeon General's Office, U. S. A.
1309 20th St. N. W.
Geological Survey. 910 M St. N. W...
1224 9th St. N. W
Washington University, St. Louis, Mo.
Rathbone, Henry Reed (a)..
Rathbun, Richard
Ray, Patrick Henry ,
Renshawe, John Henry..,
Richey, Stephen Olin
Ricksecker, Eugene ,
Ridgway, Robert (a)
Riley, Charles Valentine..
Riley, John Campbell (d)
Ritter, William Francis McKnight.
Robinson, Thomas
Rodgers, Christopher Raymond
Perry (a).
Rodgers, John (d)
Rogers, Joseph Addison (a)
Russell, Israel Cook
Russell, Thomas
Salmon, Daniel Elmer
Sampson, William Thomas (a)....
Sands, Benjamin Franklin (d)....
Saville, James Hamilton
Schaeffer, George Christian (d).
Schott, Charles Anthony
Searle, Henry Robinson (d)...
Seymour, George Dudley (r).,
Shellabarger, Samuel
Sherman, John
Sherman, William Teccmseh (?-).
Shufeldt, Robert Wilson (a)
Sicard, Montgomery (a)...
Sigsbee, Charles Dwight..
Skinner, John Oscar
Smiley, Charles Wesley...
Smith, David..
Smith, Edwin.
Spofford, Ainsworth Rand.
Smithsonian Institution
Ave. N. W.
1622 Mass.
Army Signal Office
Geological Survey. 1221 O St. N. W..
732 17th St
Geological Survey. 1505 Q St. N. W..
Smithsonian Inst. 1214 Va. Av. S. W.
Agricultural Department. 1700 13th
St. N. W.
Nautical Almanac Office. 16 Grant
Place.
Howard University. 6th St. N. W.,
cor. Lincoln.
1723 I St. N. W
Naval Observatory
Geological Survey. 1424 Corcoran St
Army Signal Office. 1116 M. St. N. W
Agricultural Dept, 1006 N St. N. W...
Torpedo Station, Newport, R. I
342 D St. N. W. 1315 M St. N. W.
Coast and Geodetic Survey Office.
212 1st St. S. E.
Room 23 Corcoran Building. 812 17th
St. N. W.
1319 K St. N. W
Surgeon Genl's Office, U. S. A., or Box
144 Smithsonian Institution.
Ordnance Bureau, Navy Department.
Naval Academy, Annapolis, Md
1529 O St. N. W
U. S. Fish Commission, 1443 Mass.
Ave. 943 Mass. Ave.
1330 Corcoran St
Coast and Geodetic Survey Office.
2024 Hillyer Place.
Library of Congress. 1621 Mass. Ave.
N. W.
1871, Mar. 13
1871, Mar. 13
1871,
1871.
1871,
1877,
1874,
1871,
1871,
1873,
1881.
1873,
1884,
1882,
1874,
1874,
1880,
1879,
1874,
1N8'_\
Mar. 13
May 13
Nov. 17
May 19
Apr. 11
Mar. 13
Mar. 13
Mar. 1
Feb. 19
Oct. 4
De<\ 20
Dec. 16
Apr. 11
Jan. 17
Jan. 3
Mar. 29
Jan. 17
Oct. 7
1884, Jan. 5
1883, Feb. 24
1882, Oct. 7
1884, Feb. 16
1874, Jan. 31
1878, Nov. 9
1877, May 19
1879, Oct. 21
1884, Jan. 19
1872, Mar. 9
1872, Nov. 16
1872, Mar. 9
1882, Mar. 25
1883, Feb. 10
1883, Nov. 24
1883, Mar. 24
1871, Mar. 13
1871, Apr. 29
1871, Mar. 13
1871, Mar. 13
1877, Dec. 21
1881, Dec. 3
1875, Apr. 10
1874, Jan. 17
1871, Mar. 13
1881, Nov. 5
1877, Feb. 24
1S79, Mar. 1
1883, Mar. 24
1882, Oct. 7
1876, Dec. 2
1880, Oct. 23
1S72, Jan. 27
LIST OF MEMBERS. XXI
NAME.
Stearns, John (a)...
Stearns, Robert Edwards Carter.
Stone, Ormond (a) ,
Taylor, Frederick William (a).
Taylor, William Bower
Thompson, Almon Harris ..
Thompson, Gilbert
Tilden, William Calvin (a)..
Todd, David Peck (a)
Toner, Joseph Meredith
True, Frederick William....
Twining, William J. (d)
Upton, Jacob Kendrick (r).
Upton, William Wirt
Upton, Winslow (a).,
Vasey, George (r)....
Walcott, Charles Doolittle...
Waldo, Frank (a)
Walker, Francis Amasa (a)..
Walling, Henry Francis (a).
Ward, Lester Frank
Webster, Albert Dowry (a).
Welling, James Clarke
Wheeler, George M. («)....
Wheeler, Junius H. (a) ....
White, Charles Abiathar...
White, Charles Henry
White, Zebulon Lewis (a).
Williams, Albert, Jr
Wilson, Allen D. (<)
Wilson, James Ormond.
P. O. Address and Residence.
Winlock, William Crawford
Wolcott, Christopher Columbus (r).
Wood, Joseph (a)
Wood, William Maxwell (a)
Woodruff, Thomas Maher....
Boston, Mass
Smithsonian Institution. 122G Mass.
Ave. N. W.
Leander McCormick Observatory,
University of Virginia.
.Smithsonian Institution. Lake Val-
ley, New Mex.
Smithsonian Inst. 306 C St. N. W
Geological Survey
Geological Survey. 1448 Q St. N. W„
New York City...
Lawrence Observ., Amherst, Mass....
615 Louisiana Ave
National Museum
,
2d Comptrollers Office, Treasury
Dept. 1746 M St. N. W.
Blown University, Providence, R. I..
Geological Survey, Nat. Museum
Army Signal Office. Ft. Myer, Va....
Mass. Inst, of Technology, Boston,
Mass.
Geological Survey, Cambridge, Mass,
Geological Survey. 1464 R. I. Ave.
N. W.
West New Brighton, Staten Island,
N. Y.
1302 Connecticut Ave
Engineer Bureau, War Department..
Lenoir, N. C
Geological Survey. Le Droit Park....
1744 G St. N. W
Providence, Rhode Island
Geological Survey. 23 Lafayette
Square.
Franklin School Buiiding. 1439 Mass.
Ave. N. W.
Naval Observatory. 723 20th St. N.W
Woodward, Joseph Janvier (<i)...
Woodward, Robert Simpson
Woodworth, John Maynard (d)..
Supt. Motive Power, Penn. Co., Fort
Wayne, Ind.
Navy Department '.'
Army Signal Office. 2020 Hillyer
Place.
Geological Survey, 1125 17th St. N. W.
Yarnall, Mordecai (d) 1871, Apr. 2
Yarrow, Harry Crecy | 814 17th St. N.W 1874, Jan. 3
Date of
Admission.
1874, Mar. 28
1S84, Nov. 22
1874, Mar. 28
1881, Feb. 19
1871,
1875,
18S4,
1871,
1878,
1873,
1882,
1878,
Mar. 13
Apr. 10
Feb. 16
Apr. 29
Nov. 23
June 7
Oct. 7
Nov. 23
1878, Feb. 2
1882, Mar. 25
1880, Dec. 4
1875, June 5
1883, Oct. 13
1881, Dec. 3
1872, Jan. 27
1883, Feb. 24
1876, Nov. 18
1882, Mar. 25
1872, Nov. 16
1873, June 7
1871, Mar. 13
1876, Dec. Hi
18S4, Mar. 1
1S80, June 19
1883, Feb. 24
1874, Apr. 11
1873, Mar. 1
1880, Dec. 4
1875, Feb. 27
1875, Jan. 16
1871, Dee. 2
1884, Apr. 12
1871, Mar. 13
1883, Nov. 24
1S74, Jan. 31
Yeates, William Smith Smithsonian Institution. 401 G St.
N. W.
Zumbrock, Anton. Coast and Geodetic Survey Office.
455 C St. N. W.
31
1884, Apr. 2y
1875, Jan. 30
Number of founders 44
" members deceased 41
'•
" absent 62
" resigned....: 16
" active 173
Total number enrolled 292
XXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
secretaries' REPORT. XXIII
ANNUAL REPORT OF THE SECRETARIES.
Washington City, December 20, 1884.
To the Philosophical Society of Washington :
We have the honor to present the following statistical data
for 1884.
At the beginning of the year the number of active members
was .... ... ... 151
This number has been increased by the addition of 35 new
members and by the return of 5 absent members. It has
been diminished by the departure of 13 members and by
the death of 5. There have been no resignations. The
net increase of active members has thus been . . 22
And the active membership is now 173
The roll of new members is
:
W. S. Barnard. William Lawrence.
T. H. Bean. J. A. Maher.
H. W. Blair. J. B. Marcou.
C. O. Boutelle. Washington Matthews.
F. T. Bowles. G. P. Merrill.
S. J. Brown. John Murdoch.
G. E. Curtis. Basil Norris.
P. P. Dewey. H. G. Ogden.
J. S. Diller. P. H. Kay.
R. E. Earll. W. M. Poindexter.
William Eimbeck. Eugene Ricksecker.
Asaph Hall, Jr. Thomas Robinson.
J. M. Gregory. B. E. C. Stearns.
D. P. Heap. Gilbert Thompson.
Romyn Hitchcock. C. H. White.
W. D. Johnson. T. M. Woodruff.
S. H. Kauffmann. W. S. Teates.
M. B. Kerr.
The names of deceased members are :
Benjamin Alvord. O. E. Babcock. H. W. Blair-
Charles Ewing. J. J. Woodward.
There have been 15 general meetings for the presentation and
discussion of papers (not including the public meeting of Dec. 6)
;
the average attendance has been 42. There have been six meetings
of the Mathematical Section ; average attendance 15.
In the general meeting 32 communications have been presented
in the mathematical section 11.. Altogether 43 communications
have been made by 32 members and one guest. The number of
members who have participated in the discussions is 38. The total
number who have contributed to the scientific proceedings is 50, or
29 per cent, of the present active membership.
Very Respectfully, G. K. Gilbert,
H. Faequhar,
Secretaries.
XXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL REPORT OF THE TREASURER.
Washington City, December 31, 188-4.
To the Philosophical Society of Washington :
I have the honor to present herewith my annual statement as
Treasurer for the year ending December 20th, 1884.
The revenue of the Society has amounted to $855.00 and the ex-
penditures have been $671.96, leaving a balance of $183.04 on hand
;
the details of this account are given in the accompanying table.
The investments of the funds of the Society have not changed
and consist, therefore, of $1,000 in a U. S. Bond at 4} per cent,
and $1,500 in U. S. Bonds at 4 per cent.
The receipts during the past year may be classified as follows :
Interest on invested fund ..... $95
5 Dues for 1882, . . . $25
16 " " 1883, ... 80
126 " " 1884, ... 630
2 " " 1885, ... 10
149 745
The dues remaining unpaid are about as follows
:
For 1882, 3 .... $15
" 1883, 10 ... . 50
" 1884, 47 ... 235
60 300
Early in February 500 copies of Volume VI of the Bulletin were
received from the printer, and 148 copies have been distributed to
active members, also 67 copies have been sent to domestic and 73
to foreign recipients ; occasional copies of other volumes have also
.
been sent to complete broken sets. The stock of publications now
on hand is about as follows
:
Bulletin, Volume 1 91 copies.
II.
" III.
" IV.
" " V. . .
" VI.
"W. B. Taylor, Memoir of Joseph Henry, 1st Ed.
2dE<~
JVC. Welling, Address on life of Joseph Henry
W. B. Taylor, Address as President
In return for the distribution of Bulletins the Society has re-
ceived about seventy-five publications from other organizations or
individuals and the Accessions Catalogue of the Library now
includes 177 titles.
Very respectfully your obedient servant,
Cleveland Abbe, Treasurer.
82
TREASURERS REPORT. XXV

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON
ANNUAL ADDRESS OF THE PRESIDENT.
XXVII

ANNUAL ADDRESS OF THE PRESIDENT,
James C. Welling.
Delivered December 6, 1884.
THE ATOMIC PHILOSOPHY, PHYSICAL AND META-
PHYSICAL.
Every nation under the sun has a philosophy of some kind, but
the philosophy we profess draws the lines of its historic traditions,
if not its " increasing purpose," from the home of our Aryan an-
cestors in Greece. It was here that the typical forms of our litera-
ture were invented, that the art of sculpture was carried to its
climax, and that the architecture of the lintel came to a transfigu-
ration in the Theseum and the Parthenon. And as if all these
glories were not enough, it is the further good fortune of the
Greeks to have at least opened up the great leading problems of
human enquiry, in physics, in psychology, and in ethics; and to
have so opened them up at the starting point of the world's Torch-
race, that the light shed on these questions more than twenty-five
centuries ago is still a matter of curious retrospection to this
generation of ours on whom the ends of the world are come.
It is to one of the oldest of the formal physical philosophies ever
framed by the mind of man for the explanation of the mechanical
structure of the Universe that I purpose to call your attention to-
night—a theory the most comprehensive in its scope, and, at the
same time, the most searching in its subtility, which has been
handed down to us by all antiquity—a theory which in its ingenuity
represents the synthetic power of the Greek mind at the highest stage
of its physical speculation—a theory which the literature of Rome
has preserved in the amber of Cicero's philosophical disquisition,
and embalmed in the immortal verse of Lucretius—a theory, in fine,
which has survived the old dialectic in which it was first conceived,
because it has come to a new birth in the forms of modern science.
I refer to what is known in history as the Atomic Philosophy of the
Greeks.
XXIX
XXX PHILOSOPHICAL SOCIETY OF WASHINGTON.
The fundamental principle of the ancient physical philosophy
—
its point of departure and its ever re-entering point of return—is
found in the famous well-worn maxim of metaphysics, that out of
nothing nothing comes, and that what is can never be annihilated.
It was in the name of this maxim and under the shadow of its
authority that the Greek physical philosophers sought to shelter
their whole right of free enquiry from the charge of impiety, and
if to us the dictum seems the merest truism, it was not so regarded
at the dawn of natural philosophy. Sometimes used as a logical
club with which to brain a stolid and incurious indifferentism, and
sometimes waved as a red flag in the face of polytheistic supersti-
tion, it meets us perpetually in all the oldest records of ancient
philosophical speculation—in the formal elaborations of Aristotle,*
in the lucubrations of Boethius,f and in the verse of poets as remote
from each other in style and creed as Lucretius, the lively Epicu-
rean,! and Persius, the sternest of Stoic moralists.§ This maxim
stirred the philosophical mind of antiquity to its lowest depth,
because it was then the type and symbol of a whole method of phi-
losophizing—a method regarded by many as not a little presump-
tuous, much as the Copernican theory of the Universe was regarded
in the sixteenth century, or much as the Formula of Evolution is
regarded to-day outside of scientific circles.
It was because the maxim seemed to so many the challenge of a
vain wisdom and of a false philosophy that the early champions of
physical philosophy sometimes felt themselves called to vindicate
the truth of this truism by an appeal to formal argument. The
necessity for such an appeal measures the scientific ineptitude of
the average mind at that early age. " If what emerges into sensible
perception," argues Epicurus with the utmost gravity, " can be con-
ceived as coming from nothing, then everything might come of any-
thing, and that, too, without any need of germs ; and if what dis-
appears from sensible perception was really destroyed into nothing,
then all things might perish without anything being left into which
* Aristotle: De Oeneratione et Corruptione, I, iii, 5, (Didot's ed., vol. 2,
p. 437.)
fBoethius: De Consolatione Philosophice, Lib. V, Prosa 1.
X Lucretius: De Rerum Natura, I, 151-227.
2 Persius: Satii-a, iii, 84.
ANNUAL ADDRESS OF THE PRESIDENT. XXXI
they were resolved." * Such was the rude flint-flake with which,
as their only weapon of logic, the early Nimrods of philosophy in
Greece defended their right to philosophize in the palseolithic stage
of natural enquiry.
As the next step in this metaphysical logic we find a distinction
drawn by the ancient Greek philosophers between things as they
are in substrate and things as they appear, disappear, and reappear
in time—between the noumenal and the phenomenal world, as we
would say to-day in the Kantian phraseology. It was the favorite
doctrine of the Eleatic school of philosophers that we get a true
conception of things only when, abstracting from their individ-
uality, their partitiveness and their changing forms, we find the
ultimate root and unity of all being in a simple, indivisible, and
unchangeable substrate, which is the true object of knowledge, be-
cause it is the true basis of all reality. This concept increased in
clearness as it passed through the minds of Xenophanes, Parmeni-
des, and Empedocles, until, in the generalizations of the last-named
philosopher, the ultimate substrate of things was resolved into four
elementary substances—earth, air, fire, and water ; each uncreated
and imperishable, each equal in quantity, each composed, within
itself, of parts that are qualitatively the same, and each forever in-
commutable with the others
;
yet each and all capable of every
variety and degree of mixture in the manifold combinations of
things as they appear in the sensible world.
On the other hand, it was held by Heraclitus that this fuu da-
mental substrate or unity of things is a mere figment of the phil-
osophical imagination, and that it is only as things are conceived
to be in perpetual flux that the forms of our knoAvledge can be
brought into correspondence with the forms of actual being. That
is, to the doctrine of the unchanging substrate of things Heraclitus
opposed the doctrine of the perpetual flux of things.
It remained to effect a synthesis and reconciliation between these
opposing views of the Eleatic and Heraclitic philosophies of nature,
while at the same time saving the fundamental dogma of all natural
philosophizing, that out of nothing nothing comes. Such a basis of
pacification was found in the terms of the Atomic Philosophy, in the
doctrine that the changing forms, positions, motions, and phases of
*Diog. Laert. : Lives of the Philosophers, sub voce " Epicurus."
XXXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
things are to be conceived as a perpetual flux, resulting from the
changing permutations and combinations of the indestructible atoms
composing the eternal substrate of nature. And thus it was that
the doctrine of ultimate atoms, incessantly modified in the forms of
their combination, but remaining forever the same in substance,
became the legitimate deduction and the crowning corollary of the
primal eldest maxim of physical philosophy. Aristotle expressly
gives this genesis of the Atomic Philosophy of Greece in its reduc-
tion by Anaxagoras. After saying that Anaxagoras hypothesized
an infinity of atoms, to explain the myriad varieties of nature, be-
cause he wished to avoid the reproach of getting something out of
nothing, Aristotle adds : " From the fact that contraries are made out
of each other, they must needs have previously existed in each other
;
for if everything that becomes must needs come either from some-
thing or from nothing, and if this latter alternative is impossible,
(about which all who treat of nature are agreed in opinion,) then
it only remains to infer that everything Avhich becomes must have
come from the things in which it pre-existed, though, on account of
the smallness of their bulks, made out of things imperceptible to
us."*
The Atomic Philosophy of the Greeks was, therefore, not a mere
exhalation of the imagination, but a logical inference from the
starting point and major premise of their natural metaphysics. The
doctrine of ultimate atoms in nature was, indeed, the necessary com-
plement and reconciliation of the conception that all things are in
elemental stir, and that yet in this elemental stir there is no crea-
tion of anything out of nothing and no annihilation of anything,
but only composition, decomposition, and recomposition.
It need not surprise us, therefore, to find that the doctrine of
ultimate atoms in nature is a universal- form of thought among
thinking men of all the most advanced races in antiquity. Into
the hidden historic springs of the Atomic Philosophy, as formu-
lated by the Greeks, it is not here proposed to enquire. Whether its
* Aristotle: Naturalis Auscultatio, I, iv, 2, (Didot's ed., vol. 2, p. 252.)
Compare, also, Lucretius, De Rev. Nat., I, 543-545:
" Quoniam supra docui nil posse creari
' De nilo, neque quod genitum est ad nil revocari,
Esse immortali primordia corpore debent."
ANNUAL ADDRESS OF THE PRESIDENT. XXXIII
germs were derived from Egypt, or from India, or from Phoenicia,
or -whether it was an original birth of the Hellenic mind, is a mat-
ter of curious historic interest which hardly admits, perhaps, of
precise and positive determination, though certain it is that India
had an Atomic Philosophy before the Greeks. However possible or
probable it may be that the early Greek philosophers borrowed
some of their lore under this head, as we know they did under
others, from the Egyptian priests ; or whatever truth there may be
in the tradition, reported by Posidonius,* (Cicero's teacher in phi-
losophy,) that one Moschus, a Phoenician, imparted the doctrine to
Pythagoras, it is very certain that the Greek philosophers have
made the doctrine their own by the logical development they gave
to it, and by the hereditament in it which they have bequeathed to
the subsequent generations of men moving along the lines of human
progress. It has been more than suspected that the doctrine dates
in Greece from the age of Pythagoras, by reason of certain spe-
cific ideas, which we can read in the spectrum analysis of the most
distant times by the light of modern anthropological science. Cer-
tain definite lines of thought are to be found in the psychology of
every epoch, and these lines betray the mental constitution of the
epoch as surely as the vapors of the elements absorb rays of the
same refrangibilities that they radiate. In the days of Pythago-
ras we discover certain psychical ideas which are seen to have
been the natural reflex of the great fundamental dogma out of
which the Atomic Philosophy sprang. I refer to the doctrine of
metempsychosis and of its correlate, the pre-existence of souls.
If it be assumed that the human soul is something generically
different from the body, and is not generated by it, then it necessa-
rily follows, according to the maxim De nihilo nihil fit, that the
soul pre-existed somewhere before the atoms of the body were put
together, and from the other branch of the maxim, that it must
continue to exist somewhere after the body is dissolved. The doc-
trine of the transmigration of souls is not, therefore, a mere vagary
of the ethnical imagination, but the natural offspring of that form
of Pythagorean dualism which distinguished the soul, as not only
generically, but genetically distinct from the body. Hence, the
*Strabo: Oeog., Lib. xvi. Cf. Sextus Empiricus : Adversus Mathematicos,
Lib. 9%
17
XXXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
doctrine reappears under one form or another in every dualistic
conception of matter and mind—now in the purple light of Plato's
imperial fancy, and now in the pallid shades of that metaphysical
theology which, in the days of Origen and St. Augustine, arrayed
the doctors of the Church into opposing schools on the great ques-
tion of Traducianism or Creationism.
In whatever way the Atomic Philosophy was begotten in* the
Greek mind, we know that on its emergence it was subjected to
the solvents of philosophical criticism, and underwent a variety
of transformations. So soon as we come within the lines of
definite history we find a bifurcation of ideas between such typical
teachers as Anaxagoras on the one hand, and Leucippus and
Democritus on the other. This dissidence of opinions had regard
to the nature and the constitution of the ultimate atoms which
compose the substance of matter. The doctrine of Anaxagoras
was qualitative; the doctrine of Democritus was quantitative.
Anaxagoras held that the atoms which compose the physical Uni-
verse in its fleeting forms, and at the same time in its enduring
substance, are eternally differentiated in kinds, and that it was by
the collocation and adhesion of like parts—of bony atoms to make
bone, of fleshy atoms to make flesh, of stony atoms to make stones
—that the actual varieties of body in the Universe were built up.
This is the famous doctrine of Homceomeria which fares so ill in
the spiritual philosophy of Plato, and which fares no better in the
materialistic philosophy of Lucretius. Aristotle tells us that
Anaxagoras was driven to adopt this hypothesis in order to relieve
the doctrine of atoms at the points where the heaviest stress and
tightest pinch seemed to be laid upon it by the dogma De nihilo
nihil fit; for how else, said Anaxagoras, could we account for the
existing varieties of matter unless there be an original and eternal
variety in its constituent elements?
Democritus simplified the theory of atoms by giving to it a purely
mechanical reduction. Conceiving atoms to be invisible by reason
of their smallness, he at the same time conceived them to be indi-
visible, not as mathematically considered, but as physically consid-
ered ; and while holding them to be infinite in number and infinite
in their-shapes, he at the same time held that they differed not at
all in inherent quality, but simply in their shapes, sizes, situations,
and motions, and that hence it was by the different combination of
ANNUAL ADDRESS OF THE PRESIDENT. XXXV
atoms differing in these mechanical aspects that all the varieties of
bodies and souls were integrated, disintegrated, and reintegrated. *
The different impressions produced on the human senses by differ-
ent bodies, according to their various mechanical constitutions,
were regarded by him as purely subjective—the mechanical results
of different concussions made on the senses by the different effluxes
of things,f and, therefore, no more requiring any qualitative differ-
ences to explain the phenomena of sensation than to explain the
phenomena of being. Weight and hardness were treated by De-
mocritus as primary qualities of bodies resulting from the greater
or less degrees in which their constituent atoms are compacted, as
compared with the interstitial voids or vacua. The secondary
qualities of bodies are simply the impressions they make on the
human senses, depending, as has just been said, on the varying
shapes, sizes, and arrangements of the atoms composing all the
varieties of material substance.
Anaxagoras had made his theory of atoms a pendant to dualism,
conceiving, as he did, that souls, both animal and rational, are eter-
nally pre-existent before the birth, and post-existent after the disso-
lution, of the bodies in which they temporarily resided. J Democ-
ritus made the animal soul and the rational soul only two more dis-
tinct varieties in the mechanical collocation of atoms varying in
shape, size, situation, and motion ; and, therefore, he had no place
in his theory for the transmigration of souls considered as entities
distinct from bodies. Souls and bodies were equally the results of
a concourse of atoms obeying in their movements the law of a me-
chanical necessity. That is, to the dualism which preceded him
Democritus opposed a pure and simple monism. Yet between the
materialism of Democritus and the dualism of Anaxagoras there is
not much to choose ; for the misty spiritualism of the latter did not
* Aristotle : De Generat. et Corrap., I, i, 4, (Didot's ed., vol. 2, p. 432;)
also Arist.: Metaphysics, VII, ii, 2, (Didot's ed., vol. 2, p. 559,) and the
Nat. Auscul., I. v, 1, (Didot's ed., vol. 2, p. 254.)
f Action from a distance, as of the magnet on iron, was also explained by
Democritus on the hypothesis of "effluxes." Zeller : Philosophie der Griechen,
Erster Theil, p. 704.
J Cud worth : Intellectual System of the Universe, vol. I, chap. 1, ( Andovor
ed,) p. 95.
XXXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
carry with it any clear conception of personal identity, and hence
Lucretius justly argued that the doctrine of a future life, as held
by many in his day, was stripped of all significance if the chain of
personal consciousness is broken at death.*
And to this fundamental antithesis of ideas lying at the bottom
of these two forms of the Greek Atomic Philosophy another anti-
thesis must be added in the Stratonical Hylozoism, which, assuming
in matter an atomic structure partly material and partly vital, pro-
ceeded to account for the genesis of animated bodies on the super-
added assumption of a plastic energy working in nature to the pro-
duction of every living thing. In a word, Strato's matter, instinct
with life, and waiting only for the first chance to be stuck together
in the composition of plants and animals, seems to have been the
metaphysical anticipation of our modern protoplasm.
f
It was in opposition alike to the physics of Anaxagoras, Democ-
ritus, and Strato, that Plato reared his splendid fabric of idealism,
while Aristotle, for his part, rejected the philosophy of atoms alto-
gether, and installed in its place for centuries the doctrine of Form
and Quality, and Substance and Entelechy, whatever that may mean.
" If," he says, " there be no other substance beyond the substances
existing in nature, then Physics is the first science; but if there be
a certain substance which is immovable, then this is before body,
and Philosophy is the first science." J That single sentence re-
capitulates the whole verbal philosophy of the Middle Ages. Plato
was so hostile to the hypothesis of Democritus that he never once
names that philosopher in all his writings, though it is the Abderite
physicist to whom he intends a disparaging allusion when in the
Timceus he impales on the shafts of his irony " a certain philosopher
of an indefinite and ignorant mind." Aristotle names him often
enough, either separately or in conjunction with Leucippus, and
treats the Atomic Philosophy with respect as an " invention framed
to explain the transformation and birth of things—explaining birth
and dissolution by the decomposition and recomposition of atoms,
* Lucret. : De Rerum Natura, Lib. iii, 851.
f Cicero aptly defines the antithesis of ideas between Democritus and
Strato. See Academ. Prior., Lib. II, xxxviii, 121. Also, De Nat. Deor.,
Lib. T, xiii, 35.
J Arist. : Met., Lib. V, i, 9; cf. Lib. X, vii, 9.
ANNUAL ADDRESS OF THE PRESIDENT. XXXVII
and explaining transformations by the arrangement and position
of atoms." *
But it is in the physical philosophy of Epicurus, as that philo-
sophy has been expounded and expanded by Lucretius, that we can
discover the fullest and clearest exposition of the doctrine of atoms,
considered as a key to the structure of the Universe. We here have
the doctrine formulated into a theodicy of naturism, a theory of
psychology, a cosmogony, and an anthropology. According to
Epicurus, in his Lucretian rendering, atoms are minute material
particles, indivisible, not by reason of their smallness, but of their
solidity which makes them indestructible and'unchangeable in their
constitution ; they have size, weight, and shape, yet are forever in-
visible to the eye ; in shape, some of the atoms are different from
the others, but, while the number of the different shapes is finite,
the number of atoms of each shape is infinite ; every atom must
have at least three cacumina (yoviag), that is, infinitesimally small
bounding points which are incapable of existing apart from the
atom, but must be conceived to coexist with it in order to give
definition to it and to enclose its "solid singleness;" some of the
atoms are hook-shaped, some only slightly jagged, some smooth,
&c. ; atoms are in incessant motion, racing through space in all
directions under the stress of their weight,f according to the fa-
voring conditions of a vacuum more or less complete, yet so that
the sum of their motions results in the supreme repose of gross
matter, except when a thing exhibits the motion of translation in
space—a form of motion which is molar and not atomic ; atoms
move besides at an enormous uniform speed, in parallel lines, up
and down, so far as there can be any up and down in a universe
equally boundless in all directions, and except so far as some of the
atoms have originally a shape which makes them capable of slight
deflections from parallel straight lines—that clinamen principioruvi
which was invented by Epicurus to explain the phenomena of so-
*Arist. : De Generat. et Cornq)., I, ii, 4 (Didot's ed., vol. 2, p. 434.)
| Epicurus derived the motion of atoms from their weight, which gives
movement in vacuo. Democritus derived the motion of atoms from an im-
pulse given to them in the beginning. So says Cicero (De Fato, 20, 46),
but for the contrary opinion, cf. Zeller: Philos. der Griechen, Erster Theil,
702, 714.
XXXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
called voluntary motion in animals and free-will in men, while at
the same time explaining how it is that this free-will is eternally-
encased in the rigid parallel lines of the other atoms. In this'way
Epicurus supposed himself to have added a useful supplementary
hypothesis to the original hypothesis of Dcmocritus, who binding
nature fast in fate had not left free the human will, because he had
omitted to provide for that third mode of motion in atoms which
is required to explain the possibility and genesis of voluntary mo-
tion and self determination.
Such is a brief and imperfect exposition of the Atomic Philoso-
phy of the Greeks—a form of physical speculation the most elabo-
rate, the most ingenious, and, to use a Latinism of Dr. Johnson,
the most concinnous which has come down to us from all antiquity.
The Epicurean physics are as much superior to the Aristotelian
and the Stoical physics as the ethics of the Lyceum and of the Porch
are superior to the ethics of the Sty ; and yet it now remains to be
said that in all this operose system of metaphysico-physical atoms
there is not an atom of scientific truth, in the modern sense of that
word. The whole speculation is a mirage, caused by unequal
refractions in the Greek intellect—by the volatility of the Greek
fancy passing through a dense, practical ignorance with regard to
everything but surface views in nature. Or, to borrow one of Plato's
favorite figures, it was a " wind-egg," begotten of metaphysic con-
ceit, and differing from the other "wind-eggs" of that time in the
greater symmetry of its shell rather than in the greater fecundation
of its contents. It had the form, but not the power of scientific
truth. If there be such a thing as atoms they must needs be chem-
ical conceptions, and the very word " chemistry " had not yet come
into the Greek language, because the rationale of such a science
had not even dawned on the horizon of the Greek intellect by the
faintest reflection from below.
Much explanation, which does not explain, has been wasted
to account for the incapacity of the Greek mind in physical
philosophy. The learned historian of the Inductive Sciences,
Dr. William Whewell, ascribes this incapacity to the alleged
fact that though this sprightly race had in their possession an
abundance of facts, and were acute observers and critics, their
ideas " were not distinct and appropriate to the facts."* It would
* William Whewell : History of the Inductive Sciences, vol. I, p. 87.
ANNUAL ADDRESS OF THE PRESIDENT. XXXIX
hardly be possible to frame an explanation more pointless. If there
has ever been a hypothesis framed with more " distinct ideas " than
that of the Greek atomists, I am not acquainted with it, and it is
precisely because it was so "appropriate" to the surface facts of the
Greek observation that it was so illusory. It was fitted to these
facts with a concinnitas that is most admirable from a psychological
point of view. It was invented to fit them, and its whole raison
d'etre was that it did fit them, so far as ideas and words could make
it fit. For this purpose it was revised, modified, contracted, en-
larged, supplemented, until it seemed to fit every sinuosity of the
facts of nature, as far as the facts of nature were open to the appre-
hension of the Greeks in the 5th century before Christ. The hy-
pothesis was strong just where it seems weak to Dr. Whewell, and
it is precisely because it was so ideally strong that it was so physic-
ally weak, and it is precisely because it fitted the facts so well that it
was a delusion and a snare. Men rested in it with a sense of satisfac-
tion which simulated the rest of a mind turning on the poles of truth.
It satisfied the highest cravings of Greek physical enquiry in the
then contemporaneous stage of mental evolution in Greece. The
Greek mind of that age had not reached a stage of development
which required anything more than metaphysical hypotheses for the
explanation of physical facts, because it had not reached a stage
of evolution which capacitated it to frame hypotheses in physics capa-
ble of anything more than metaphysical verification. And hence
it was in the ingenuity of a plausible hypothesis, and in the nicety
with which it fitted the superficial facts that the subtle and artistic
mind of the Greeks found the sole interest and zest which a physi-
cal hypothesis had for them or could have. "Ancient logic," says
Prof. Jowett, " was always mistaking the truth of the form for the
truth of the matter." * The conscious incapacity of the Greeks
for physical science was so great that we find the best class of minds
among them absolutely revolting at the very idea of such a science.
Socrates, for instance, had no patience with it. Plato represents
him in the Phcedo as at the same time deploring misology—the
hatred of formal ideas—and yet, in almost the same breath, confess-
ing himself a misologist in the presence of mechanical conceptions
of nature. He liked the doctrines of Anaxagoras well enough, so
* Jowett's Plato, vol. I, p. 37G.
XL PHILOSOPHICAL SOCIETY OF WASHINGTON.
far as they moved in mind, but he detested them, to use the words
put in his mouth by Plato, so far as they moved in ' fc air, and ether,
and water, and such like inconsequences ;" * and, detesting them, he
falls back upon a purely anthropomorphic conception of the Uni-
verse—anthropomorphic because it is avowedly anthropocentric,
with Socrates for its centre. The whole passage is a most instruct-
ive page in comparative psychology, now that we can read it in
the light of modern anthropological science.
It is no part of my present purpose to carry the history of the
Atomic Philosophy into Roman speculation. The Romans took all
their ideas in mental, moral, and jmysical philosophy at second-hand
from the Greeks.f Strong in the practical arts of war and polity,
they were content to be in literature imitators and in philosophy
eclectics. Equally inept for the deft metaphysical analysis of the
Greeks and for their fine artistic synthesis, the Romans none the
less contributed, on the practical side of life, to the definite exposi-
tion of the contents of all the philosophical systems of the Greeks.
Hence we could ill spare the ponderous banter of Cicero when he
mocks at the weak points of the Atomic Philosophy,^; and still less
could we spare that reasoned elaboration of its strong points which
has made the De Rerum Naiura of Lucretius the most systematic,
the most complete, the most earnest, and the most realistic of all
the reductions which the Atomic Philosophy has ever received. But
after allowing for all his skill in the episodical handling of the rival
systems of Heraclitus, Empedocles, and Anaxagoras, for his power
of description, for the vivacity of his narrative, for the force and
often the beauty of his illustrations and analogies, it must still be
conceded that there is much more of original poetry than of original
philosophy in these glowing hexameters of the Epicurean philoso-
pher-poet.
In a history of the Atomic Philosophy we can leap the chasm of
the Middle Ages at a single bound. The physical philosophers of
* Phcedo, § 47; Jowett's Plato, vol. I, p. 427.
fFor evidence as to the imbecility of the Koman mind in physical phi-
losophy, see the 2nd Book of Cicero's " Prior Academics," which is a long
wail over the want of truth, or of tests of truth, in physical speculation.
%De Natura Deorum, I, 18, 54, 66, 69, 73, 120; cf. De Fato. I. x, xi,
xx; De Flnibus, I, vi—vii ; Tusc. Disput. I, xi, 22; xviii, 42.
ANNUAL ADDRESS OF THE PRESIDENT. XLI
that time were not discussing the concourse of atoms, fortuitous or
otherwise, but were carefully pondering, with Doctors Divine and
Angelical, Subtile and Irrefragable, the difference between Ens and
Essentia, between materia quomodolibet accepta and materia signata,
between quidditas per se and hcecceitas per se, between ultima entitas
entis and ultima actualitas formce. As we plod our weary way
through the Quodlibeta of these venerable doctors, we can but envy
the angels one of the faculties ascribed to them by St. Thomas
Aquinas—that of being able to pass from point to point without
passing through intermediate spaces.
Bacon,* as he stood at the threshold of the new dispensation of
physical science, had made a plea for the forgotten philosophy of
Democritus, but when the metaphysical philosophy of Europe came
to a new Avatar in the brain of Descartes, we find that thinker
denying a discrete conception of matter, and arguing for the con-
trary conception of continuous extension, of the identification
of extension with substance, and, hence, of the infinite divisi-
bility of matter. He says : " It is easy to demonstrate that
there cannot be atoms ; that is, parts of bodies or of matter which
are of an indivisible nature, as some philosophers have imagined,
since, however small we may suppose these parts, inasmuch as they
must needs have extension, we conceive that there is not one of
them which cannot still be divided into two or more still smaller
parts ; whence it follows that it is divisible." f It will here be seen
that Descartes falls into a confusion of ideas with regard to the
atoms of the ancient philosophers. They did not conceive that the
atom was indivisible because of its smallness, but because of the
indestructible solidity which made it incapable of being cut, or
broken, or bent, and which also made it impervious to heat or hu-
midity, x
"
;:
"See, especially, Cogitationcs dc Natura Rerum, and De Principiis atque
Originibus, &c. Works, (Ellis & Spedding's ed., London,) vol. Ill, pp. 15,
82, ct seq.; cf. Advancement of Learning, Book II, vii, 7, (Ellis & Sped-
ding's ed.,) vol. Ill, p. 358.
f For a formal criticism on Democritus' theory of atoms see Principes de
la Philosophic, OEuvrcs de Descartes, (Cousin,) tome III, p. 516, and cf.
Aristotle: De Generatione et Corrujitione, I, ii, 11-21, where this criticism is
anticipated and surpassed.
J" Corpora Individua propter solid itatan,
,f Cic, De Fin., I, vi, 17; cj.
Lucret., I, lines 532-3.
XLII PHILOSOPHICAL SOCIETY OF WASHINGTON.
And this supposed conflict between the infinite divisibility of
matter, mathematically considered, and the actual indivisibility of
atoms, physically considered, is a pure logomachy resulting from
what the lawyers would call a misjoinder of parties and a misjoinder
of issues. The mathematician, contending for the infinite divisi-
bility of matter, proceeds from the idea of space to a fact in nature,
while the atomist, contending for the actual indivisibility of the
atom, proceeds from an assumed fact in nature to the idea of space,
and so, as has been said, the duellists cross swords in the air over
the head of a phantom standing between them, and never succeed
in touching each other.*
From this time onward, for many years, the opinions of philoso-
phers concerning the nature or reality of atoms seem to have
floated in a state of uncertainty between the views of the ancients
and the views of Descartes. For instance, we find Henry More,
the platonizing metaphysician of England, in the 17th century,
adventuring the following dogmatic definition of matter : " I have
taken the boldness to assert that matter consists of indiscerptible
parts, understanding by indiscerptible parts particles that have,
indeed, real extension, but so little that they cannot have less and
be anything at all, and, therefore, cannot be actually divided. The
parts that constitute an indiscerptible part are real, but divisible
only intellectually, it being of the very essence of whatever is to
have parts or extension in some measure or other, for, to take away
all extension is to reduce a thing only to a mathematical point."f
For the physical atom of Greek metaphysics, Leibnitz, it is known,
substituted the monad or formal atom, considered as the continent
and complex of an infinite number of essences. Leibnitz tells us
that so soon as he had thrown off the yoke of Aristotle he plunged
into the vacuum and atomic hurly-burly of Democritus, but that he
could find no rest there, because he could not account for the gene-
sis of mind in man on any mechanical theory of purely physical
atoms. Hence the invention of the Leibnitzian Monadology and
Pre-established Harmony—a form of metaphysical philosophizing
which reflects the mental evolution and intellectual environment
*See "Westminster Eeview, vol. 59, p. 178, cf. Samuel Brown: Lectures
on the Atomic Theory, Edinburgh, 1858.
f Quoted in Munro's Lua-etuts, vol. 2, p. 158.
ANNUAL ADDRESS OF THE PRESIDENT. XL III
of the 17th century, as exactly as the metaphysical speculations of
Anaxagoras and Democritus and Epicurus represent the mental
evolution and intellectual environment of the Greeks two thousand
years before. The atom of Leibnitz instead of being an indivisible
and sempiternal "solid singleness" is a created monad, a "manu-
factured article," deriving its perpetuity and power from the im-
manent and perpetual " fulgurations of Divinity."* It is the
curious destiny of the atomic philosophy, let me here say, in paren-
thesis, that it has subtended three very distinct orders of meta-
physic—the polytheistic metaphysic of Greece and Rome, the
theistic metaphysic of the Renaissance period, and the scientific
metaphysic of our own day.
According to Leibnitz separate classes of monads have separate
qualities. Different degrees of aggregation in monads, differing in
kind, make the varieties of matter. The natural mutations of
monads proceed from an intestine force which is the principle 01
change in matter. In all simple substance there is a plurality of
relations and affections, so that a residuum of relations and affec-
tions remains after every transfer of affections and relations in the
production of material changes. These material changes proceed
according to the law of continuity, for all change of the created
monad is only the modulus of its perdurancy.f The monad is
inconceivable, except as a creation of Divinity. When created, it
is destructible only by the decree of Omnipotence.! Monads
work no changes in each other's inner constitution, and therefore
act on each other according to a Divine Pre-established Harmony,
which makes each monad the mirror of the Universe, and the con-
tinuous register of all physical changes, past, present, and future.
Hence the order of the movement and the continuity of the pro-
cess which have resulted in the formation of the only world pos-
sible and the best world possible. It will be seen that we are here
*" Dieu seul est I'unite primitive ou la substance simple originaire, dont
toutes les monades creees ou derivatives sont des jjroductions, et naissent, pour
ainsi dire, par des fulgurations continuelles de la Divinite, de moment a mo-
ment." (Monadologie, prin. 47). Leib. : Opera Phil., Lat. Gal. Germ, om-
nia. Berlin, 1840, p. 708.
f Leibnitii Principia Philosophies, More Geometrico danonstrata, p. 38.
J Jfiirf., pp. 71, 74.
XLIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
far enough away from the Epicurean atoms, but we are still work-
ing with the atoms of pure metaphysics.
It is equally in accordance with the chronological order of time,
and the logical order of scientific ideas, that we should next turn
to Newton. Aud of Newton, the greatest name in all physical
philosophy, it need only be said that in his work on Optics he re-
turned to a conception of atoms, which, except that it proceeds on
the assumption of a Deity and of final cause, is substantially identi-
cal with that of Leucippus, Democritus, and Epicurus. He says :
" All these things considered [that is, the chemical facts he had
just recited], it seems probable to me that God in the beginning
formed matter in solid, massy, hard, impenetrable, movable parti-
cles, of such sizes and figures, and with such other properties and
in such proportion to space as most conduced to the end for which
He formed them; and that these primitive particles, being solids,
are incomparably harder than any porous bodies compounded^of
them, even so very hard as never to wear or break in pieces—no
ordinary power being able to divide what God himself made one
in the first creation." This definition reminds us of Lucretius.
In continuation Newton adds : " While the particles continue
entire they may compose bodies of one and the same nature and
texture in all ages ; but should they wear away or break in pieces,
the nature of things depending on them would be changed. Water
and earth composed of old worn particles would not be of the same
nature and texture now with water and earth composed of entire
particles in the beginning. And, therefore, that nature may be
lasting, the changes of corporeal things are to be placed only in the
various separations and new associations, and motions of these
permanent particles."
The very form of this last-cited statement carries us back to
the cradle of the Atomic Philosophy.* But it is not so much
the form of Newton's statement which excites our admiration
as the connection of thought in which it stands. The whole of
* dijfidxpiTO? ds xai Aeuxcmzo? -oirj/ravr-s za (Tyrj ;j.ara J rijv alXoiwaiv
xai Trfj yivtG'.j Ix toutwj notouat, d'.axp!<7£'. /xev /.a\ aay/.pias: yivsatv /.a).
<pi%>pdv, rafit dk xa\ ftiffst dXXoianfiv. Aristotle: Hip: reveoswg xai
<P$opa?, I, 2, 4. (Didot's ed., vol. 2., p. 434.
)
ANNUAL ADDRESS OF THE PRESIDENT. XLV
the "31st Query," under which this passage occurs in the book of
"Opticks," is occupied with certain chemical analyses which Newton
had made in his laboratory. Newton, we know, was an alchemist,
and spent laborious days and nights in trying to discover the secret
by which base metals might be rendered noble ; but I can hardly
concur with Prof. Jevons when he says that Newton's " lofty powers
of deductive investigation were wholly useless " in the conduct of
these experiments.* There is some gold at the bottom of even
his alchemical crucible. He was the first to put the conception of
atoms in their rightful logical connection with the phenomena of
practical chemistry.f
It would here be in order to follow Joseph Boscovich in his pro-
found theory of the constitution of matter, if in doing so we might
not fall into the danger of drifting too far from the atom considered
as a minim of corporeal singleness. With him the atom is a point
of attractive and repulsive forces rather than an ultimate physical
element ; and as it was really the atom of chemical physics which
Democritus posited in his mind without knowing it, thus setting up
the altar of science to an " unknown god," it is time that we
should hasten towards the epoch when Chemistry came to rend the
vail from the face of this Isis whom the Greek atomists had so long
and so ignorantly worshipped.
It is in the writings of the Hon. Robert Boyle, pleasantly de-
scribed by his Irish biographer, with a somewhat Irish collocation
of ideas, as " Father of Chemistry and brother of the Earl of Cork,"
that we find the period of transition, when the old order of meta-
physical atoms is changing to give place to the new order of
physical atoms as weighed and measured by modern chemistry. In
his essay on " The Intestine Motions of the Particles of Quiescent
Bodies," J as also in his essays on Fluidity and Firmness, he threw
out some positive ideas on the old atomic philosophy. He sup-
poses it to be of Phoenician derivation, and even tries to effect a
reconciliation between that philosophy and the Cartesian notion of
continuous substance by drawing on the materia subtilis of the
French philosopher (which was conceived to pass constantly, like a
* Jevons: Principles of Science, vol. II, p. 133.
-j- Opticks, Book III, Query 31.
J Robert Boyle's Works, vol. I, p. 444.
XLVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
stream, through the pores of the solidest matter) as a very good
analagon for the racing atoms of Epicurus.
It is, however, in his essay entitled an "Attempt to make chemi-
ical experiments useful to illustrate the notions of the corpuscular
philosophy," * that he approaches this discussion with a bold front.
He there says : " The corpuscular doctrine, rejecting the substantial
forms of the schools, and making bodies to differ but in magnitude,
figure, motion, or rest, and situation of their component particles,
which may be always infinitely varied, seems much more favorable
to the chemical doctrine of the possibility of working wonderful
changes and even transformations in mixed bodies. . . . As
many chemical experiments may be happily explicated by the cor-
puscularian notions, so many of the corpuscularian notions may be
commodiously either illustrated or confirmed by chemical experi-
ments." f
It will be seen at once, in the very dialect and purport of such
language, that we have reached, even in Boyle, a turning point of
the whole Atomic Philosophy. His words import that Ave are to use
" the corpuscularian notions " to explicate chemical experiments,
and that, in turn, the corpuscularian notions may find a new and
solid basis in chemical experimentation. Men have changed their
whole Welt-Anschauung, as compared with that of the Greeks in
the days of Epicurus, before such processes of thought and such
instruments or methods of enquiry become possible. It is only as
the thoughts of men are widened with the process of the suns that
they take in, or can take in, those wider horizons and deeper vistas
of truth which are opened to the human mind by the ascending
hierarchies of the physical sciences. We have now passed the
border-line which separates the metaphysico-physical atoms of Epi-
curus from the physico-metaphysical atoms of modern chemical
science.
I can afford to pass over this part of my story sicco pede, for
we shall henceforth have to deal only with the atoms required by
the hypotheses of positive and experimental science to explain the
actual facts and processes of nature, not as those facts and processes
lie on the surface of things, but as extorted from the very bosom
*Kobert Boyle's Works, vol. I, p. 354.
flbid., pp. 358,359.
ANNUAL ADDRESS OF THE PRESIDENT. XLVII
of nature by the racks and thumbscrews of physical enquiry. In-
stead of taking our atoms as they were distilled and attenuated by
the refining brains of an Anaxagoras, a Democritus, an Epicurus,
or a Leibnitz, we can now take them as weighed and measured by
the quantitative, qualitative, or volumetric analysis of modern
chemistry, in ways that Anaxagoras or Democritus or Epicurus
or Leibnitz never dreamed of in their philosophy. The distance
between the 5th century before Christ and the year 1800 is meas-
ured as well by John Dalton a& by John Howard. John Dal ton
and John Howard would have each been impossible in the days
of Democritus—the one as much so as the other. John Howard
plunged into the reek of European prisons at the impulse of a
Christian philanthropy unknown to the Greek, with all his love of
the Good, the Beautiful, and the True. John Dalton plunged into
the reek of the Lancashire marshes,* at the impulse of an abstract
science unknown to the Greek with all his love of dialectics, of art,
and of aesthetic culture. John Howard, to use the fine phrase of
Burke, taught men who love mercy to " take the gauge and dimen-
sion " of human misery. John Dalton taught men who love truth
in disinterested studies to take the gauge and dimension of the ele-
ments which compose the physical Universe. Who was this John
Dalton that stands in such typical relation with the scientific
thought of our century?
Given, a man "meditative and ratiocinative ;" a meteorologist,
curious in all eudiometrical research, and, therefore, perpetually
experimenting on the constitution of mixed gases; a teacher of
arithmetic, so given to mental numeration that on his first visit to
London he counts all the carriages he sees while wending his way
to the Friends' Meeting House on a Sunday ; a chemist, who took
the diffusion and absorption of elastic fluids as his special province
of investigation ; a theorist, who never theorized without an exper-
iment, and an experimenter who never experimented without a
theory, and you have John Dalton, the father and founder of the
Modern Atomic Philosophy.
As early as the year 1802, in some experimental combinations of
oxygen with nitrous gas, Dalton discovered that " the elements of
oxygen combined with a certain portion of nitrous gas, or with
twice that portion, but with no intermediate quantity." Though he
* He obtained his inflammable gas from these marshes.
XLVIII PHILOSOPHICAL SOCIETY OP WASHINGTON.
called attention at the time to "the theory of the process," he does
not seem to have apprehended the generality of the principle of
definite and multiple proportions till a few years later, when the
doctrine dawned on him in the course of some investigations into
the constitution of olefiant gas and carburetted hydrogen gas.*
Richter, before him, had ascertained the quantity of any base
required to saturate one hundred measures of sulphuric acid, and
had formed a table exhibiting the proportions of the acids and
alkaline bases constituting neutra} salts, but Dalton took this table
and translated it into the relative weights of the ultimate atoms
composing these saline compounds.f
The doctrine of atomic weights had thus already become a work-
ing hypothesis in chemistry, no longer an idle speculation, and we
soon find Berzelius writing to Dalton that " multiple proportions
are a mystery without it." J
From this time onward the history of chemistry has been studded
with fresh confirmations of the new atomic logic, while ever and
anon prophetic glints of truth, implicit in every true physical
hypothesis, have leaped into the light of ocular demonstration
with each advancing stage in chemical science. Time would fail
to tell the beads of the atomic rosary. The doctrine of fixed,
multiple, and volumetric combinations, as formulated by Avo-
gadro in 1813
; § the determination of the proportions in which
bodies combine according to the number and disposition respect-
ively of their molecules, as announced by Ampere in 1814, with
special reference to the clear-cut distinction between molecules
and their integrant atoms, (already presaged before Ampere by
Laurent and Gerhardt;) || the relation between the atomic weights
of bodies and their specific heats, conjectured by Dalton and estab-
lished by Dulong and Petit in 1819;^[ the law of isomorphism, an-
nounced by Mitscherlich at the close of the same year, from which
it appeared that " a similar atomic constitution determines not only
*Henry: Memoirs of the Life and Scientific Researches of John Dalton.
p. 80.
flbid., p. 85.
X Ibid., p. 100.
\ Wurtz : The Atomic Theory, p. 36.
!| Annates de Chimie, vol. 90, p. 43.
\ Wurtz : The Atomic Theory, p. 52.
ANNUAL ADDRESS OF THE PRESIDENT. XLIX
the analogy of chemical properties, but also the similarity of physi-
cal forms ; " * the discoveries in electrolysis, with their bearing on
atomicity, as published by Faraday in 1834, in the Seventh Series or
his Experimental Researches
; f the labors of Berzelius in clarify-
ing the atomic weights of the elements ; the " law of Octanes," an-
nounced by Newlands in 1865, according to which the elements were
divided into groups, having numbers differing by seven, or some
multiple of seven
; J the enlarged Periodic System of the elements,
as published by Mendelejeff in 1869, with the prognostication of
undiscovered metals required to make the system complete—among
them a metal which the Russian chemist proceeded to name " ekaalu-
minium" in advance of its discovery ;§ the discovery of the missing
metal in 1875, by Lecoq de Boisbaudran, who found it in a bleude
from the mines of Pierrefitte, in the Pyrenees, and gave to it the
name of "Gallium," without knowing that he had lighted on the
"missing link" of Mendelejeff; || the extension of this periodic
system by Lothar Meyer, with his Curve of the Elements, showing
that the ductility, fusibility, and volatility of bodies are functions
of their comparative atomic weights ; the periodic system, as re-
vised and extended during this very year, by Prof. Carnelley, in the
light of the experimental boiling and melting points and heats of
formation of the halogen compounds of the elements,^} (chlorides,
bromides, and iodides;) Carnelley's tables of color relations in
chemical compounds as indicating the influence of atomic weights ;**
and, lastly, Carnelley's new reduction of the periodic system of the
elements considered in the light of their occurrence in nature, with
the helpful inferences to be drawn from it ***—these, and such like
discoveries as these, following in the wake of the modern atomic
* Experimental Researches in Electricity, vol. I, pp. 230-258.
f Wurtz : The Atomic Theory, p. 58.
J !Ncwlands : The Discovery of the Periodic Law, &c, p. 14.
\ Annalen der Chemie und Pharmacie, Supplement Band 8, p. 133 et scq.
|| Comptes Retidus, t. LXXXI, p. 493. How fully Mendelejeff recognized
in gallium the characters wanted to fill the gap in his periodic system, see
Comptes Rendus, same volume, p. 969.
fl Philosophical Magazine for July, 1884.
** Phil. Mag. for August, 1884.
***Fhil. Mag. for September, 1884
18
L PHILOSOPHICAL SOCIETY OF WASHINGTON.
theory, have abundantly vindicated its value as an instrument of
chemical research, while conspiring to vindicate its truth by giving
to its votaries that ability of prediction which is the crucial test of
science. The theory, besides, has sometimes "snatched a grace
beyond the reach of art " by working retroactively to the purifica-
tion of chemical method from errors and defects incident to the
most careful manipulations of the practical chemist.
Standing in the presence of chemical science, as now constituted,
Baron Liebig has expressed the opinion that we can scarcely con-
ceive how it could have been developed without the Daltonian
hypothesis. And yet the atom of Dalton, considered in its rela-
tion to our natural senses, is just as incapable of visible and tangi-
ble demonstration as the atom of Democritus. For this reason it
is known that Faraday could never fully reconcile himself to the
modern doctrine of atoms.* But, in fact, there is a genetic and a
generic difference between the ancient and the modern conception.
The former is the offspring of the philosophical imagination
toying with analogy. The latter is the offspring of the philosophi-
cal imagination gendering with the homologies of reason. The atom
of Democritus sprang into thought under the plastic forms by
which he figured to himself at will the invisible relations and
constitution of matter. The atom of Dalton sprang into thought
from a rigid mathematical mind figuring to itself certain de-
terminate relations which had become visible in elastic fluids.
The atom of Democritus was, by the terms of its genesis, incapable
of verification. The atom of Dalton was, by the terms of its
genesis, capable of verification, if true, in all the gases of nature.
Metaphysic thought born of the analogical reason can never con-
clusively prove its legitimacy. Metaphysic thought born of the
homological reason can always prove its legitimacy, and, until it
does, has no rights of heirship in the kingdom of science. The
essential quality of a metaphysico-physical hypothesis is that it
should be plausible; the essential quality of a physico-metaphysical
hypothesis is that it should be apodictic The former is " magistral
and peremptory;" the latter is "ingenuous and faithful." The
former is contrived in such sort as to be "soonest believed," the
* Faraday : Experimental Researches in Electricity, vol. 2, p. 284. But
cf. vol. I, p. 249.
ANNUAL ADDRESS OF THE PRESIDENT. LI
latter is contrived in such sort as to be "easiliest examined," to
cite the words of Bacon.*
The Atomic Philosophy may, therefore, be said to offer a good
type of all that is valid in physical metaphysics, and of all that is
invalid in metaphysical physics. As the child in the infantile stage
of his development dwells delightedly amid fays and talismans,
because his metaphysic is stronger than his physics, so the savage
man, artless child of nature, is easily pleased with the rattle of
some lying legend, or tickled with the straw of some preposterous
myth—the more preposterous the better. A cultivated race
whose imagination is creative and artistic, but whose reason has
not yet been developed by the processes of a rigorous logic, will
demand, as has been already said, an artful and curious felicity in
their physical theories—but they will demand nothing more, be-
cause when this demand is met, their highest intellectual demand
has been met. It is not until "the heir of all the ages" has learned
to change the organon and method of his physical enquiries, and to
put his reason over his imagination, by making imagination the
hand-maid of reason, that Science is born. Long before this stage
has been reached the children of Science may come to the birth, but
there is not strength to deliver, because the true maieutic of science
—
experimentation with rational hypothesis, and rational hypothesis
with experimentation—has not yet come to the teeming mind of
philosophy. The goddess Experimentation is the Lucina of Science.
The free surrender of all metaphysical conceptions to the hands of
this Lucina, with the distinct knowledge that she will strangle them
if they are not well formed, is the birth-pang of the scientific spirit.
Until this stage of mental evolution is reached we shall have as
many theories of the Universe as we have stages of culture, for
every stage of culture will have a physics of its own, because it has
a metaphysic of its own. Hence, the endless varieties of cosmol-
ogy—the Hottentot physics, the Indian physics, the Stoical physics,
the Epicurean physics, the Leibnitzian physics, the Cartesian phys-
ics, and such like—all the coinage of the metaphysical imagination.
Grote enumerates as many as twelve distinct physical philosophies
which divided speculative opinion in Greece during the century
and a half between Thales and the Peloponnesian war.
*The Advancement of Learning, Book I, v, 9.
LII PHILOSOPHICAL SOCIETY OF WASHINGTON.
It is the mission of science to bring the physics of the world into
unity by reading the phenomena of the world in the dry light of
reason, and by continuing to spell and parse the hieroglyphs of
Nature until the rational processes of our logic are brought into
demonstrated correspondence with the actual processes of Nature.
Science still keeps metaphysic in her service. But instead of
weaving whole fabrics from the metaphysical loom and devising
ingenious tissues which only reveal the nakedness of reason, Science
in passing from the known to the unknown employs metaphysic
as the gossamer spider employs the single thread on which she
sways and balances her movements between two solid points. The
thread is tied to something solid as the condition of reaching some-
thing solid after her aerial flight. So the man of science, work-
ing in and under the limitations of physics, works on the lines
of metaphysic thought when he frames the tentative hypotheses
with which he returns again to the patient, practical study of
nature.*
The scientific man reads the Universe backward by the inductive
syllogism, because Nature has proceeded forward in her evolutions,
according to an unbroken chain of antecedent causes. The physi-
cal Universe is indeed a fasciculus of natural syllogisms colligated
into the compactest unity, and so holding all things, forces, and
functions under the bonds of logic. The scientific man, at any
given stage of his enquiry, has before him only the conclusions or
at best only the minor premises and the conclusions of this world-
process. And he knows that these conclusions of the natural syllo-
gistic process have been reached through a perpetual flux in the
universal complex of things, forces, and functions—a flux which
dates from the beginning of star-mist and nebula, or from the
beginning of that more elementary fluid out of which star-mist and
nebula were generated, according to the scientific metaphysic of the
present day. Is it any wonder, then, that many of the major
premises of Nature's physical syllogisms should still be wrapt in
impenetrable mystery to us, as many of the major premises which
* Bacon's oft-quoted contrast between metaphysicians, who, he says, spin
''laborious cobwebs of learning," like spiders, and physical philosophers,
who ''work according to the stuff, and are limited thereby,'' seems hardly fair
to the spider. Advancement of Learning, Book I, iv, 5.
ANNUAL ADDRESS OF THE PRESIDENT. LIII
we have spelled out were wrapt in an impenetrable mystery to the
Greeks in the 5th century before Christ?
As there is a needs be that much of metaphysic thought must
be blended with the psychological processes which lead to every
passage from the known to the unknown', so every great discovery
of the physical philosopher tends to widen the metaphysical horizon
within which he works. The world was never so full of metaphysic
as it is to-day, when physical science is transforming the minds of
men not so much by the secular boons it is dropping in the lap of
modern civilization as by its underlying doctrines ; and these doc-
trines are often the mere metaphysical reflex or obverse of the
physical truths they subtend. The psychological processes of every
age are conditioned by its logical method, and its logical method is
justified to itself by its metaphysic—by those necessary conceptions
and fundamental relations which it takes to be architectonic of the
Universe. What, for instance, can be more metaphysical than the
latest conception of our highest physical science—the conception of
vortex atoms moving in an imaginary frictionless fluid where the
origin and the end of the motion are equally inconceivable ? Or,
take Mr. Darwin's doctrine of hypothetical gemmules " inheriting
innumerable qualities from ancestral sources, circulating in the
blood and propagating themselves, generation after generation, still
in the state of gemmules, but failing to develop themselves into
cells because other antagonistic gemmules are prepotent and over-
master them in the struggle for points of attachment " *—in what
respect is this doctrine one whit less metaphysical than St. Augus-
tine's doctrine of original and hereditary sin ? Or, when the late
Prof. Clifford tells us that "the Universe consists entirely of mind-
stuff; " that " matter is a mental picture, in which mind-stuff is the
thing represented," and that " reason, intelligence, and volition are
properties of a complex which is made up of elements themselves
not rational, not intelligent, not conscious"—how does his "mind-
stuff" differ from the " mind-stuff" of Pythagoras, f except in the
* Gallon: Hereditary Genius, p. 367; cf. Darwin: Animals and Plants
under Domestication, (London,) vol. 2, p. 402. For a criticism on this
physiological doctrine, see Encyclopaedia Britannica, ("Atoms,") vol. 3,
p. 42.
fFor the "mind-stuff" of Pythagoras, see Cicero, De Nat. Deorum, I,
xi, 27. For the "mind-stuff" of Clifford, see " Mind," January, 1878, p. 60.
LIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
greater ingenuity and method of the metaphysic art with whieb
it is conceived ?
If within the limits of this discussion I had the time, and if,
under the limitations of my knowledge, I had the ability, to carry
this enquiry into the realm of molecular physics and dynamics,
where such star-eyed mystagogues as a Clausius or a Rankine, a
Clerk-Maxwell or a Sir William Thompson have borne the thyrsus
of science before us, it would be easy to show that, under their guid-
ance, we have escaped the pitiless parallel lines of the Epicurean
atoms only to find ourselves inextricably implicated in the knotted-
ness and linkedness of the vortex rings of atoms as they execute
their infinite evolutions and involutions, vibrating now in one period
and now in another behind that vail of matter where they can be
descried only by the shadowy lines they reveal to the spectroscopic
imagination. " It is the mode of motion," says Clerk-Maxwell,
" which constitutes the vortex rings, and which furnishes us with
examples of that permanence and continuity of existence which we
are accustomed to attribute to matter itself. The primitive fluid,
the only true matter, entirely eludes our perceptions when it is not
endued with the mode of motion which converts certain portions of
it into vortex rings, and thus renders it molecular." *
Of these vortex rings we must say, in the dialect of the schools,
cognoscendo ignorantur, sed ignorando cognoscuntur. Withheld from
positive conception, yet necessitated to scientific thought and spec-
ulation by the exigencies of the knowledge we can conceive posi-
tively, they afford a good illustration of the physical metaphysic
which has wafted the scientific mind of the present generation into
an empyrean as much higher than the empyrean of Plato as the
spectroscopic vision of modern science is more far-reaching than the
highest flight of metaphysic wit among all the physical atomizers
who ever lived or dreamed in Greece. Every chemical atom, says
Sir John Herschel, is forever solving differential equations, which,
if written out in full, might belt the earth. "An atom of pure
iron," says Jevons, " is probably a vastly more complicated system
than that of the planets and their satellites."
Between metaphysical physics and physical metaphysics there is
a world-wide difference. The invisible ether posited behind the
* Encyclopaedia Britannica, sub voce "Atom.
ANNUAL ADDRESS OF THE PRESIDENT. LV
vail of matter by the East Indian philosophy of the Upanishads, or
by the visionary dialectic of Cleanthes, was posited there by meta-
physical physics. The invisible fluid posited by modern science
behind the vail of matter is posited there by physical metaphysics.
The vortices of Democritus as well as the vortices of Descartes
are the creations of metaphysical physics. The vortices of Helm-
holtz and of Sir William Thompson are the creations of physical
metaphysics. The fixed and crystalline sphere of the old Ptole-
maic astronomers was an invention of metaphysical physics. The
solid ether which transmits to us the light of the stellar Universe,
and which, as Sir John Herschell remarks, is the modern "realiza-
tion of the ancient idea of the crystalline orb," is the invention
of physical metaphysics. When Lucretius finds in the iridescent
hues of the peacock's tail, as it shimmers in the sun, a fresh type
and instance of Nature's prodigality in the display of atoms, he
does but yield another contingent to the barren store of his meta-
physical physics. When Dr. John Tyndall finds in the iridescences
of the common soap bubble a proof that stellar space is a plenum
filled with a material substance that is capable of transmitting
motion with a rapidity that would girdle the equatorial earth eight
times in a second, he does but yield another contingent to the fertile
store of his physical metaphysics. When Dr. George Cheyne, of
Scotland, expressed the opinion in the last century, that " all ani-
mals, of what kind soever, were originally and actually created at
once by the hand of Almighty God, it being impossible (he said ) to
account for their production by any laws of mechanism ; " and
when he further held that " every individual animal has, in minimis,
actually included in its loins all those who shall descend from it,
and every one of these again has all its offspring lodged in its loins,
and so on ad infinitum," and that " all this infinite number of ani-
malcules may be lodged in the bigness of a pin's head,"* he preached
a biological doctrine which sounds in the terms of metaphysical
physics. When Mr. Darwin in his provisional theory of Pangenesis
assumes the existence of the gemmules which inherit innumerable
qualities from ancestral sources, and which prelude as gemmules
that struggle for existence which antedates and therefore condition-
ates the terms of the human struggle witnessed in society, commerce,
and national life, he expounds a biological doctrine which sounds
just as clearly in the terms of physical metaphysics. When old
* J. Brown: Locke and Sydenham, p. 270.
LVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
Heraclitus proclaimed that the Universe with all it contains sprang
into being from elemental heat, and was destined to be resolved
again into the elemental heat from which it sprang, and thus in a
ceaseless round to continue the cycle of being, he taught a doctrine
of conservation and correlation of energy which had its root in
metaphysical physics. When Dr. John Tyndall declares that " all
our philosophy, all our poetry, all our science, all our art—Plato,
Shakespeare, Newton, and Raphael—are potentially in the fires
of the sun," and so tucks away the genius of a Darwin in the folds
of a nebular blastema, he teaches a doctrine of equivalence which
has its root in physical metaphysics.
It will thus be seen that under the dominion of Science the world
has use for as much metaphysic as ever before, but only for a meta-
physic radically different from the old metaphysic in its point of
departure as also in the tests of its validity, and, therefore, radi-
cally different in the tenure by which it is held. The votaries of
the old metaphysical physics proceeded from what was unknown to
explicate and explain the known appearances of things, and rested
content in explanations which seemed to consist with those appear-
ances. The votaries of the modern physical metaphysics proceed
from what is known to explicate and explain what is unknown in
the deeper relations of things, and rest content in explanations only
so long as, and so far as, they seem consistent with experimental
proofs or with the broadest homologies of the deductive reason.
When the law of simple multiples in chemical combinations was
given to the world by Dalton, and was expressed by him in atomic
language, he had really made a great departure from the physical
methods of Democritus, though it is curious to observe that there ia
a perfect identity between the metaphysical ideas underlying hia
logic and the metaphysical ideas of his Greek predecessor. The
method of each proceeds on the assumption of the indestructibility
of matter, and it is from this platform that the English chemist
reaches out his hand to the Greek philosopher in token of a com-
mon metaphysic. " No new creation or destruction of matter,"
wrote Dalton, in his celebrated paper on " Chemical Synthesis," "is
within the reach of chemical agency. We might as well attempt
to introduce a new planet into the solar system, or to annihilate
one already in existence, as to create or destroy a particle of hydro-
ANNUAL ADDRESS OF THE PRESIDENT. LVII
gen." * Democritus knew nothing of hydrogen, but he saw as
clearly and said as plainly as Dalton that the antecedent premise
of all physical philosophy must be found in the metaphysical maxim
that " out of nothing nothing comes, and that nothing which is can
ever be annihilated." f
And this maxim, with which the old Greek philosophy began, is
about all of solid and sound that remains to us from the physical
philosophizing of the ancients. It is true, as Mr. Balfour Stewart
remarks, that the ancients had in some way grasped the idea of the
essential unrest and energy of things ; that they had the idea o±
small particles or atoms as the constituent elements of matter, and
divined the existence of an ethereal medium extending through all
space ; but there is no evidence at all to support the statement
that any one or all of these doctrines proceeded from even a ru-
dimental conception of " the most profound and deeply seated ot
the principles of the material universe."
There is, however, one respect in which it may be justly said that
Democritus stands at the head of the long line of natural philoso-
phers who since his day have been explicating for us the structure
of the physical universe. He was the first who ever attempted a
purely mechanical solution of the problem of physical being. It is
the singular glory of the atomic philosophers that alone, among the
jarring schools of Greece, they saw that a science of the Universe
was possible only on the assumption that the phenomena of the
physical universe are bound together by necessary law, and this
law mechanical in the modes of its operation. They had no science,
it is true, in the modern sense of the word, but it is no small dis-
tinction which they have won in standing at the head of an intel-
lectual succession which embraces in its ranks a Copernicus and a
Galileo, a Newton and a Laplace, a Dalton and a Faraday. J
* Henry: Memoirs, &c, of Dalton, p. 88.
fDiog. Laert., sub voce "Democritus," where it is particularly recorded
that he assumed as his point of departure the maxim "Out of nothing
nothing comes," &c.
J "Was die Atomiker von ihren Vorgangern unterscheidet, ist nur die
Strenge und Folgerichtigkeit mit der sie den Gedanken einer rein material-
istischen undmechanischen Naturerklarung durchgefuhrt haben ; diesekann
ihnen aber urn so weniger zum Nachtheil gedeutet werden, da sie damit nur
die Schlusse gezogen haben welche durch die ganze bisherige Entwicklung
gefordert, und wozu in den Annahmen ihrer Vorganger die Vordersiitze ge-
geben waren." Zeller: Philos. d. Griechcn, Erster Theil, 765.
LVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
With two short lessons cited to point the moral of this long story,
and I have done. The first of these moralities shall" be a warning
against the folly of the old atomists in attempting to philosophize
beyond the conditions of their knowledge. They reared imposing
fabrics in astronomy, in physics, in psychology, and in anthropology,
but they built without laying their foundation in any deep knowl-
edge of nature, and laid the successive courses of their system-
building in the untempered mortar of an incoherent logic. And
the moral needs to be pointed as much for the admonition of modern
scientific workers, with their cheap and easy cosmologies, as for the
reproach of the old physiologers of Greece. One of our poets has
sung
:
From an old English parsonage
Down by the sea,
There came in the twilight
A message to me.
Its quaint Saxon legend,
Deeply engraven,
Hath, as it seems to me,
Teaching from heaven
;
And all through the hours
The quiet words ring,
Like a low inspiration,
"Doe tfje tterte tfjgnfle."
The message is as full of inspiration for guidance in physical
philosophizing as for guidance in moral conduct. Tantum series
iuncturaque pollet.
The only other morality which time permits to be pointed at the
end of this review is a warning against intellectual impatience
—
not that intellectual impatience rebuked by the maxim just cited,
and which seeks to leap at a single bound the limitations of knowl-
edge in any given age—but the intellectual impatience which cavils
at the short-comings of the men who dug the first ditches and
planted the first hedges around the vineyards of science. They
were humble pioneers, but they opened the way into that land of
Beulah where the men of science sit to-day beneath their own
vines and fig-trees, with none to make them afraid. Even after
John Dalton had come to place the key of the new Atomic Philoso-
phy in the hands of men, it was a saying of Mitscherlich that it
took fourteen years to discover and establish a single fact in
ANNUAL ADDRESS OP THE PRESIDENT. LIX
chemistry. Let us not wonder, then, that it took more than two
thousand years to perfect the doctrine of atoms as a clew to the
" mystery of matter." Democritus invented a mechanical key
of wonderful ingenuity, but it would not unlock anything that
could not be unlocked without it. Newton divined that the
key must be fitted to the two great wards of chemical attrac-
tion and chemical repulsion, but still the key would not turn in the
adamantine lock of Nature. Dalton found that the secret of the
combination must be sought in wards nicely graduated according to
certain fixed, definite, and multiple numbers, and, since his day,
door after door in the chemist's " chamber of imagery" has seemed
to swing open at the touch of this talisman. And even, if in the
next two thousand years, or in the next twenty years, the theory of
John Dalton should be absorbed in some deeper truth, there will
still be room in the pantheon of science for the memorial bust of
the plain Manchester arithmetician, so long as men recall how far
that little candle, which he lighted with inflammable gas obtained
in the rudest way from the ponds of Lancashire, has thrown its
quickening beams across the whole tract of modern chemistry.

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
GENERAL MEETING.

BULLETIN
GENERAL MEETING
244th Meeting. January 5, 1884.
The President in the Chair.
Twenty-eight members and guests present.
The Chair announced the death, since the last meeting, of
General A. A. Humphreys, one of the founders of the Society.
Mr. J. R. Eastman made a communication on
THE ROCHESTER (MINNESOTA) TORNADO,
describing the ground as it appeared a few days after the storm,
and showing that the phenomena did not indicate cyclonic motion.
All disturbed objects were thrown in essentially the same direction,
and were pressed down rather than lifted.
Mr. Elliott related that twenty-five years previous he had
crossed a storm-track consisting of a double line of fallen timber,
with an interval in which the timber was standing. Mr. Eastman
thought this phenomenon should be referred to two separate
cyclones, possibly moving as companions.
Mr. Dall described storm tracks in the Escanaba region in
which the trunks of prostrate trees pointed uniformly in one
direction, the path of destruction being definitely limited at the
margins.
Mr. E. Farquhar suggested that a highly inclined storm axis
might account for the uniformity in the direction of the wind in
the zone of destruction.
4 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. W. H. Dall read a paper on
RECENT ADVANCES IN OUR KNOWLEDGE OF THE LIMPETS,
summarizing the researches of Spengel on the sensory organs or
osphradia; Cunningham on the renal organ and renopericardial
pore in Patella and Patina; Fraisse on the eye in Patina, Fissurella
and Haliotis, and the speaker on the presence of an intromittent
male organ in Cocculina. He stated that among the Acmceidce and
Patellidce the type of eye differs, and while in Patina it is of a very
rudimentary character, in other genera it might be well developed,
as, for instance, in Ancistromesus, which has as well developed eyes
as Fissurella. He also alluded to the gradual progress in classifi-
cation afforded by anatomical investigation during the past few
years, and observed that nearly all the known forms except Propili-
dium and Scutellina were amenable to classification ; our ignorance
of the branchias in the former, and the dentition in the latter,
operating to prevent a final classification in these two cases, until
more is known. Those authors who study the embryology and
histology usually from a single species, generally ignore the wide
differences of adult anatomy between the genera of Limpets, and
sow their generalizations on a basis of classification which is little
in advance of that of Lamarck and his immediate successors.
Professor C. H. Hitchcock being present was invited by the
Chair to address the Society, and responded briefly.
The President of the Society then pronounced a brief eulogy on
General Humphreys, characterizing him as a man who had left
behind him an honorable name as well for his distinguished
achievements in science and in war as for the virtues and graces
which adorned his private life. Mingling among his fellow-men
with the utmost unobtrusiveness, and as gentle in spirit as he was
brave in conduct, he brought the highest intelligence as well as the
highest conscientiousness to the discharge of all the duties—scien-
tific, military, and administrative—with which he filled his long
and useful life: a life fitly closed by the serenity and peace of his
beautiful death.
general meeting. 5
245th Meeting. January 19, 1884.
The President in the Chair.
Forty-five members and guests present.
The Chair read a letter from the Biological Society of Washing-
ton inviting the members of the Philosophical Society to attend
its meeting of January 25th, for the purpose of listening to the
annual address of its President, Dr. C. A. White.
Announcement was made of the election to membership of
Messrs. George Edward Curtis and Patrick Henry Ray.
Mr. I. C. Russell made a communication on
THE EXISTING GLACIERS OF THE HIGH SIERRA OF CALIFORNIA.
[Abstract.]
During the summer of 1883 I had an opportunity of tracing to
their sources some of the ancieut glaciers of the High Sierra in
the region between Mono Lake and the Yosemite Valley.
From the glacial records seen during a number of excursions
into the mountains it was evident that the High Sierra had formerly
been so deeply covered with ice that only the culminating peaks
and ridges escaped the general glaciation. From the vast neve" of
the mountain tops flowed long winding rivers of ice, both to the
eastward and westward through the canons and valleys. In nearly
all cases the glaciers occupied drainage lines of pre-glacial date,
which they modified and enlarged, but, with the exception of the
cirques about the higher peaks and crests, they failed to originate
any of the more prominent topographical features of the range.
The glaciers of the Sierra Nevada were not connected with a north-
ern ice-sheet, but were of local origin and of the same type as the
Swiss glaciers of the present day, but of far greater magnitude. If
the canons and valleys of the Sierra are traced upward, it is almost
invariably found that they head in cirques or amphitheaters, in
some of which small glaciers still linger
—
perhaps remnants of the
mighty ice-rivers that formerly flowed from the same fountains.
The first glacier visited by the writer was on the northern side of
Mt. Dana, at an elevatiou of about 11,500 feet above the sea, and
at the head of a deep canon which drains into Leevining creek,
19
6 PHILOSOPHICAL SOCIETY OF WASHINGTON.
oneofthe tributaries ofMouo Lake. The Mt. Dana glacier is approx-
imately 2,500 feet long and ofsomewhat greater breadfh. Although
small, and in fact but a " pocket edition " of what may be seen on
a far grander scale in many mountains, yet it is a veritable glacier,
with nearly all the features that characterize such ice-bodies
in other countries. The distinction between the snow-ice of the
neve and the more solid blue or greenish-blue ice of the glacier
proper is clearly marked—as was observed to be the case also
in a number of neighboring glaciers. An irregular open fissure
crosses the head of the neve, corresponding to the " bergschrund "
of the Swiss glaciers, while a number of parallel fractures on the
border of the glacier at the foot of the snow-field form marginal
crevasses with walls of solid blue ice. Near the terminus of the
glacier alternating sheets of porous, white ice, and of more compact
bluish ice were observed, which produce a distinct laminated or
ribboned structure. Dirt-bands were plainly visible, sweeping
in undulating lines across the surface of the glacier ; and similar
bands are a conspicuous feature in nearly all the ice-bodies seen in the
High Sierra. About the foot of the Mt. Dana glacier a true terminal
moraine is now in process of formation. The fall of stones and
dirt from the ice onto the moraiue was noticed many times during
our visits. Some of the rounded stones from beneath the ice are
battered and scratched and have evidently received these markings
within the past few years.
On the northern side of Mt. Lyell another glacier was visited,
which is the source of the Tuolumne river. The Mt. Lyell glacier is
somewhat larger than the one on Mt. Dana, and, like it, exhibits
characteristic glacial phenomena. A protrusion of compact, banded
ice from beneath a snow-field at the head of an amphitheatre was
here again observed, as well as the presence of moraines, crevasses,
dirt-bands, etc. On the lower portion of this glacier were observed
" ice-pyramids " of the form represented in the figure on the follow-
ing page.
At the northern base of a pyramid there invariably occurs a
stone or a mass of dirt, that is depressed below the general surface
of the glacier, as is indicated in the sketch. The pyramid invariably
points toward the noon-day sun. Its mass is composed of porous
and banded ice, like that forming the general surface of the glacier,
but its northern face is sheeted with compact, bluish ice. The
GENERAL MEETING.
northern face is also concave, as represented in the sketch, and
usually conforms to some extent with the shape of the stone at ita
base.
Fig. 1. An Ice-Pyramid.
On another glacier, discovered at the head of Parker creek, one
of the tributaries of Mono Lake, all the glacial phenomena- men-
tioned above are well displayed, and, in addition, " glacier-tables "
were observed in considerable numbers. The following figure repre-
sents several of the glacier-tables of the Parker creek glacier,
grouped for convenience of illustration
:
* jsm^cS^-^
Fig. 2. Glacier-Tables.
8 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The largest perched-block now being carried along by this glacier
measures 34 by 28 by 10 feet, and is supported on a column of ice
five or six feet thick, eight feet high on its northern side, and six
feet high on its southern. Many masses of rock larger than the
one measured were seen in the terminal moraine that circles about
the foot of the glacier.
The motion of these glaciers was not observed, but that it exists
is manifest from the nature of the crevasses and the curvature of
the dirt-bands. The rate of flow of a glacier on Mt. McClure was
measured several years since by Mr. Muir, who found it to be 47
inches in 46 days (from August 21st tt October 6th, 1872).*
Six glaciers are known to the writer within the southern rim of
the hydrographic basin of Mono Lake, and about twice this num-
ber were seen about Mt. Conness, Mt. McClure, Mt. Lyell, Mt.
Ritter, and the Minarets.
Many of the glaciers mentioned above have been previously re-
ported in popular articles by Mr. John Muir, but the fact that they
are true glaciers having been denied by eminent geologists, it is de-
sirable to have a more accurate description of them.
[The communication was illustrated by photographic lantern
views. Its subject-matter will be more fully presented in the Fifth
Annual Report of the United States Geological Survey.]
Mr. Gilbert Thompson described certain glaciers on Mount
Shasta believed to be new to science. Their discovery increases
the number of known glaciers on the flanks of Shasta to seven.
Mr. Holmes described modern glaciers of the Rocky Mountains
observed by himself. Those of the Wind River Mountains are
from one-fourth mile to one mile in length. He illustrated by a
sketch the position of three small glaciers in the gorges of Mount
Moran, in the Teton Range, at an altitude of 10,000 feet.
Mr. Powell remarked that the chief interest of these small
modern glaciers lies in the fact that they illustrate the process by
which the drift has been distributed, and aid in completing the
theory of the ancient glaciation of the country.
Mr. Mark B. Kerr mentioned the occurrence of a probable
glacier in the Salmon Mountains, a division of the Coast Range.
* American Journal of Science, Vol. V, p. 09; 1873.
GENERAL MEETING. 9
Mr. Harkness set forth the apparent difficulty of discrimina-
ting between a neve
1
and a glacier proper, and requested that some
geologist would define the term " glacier."
Mr. Emmons said that a true glacier is an ice river, conform-
ing in shape to the more or less restricted channel in which it
flows, and this characteristic might form a base of distinction be-
tween the true glacier and the neve-field, the latter being com-
parable to the lake which forms the source of a mountain stream.
Thus the n6ve would become a glacier only when from a broad and
shallow ice-field it had become compressed into a narrower and
deeper mass, between confining walls.
Other remarks were made by Messrs. E. Farquhar, Gilbert,
Dall, and Elliott.
Professor W. C. Kerr made a communication on
THE MICA MINES OF NORTH CAROLINA.
[Abstract.]
The profitable mines are restricted to a plateau limited eastward
by the Blue Ridge and westward by the Smoky Range. These
were anciently worked on a very extensive scale. Few other modern
mining operations have been so profitably conducted as those at the
points occupied by the early miners. The ancient work was per-
formed with blunt-pointed tools—doubtless of stone—and was con-
fined to the partially decomposed portions of the granite veins, but
large pits were nevertheless excavated. One of these measures
150 by 75 feet, and, despite a partial filling with debris, retains a
depth of 35 feet. Facts connected with the arboreal vegetation
show that some, and perhaps all of these openings were aban-
doned as much as five hundred years ago. The modern industry
began in 1868, and, although it has assumed considerable import-
ance, is not yet conducted in a systematic way.
The character of the mica and its associated minerals were dis-
cussed and illustrated by specimens.
10 philosophical society of washington.
246th Meeting. February 2, 1884.
The President in the Chair.
Forty-eight members and guests present.
The Chair announced the election to membership of Mr. Thomas
Robinson.
Mr. C. V. Riley made a communication on
RECENT ADVANCES IN ECONOMIC ENTOMOLOGY.
The paper set forth the part which insects play in the economy
of nature, and particularly their influence on American agriculture.
The earlier writei*s on applied entomology in the United States, as
Peck, Harris, Fitch, Walsh, LeBaron, Glover, did some excellent
work in their studies of the habits and life-histories of injurious
species, but the most important results followed when such studies
were combined with field work and experiment by competent persons
and upon scientific principles. A number of the remedies proposed
in the agricultural press are foolish and based on misleading em-
piricism. Economic entomology as a science is of comparatively
recent date. It implies full knowledge of the particular injurious
species to be dealt with and of its enemies, of its relations to other
animals and to wild and cultivated plants. In short, the whole
environment of the species must be considered, especially from the
standpoint of the farmer's wants. The habits of birds, more par-
ticularly, and the bearings of meteorology and of the develop-
ment of minute parasitic organisms must be considered. Experi-
ments with insecticides and appliances will then be intelligent
and successful in proportion as the facts of chemistry, dynamics,
and mechanics are utilized.
The complicated nature of the problem was illustrated by the
life-history of Phylloxera vastatrix Planchon, and the difficulties
often encountered in acquiring the facts were illustrated by the late
work on Aletta xylina (Say).
The chief insecticides considered for general use and applicable
above ground were tobacco, white hellebore, soap, arsenical com-
pounds, petroleum, and pyrethrum ; those for use under ground,
naphthaline, sulpho-carbonate of potassium, and bisulphide of car-
GENERAL MEETING. 11
bon. The most advantageous and improved methods of utilizing
each were indicated. Recent experiment showed that kerosene
emulsious, such as had been recommended lately in the author's
official reports, are superior to bisulphide of carbon when used
under ground against the Grape Phylloxera, and the discovery is
deemed of great importance, especially to the French people and
those on our Pacific slope. Contrary to general belief, pyrethrum
powder was shown to have a peculiar and toxic effect on higher
animals as well as on the lower forms of life. Its deadly influence
on lower organisms led the author to strongly recommend its use
as a disinfectant, and to express the belief that it will yet come to
be used in medicine. Dr. H. A. Hagen's recommendation of the
use of yeast ferment was touched upon. It has proved of little or
no practical avail, and some of the publications on the subject were
characterized as unscientific. The use of malodorous substances
as repellancs, which was much relied on in the early days of econ-
omic entomology and strongly recommended by the two Downings,
has lately been agitated as a new principle for the prevention of
insect attack by Prof. J. A. Lintner. The principle can be applied
in exceptional cases to advantage, but experiment gives little hope
of its utility against most of our worst field insects. Prof. S. A.
Forbes is engaged in interesting researches, having for object the
utilization of micro-organisms, but with more promise for pure than
applied science.
Of recent progress in mechanical appliances, the paper dealt
with those lately perfected under the author's direction by Dr. W.
S. Barnard, one of his assistants. This part of the subject was
illustrated by models and by plates from the forthcoming fourth
report of the United States Entomological Commission.
The paper concluded with the following plea for applied science
:
" Matters of fact do not tend to provoke thought and discussion
;
and I must confess to some misgivings in bringing these practical
considerations before a body which reflects some of the highest and
purest science and philosophy of the nation. From the days of
Archimedes down to the present day there has existed a disposition
to decry applied science and to sneer at the practical man. Yet I
often think that science, no matter in what fine-sounding name we
clothe her, or how high above the average understanding we stilt
her, is, after all, but common sense employed in discovering the
12 PHILOSOPHICAL SOCIETY OF WASHINGTON.
hidden secrets of the universe and in turning them to man's wants,
whether sensual or intellectual. Between the unbalanced vapor-
iugs of the pseudo-scientific theorizer and the uninformed empiric
who stumbles upon a discovery, there is the firm middle ground of
logical induction and deduction, and true seience can neither be
exalted by its inapplicability, nor degraded by its subserviency to
man's material welfare. The best results follow when the pure and
the applied go hand-in-hand—when theory and practice are wedded.
Erstwhile the naturalist was honored in proportion as he dealt
with the dry bones of his science. Pedantry and taxonomy over-
shadowed biologic research. To-day, largely through Charles Dar-
win's influence, we recognize the necessity of drawing our inspira-
tion more directly from the vital manifestations of nature in our
attempt to solve some of the many far-reaching problems which
modern science presents. The fields of biology, morphology, physi-
ology and psychology are more inviting than formerly. Nor is
the lustre that glorifies the names of Stevenson, Watts, Faraday,
Franklin, Morse, Henry, Siemens, and a host of yet living investi-
gators dimmed because they made science useful. Goethe makes
Wagner say :
" 'Ach wonn man so in sein Museum gebannt ist
Und sioht die Welt kaum einen Feicrtag
Kaum durcli oin Fernglas, nur von Weiton
Wio soil man sie durch Ueberredung leiten?'
" If to-day, right here in Washington, there is great activity in
the field of original r&search ; if the nation is encouraging it in a
manner we may well be proud of, the fact is due in no small degree
to the efforts of those, many of them members of this Society, who
have made practical ends a means* rather than to those who would
make science more exclusive, and who are indifferent to practical
ends or popular sympathy. Such, at least, is my apology for the
nature of this paper."
In response to an inquiry by Mr. White, Mr. Riley said that
the ox-eye daisy had been subjected to a thorough test under his
supervision and the result had shown that it has none of the insect-
icide qualities of pyrethrum.
GENERAL MEETING. 13
Mr. S. M. Burnett made a communication entitled
WHY THE EYES OF ANIMALS SHINE IN THE DARK.*
[Abstract.]
Erroneous opinions have been held and expressed, not only by
the non-scientific, but also by some persons holding high positions
in the scientific world, in regard to the phenomena of luminosity of
the eyes of animals, and particularly of cats, when they are in ob-
scurity. It is not due, as has been commonly supposed, to phosphor-
escence, but to light reflected from the bottom of the eye, which
light is diffused on account of the hypermetropic condition that is
the rule in the lower animals.
In response to a question by Mr. White, Mr. Burnett said that
human eyes affected by hypermetropia do not yield similar results,
partly because the human pupil is too small and partly because the
bottom of the human eye is not so strongly reflecting a surface as
that of most animals.
Mr. Harkness remarked that in determining the degree of di-
vergence of rays emitted by an eye, from an image situated upon
its retina, it is necessary to consider the magnitude of that image
as well as its distance from the focal plane of the lens. The diver-
gence of the rays coming from any one point of the image is deter-
mined by the interval which separates the retina from the focal
plane of the lens, while the divergence of the rays coming from
any two points of the image depends principally upon the size of the
image itself. The total divergence is the sum of the divergences
produced by these two causes, and the neglect of that due to the
size of the image will probably account for the discrepancy between
the observed angle of divergence and that computed by Dr. Burnett.
It also seems desirable to bear in mind the distinction between
fluorescent and phosphoresent light ; the former disappears as soon
as the incident waves are cut off; the latter does not.
* This paper u published in full in the Pop. Sci. Monthly for April, 1884;
Vol. XXIV, pp. 813-818.
14 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Mr. A. B. Johnson made a communication on
SOME ECCENTRICITIES OF OCEAN CURRENTS.
[Abstract.]
The records of the Light House Board show that no less than
eleven buoys of various patterns have gone adrift from the waters
of the United States and been found at distant points where ocean
currents have carried them. Many of these were not so fully iden-
tified that their precise original station could be indicated. In the
case of a few, it has been determined that they were swept from
the harbor and bay of New York by the outgoing ice in the winter
of 1880-81 when nineteen buoys were carried to sea.
1. In the spring of 1871, a buoy was picked up on the west coast
of Ireland.
2. In March, 1871, the Norwegian vessel Vance picked up a buoy
in lat. 42° 22', long. 26° 38'.
3. In February, 1881, a buoy went ashore on one of the cays
near Turk's island. This was recognized as a New York buoy.
4. May 17, 1881, the steamer William Dickinson passed a whist-
ling buoy in lat. 29° 46', long. 77° 38.
5. In March, 1881, a buoy of the largest size, likewise referred
to New York, was found near Bermuda.
6. In February, 1882, a Sandy Hook buoy was found near Ber-
muda.
7. In February or March, 1882, a buoy was washed ashore at
Pendeen Cove, Penzance Bay, England.
8. In the spring of 1882, the Swedish bark Abraham Lincoln
picked up a buoy in lat. 32° 30', long. 28° 40'.
9. October 22, 1883, a buoy was picked up on the east side of
Teneriffe in lat. 28° 21', long. 16° 15'.
10. October, 1883, a second buoy was picked up fifteen miles
from the east coast of Teneriffe.
11. August 20, 1883, the British bark Jane Richardson picked
up a buoy in lat. 24° 11', long. 32° 43'.
GENERAL MEETING. 15
All were identified as the property of the United States by letters
cast in the plates.
The charted currents of the ocean readily explain the courses
and account for the positions of many of these buoys, but others
appear anomalous.
Mr. Jenkins cited an instance of a bell-buoy, carried away from
the coast of the United States in 1850, which was seen and heard
while adrift and finally stranded on the southwest coast of Ireland.
Mr. Welling suggested that the phenomena might not be refer-
able to ocean currents exclusively, but in part to wind currents.
Mr. Johnson judged from the forms of the buoys that their move-
ments would be controlled more by currents than by winds.
Mr. H. Farquhar and Mr. Jenkins were of opinion that the
buoy picked up off Florida might have been carried there by the
southward coast-current. Mr. Dall concurred, but thought it also
possible that it had made the entire circuit of the Sargasso sea.
Mr. Dall, referring to Mr. Welling's suggestion, said that
wind and current worked together, and their effects could not be
discriminated. The wind does not blow prevailingly in any direc-
tion without coercing currents to correspondence.
247th Meeting. February 16, 1884.
The President in the Chair.
Fifty-four members and guests present.
The Auditing Committee reported through its Chairman, Mr. C.
A. White, that it had examined the accounts of the Treasurer for
1883, finding the same properly vouched in respect to expenditures
and receipts. On motion of Mr. Dutton, the report was accepted.
The Chair announced the election to membership of Mr. Henry
Wayne Blair and Mr. Herbert Gouverneur Ogden.
Mr. F. W. Clarke made a communication on
THE PERIODIC LAW OF CHEMICAL ELEMENTS.
After giving an account of the law as worked out by Newlands,
Mendelejeff, and Lothar Meyer, he exhibited an enlarged copy of
16 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Meyer's atomic volume curve, drawn with the latest values for both
atomic weight and specific gravity. On the same .sheet was also
drawn a similar curve, illustrating the connection between atomic
weight and melting point, and it was shown that in the latter the
highest portions correspond to the lowest depressions in the atomic
volume curve. The opinion was expressed, in view of the regu-
larities exhibited by these curves, that the elements had originated
by some method of evolution, and that a future transmutation of
one element into another was not improbable.
In reply to a question by Mr. Farquhar, Mr. Clarke said that
search was being made for similar evidence of system iu the spectra
of the elements, but that the subject was rendered difficult by
reason of the fact that not all the lines of the spectra fall within
the range of visibility.
Mr. Antisell remarked that while the determination of the
atomic weights of the elements was one of the most important
labors which the modern chemist could be occupied with until a
final constant numerical result should be arrived at, and until the
other properties of matter which appear to have some definite
relation with the atomic weight were rigidly investigated, there was
necessity for continued effort to search into those hidden relations
;
but if by such investigation it was believed that we could arrive at
any certainty about atoms, their form and structure, or about matter
itself, we should be much disappointed. Situated as we are on a
cold planet, we are precluded from ever arriving, by the study of
matter from a standpoint merely terrestrial, at any ideas of the
ultimate nature of atom or molecule, or whether there be really
any such thing as "elements" or one form of matter wholly dis-
tinct from another. To arrive at a knowledge of matter, pure and
simple, we must have ready means for dissociating all compound
matter, and we have at our command at present no such methods
or apparatus on this globe. Subjection to intense heat is required,
and our most glowing furnaces and the arc light itself is insufficient
for the purpose. It calls for the exhibition of such heat as is pro-
duced in the sun and its atmosphere to reduce our elements, as we
term them, to the more simple condition of matter as it exists under
solar temperature, and the present spectroscope and its future im-
provements by which such dissociation is to be studied. The
GENERAL MEETING. 17
investigations of Huggins and Lockyer and other spectroscop-
ists have revealed to us the presence of several of our so-called
elements in the solar atmosphere; but constant observation has
raised in the minds of these observers grave doubts whether the
spectral lines of the elements, as obtained by observation of them
in our atmosphere, are universally of such or whether only con-
ditionally so, that is true only in our cold atmosphere. Doubts
have arisen as to the spectral lines of elements being permanent
characters of their essential nature, seeing that the spectral lines
of an element, which at one time resemble those of copper, are
found to be interchangeable and attached to a different element, as
calcium, and that there are elements which possess the character of
giving multiple spectra, as carbon, for example, which, under these
solar temperatures, yields no less than three distinct and charac-
teristic spectra.
In view of these apparently contradictory and confusing results,
obtained by the examination of matter found in the solar atmos-
phere, which are so different from those obtained from matter in
our own atmosphere, it behooves us to be very cautious in asserting
the existence of any distinct elements so called, or whether there be
only one matter under various cosmical conditions.
Other remarks were made by Messrs. Doolittle and White.
Mr. H. A. Hazen made a communication on
THE SUN-GLOWS,
opposing the theory that they are due to dust, either cosmic or vol-
canic, and advocating a theory involving electrical action in con-
nection with frost particles.*
A general discussion followed, in which Messrs. Elliott, Paul,
Robinson, Hall, Dutton, Gilbert, and E. Farquhar, partici-
pated.
Mr. Elliott advocated the electrical origin of the glows, basing
his argument on the simultaneousness of the phenomena through-
out the planet, on the transparency of the glow as shown by obser-
vations on Lyrce, and on the extraordinary abundance of sun
spots for the past few weeks.
* This paper is published in full in the American Journal of Science for
March, 1884; Vol. XXVII, pp. 201-212.
18 philosophical society of washington.
248th Meeting. March 1, 1884.
The President in the Chair.
Forty-two members present.
The Chair announced that Messrs. Charles Otis Boutelle,
Gilbert Thompson, Willard Drake Johnson, and Eugene
Ricksecker had been elected to membership.
It was announced from the General Committee that standard
time would hereafter be recognized in the opening and closing of
the meetings.
Mr. R. D. Mussey read a paper entitled
THE APPLICATION OF PHYSICAL METHODS TO INTELLECTUAL
SCIENCE.
The aim of the paper was to show in how far those methods
which had been successfully employed in the investigation of the
phenomena of nature, and which were denominated the Physical
Sciences, were applicable to those sciences, the subject-matter of
which were mental operations and their results, and which, for dis-
tinction, might be named the Intellectual Sciences. Some illustra-
tions were given of the application of these methods to the study
of the law; and the paper concluded with the remark that its
writer desired it to be regarded as a suggestion rather than a solu-
tion of the problem stated: "How far and in what way physical
methods and physical sciences help thinkers to say Therefore."
Remai-ks were made by Mr. Robinson.
Mr. I. C. Russell made a communication on
DEPOSITS OF VOLCANIC DUST IN THE GREAT BASIN.
[Abstract.]
In contrast with the aridity of the Great Basin at the present
time, geologists have shown that during the Quaternary it was
crowded with lakes. In studying the sedimentary deposits of one
of these fossil lakes, named Lahontan by Mr. King, I found strata
GENERAL MEETING. 19
of white, unconsolidated, dust-like material, which is undistin-
guishable in general appearance from pure diatomaceous earth.
Beds of this material, varying in thickness from a fraction of an
inch to four or five feet, were observed at a number of localities
in the sides of the canons that have been carved in lacustrine
strata of Lahontan age by the Humboldt, Truckee, Carson, and
Walker rivers. Deposits identical with those of the Lahontan
sections were observed at a number of localities among the moun-
tains of Nevada and California at an elevation of several hundred
feet above the former level of Lake Lahontan and at a distance of
forty or fifty miles from its borders, thus showing that the deposits
were both sub-aerial and sub-aqueous in their mode of accumu-
lation. Further exploration revealed the fact that similar beds
occur abundantly in Mono Lake Valley, where they may be seen
to pass into well-characterized fragmental deposits of pumice and
obsidian, thus suggesting that the finer material was also of volcanic
origin. Experiment confirmed this hypothesis. Under the micro-
scope the dust from a number of widely separated localities was
found to consist almost wholly of angular flakes of transparent
glass, with scarcely a trace of crystallized matter. When a sam-
ple of pumice from near Mono Lake was reduced to a fine powder,
it was found to present the same physical and optical properties
as the dust in question, with which it also agreed closely in chem-
ical composition, as shown by analyses made by Dr. Chatard, of
the Geological Survey.
The Mono Craters, from which this dust is supposed to have been
erupted, form a group of cones about fifteen miles in length, situ-
ated in the southeastern part of the Mono Lake Valley, California.
These extinct volcanoes are composed almost entirely of pumice
and obsidian, in the condition both of coulees and lapilli, the latter
constituting cones of great symmetry and beauty, the grandest of
which have an elevation of nearly three thousand feet above Mono
Lake. Some of these craters were in eruption during Quaternary
times, while others were active after the ancient lakes and glaciers
of the region had passed away. Many times during their history
vast quantities of lapilli and dust were thrown out. As the
volcanic dust interstratified with the sediments of Lake Lahontan
is undistinguishable from that deposited in the Mono Basin, there
is little room for doubting that they had a common origin. The
20 PHILOSOPHICAL SOCIETY OF WASHINGTON.
greatest distance from the Mono Craters at which the dust was
observed, was in the Humboldt Canon, about two hundred miles
northward of the point of eruption.
At three localities in the Lahontan Basin the bones of extinct
mammals were found closely associated with the deposits described
above, thus furnishing the suggestion that the showers of fine vol-
canic dust were, at least to some extent, fatal to animal lire.
Mr. Antisell said it was useless to look for the source of vol-
canic dust in existing volcanoes on the land. Pumice in the
character of fine particles, as exhibited, is exclusively the product
of submarine eruption. Other remarks were made by Mr. Hark-
NE8S.
Mr. Lester F. Ward read a paper entitled
80ME PHYSICAL AND ECONOMIC FEATURES OF THE UPPER MIS-
SOURI SYSTEM,
in which he described the process by which the valleys of the Lower
Yellowstone and Upper Missouri are formed, and pointed out the
importance and the feasibility of utilizing the water of these rivers
for purposes of irrigation.*
Mr. Gilbert said that Mr. Ward's description of the process
by which the Missouri constructs its flood plain was verified by a
nearly identical group of phenomena observed by himself on the
lower course of the Colorado. Mr. Elliott concurred with the
speaker's view that the system of irrigation should be inaugurated
by national action rather than local. Mr. Riley was of opinion
that the proposed plan of irrigation was entirely feasible, and said
that the final solution of the grasshopper problem lay in the culti-
vation of the northern plains.
Mr. Burchard said that while the political advantage of a con-
tinuous belt of settlement uniting the Atlantic and Pacific States
was undeniable, he questioned the advisability of increasing at
present our agricultural production.
* This paper was subsequently separated into its two natural divisions,
and the part relating to the "physical features" was published with illus-
trations in the "Popular Science Monthly " for September, 1884 (Vol. XXV,
pp. 594-605), while that relating to the "economic features" appeared in
"Science" for August 29, 1884 (Vol. IV, pp. 166-168).
GENERAL MEETING. 21
249th Meeting. March 15, 1884.
The President in the Chair.
Fifty members present.
The Chair announced the election to membership of Messrs.
Mark Brickell Kerr, Samuel Hays Kaufmann, Joseph
Silas Diller, Charles Henry White, and William Law-
rence.
Mr. G. K. Gilbert made a communication on
THE DIVERSION OF WATER COURSES BY THE ROTATION OF THE
EARTH.
[Abstract.]
It being admitted that the rivers of the northern hemisphere are,
by the rotation of the earth, pressed against their right banks, and
those of the southern hemisphere against their left banks, it re-
mains to determine whether this pressure is quantitatively sufficient
to appreciably modify the courses of rivers. Opinion is divided,
and the results of observation have been largely negative. Those
who regard the cause as insufficient to produce observable results
have approached the subject from two points of view, which are
illustrated by the discussions of Messrs. Bertrand and Buff. The
former computes that a river flowing in N. lat. 45° with a velocity
of three metres per second exerts a pressure on its right bank of
fs^sv of its weight, and regards this pressure as too small for con-
sideration. The latter points out that the deflecting force, by com-
bining with gravitation, gives the stream's surface a slight inclina-
tion toward the left bank, thereby increasing the depth of water
near the right bank, and consequently increasing the velocity of
the current at the right. This increment of velocity has a certain
erosive effect, but it is regarded as less than that assignable to wind
waves on the same water surface, so that the prevailing winds have
a more important influence than the rotation of the earth.
The object of the paper is to consider the theoretical effect from
a new point of view. The form of cross-section of a stream flow-
ing in a straight channel depends on the loading and unloading of
detritus, and is essentially stable, its character being naturally
22 PHILOSOPHICAL SOCIETY OF WASHINGTON.
restored if accidentally or artificially modified. The distribution
of velocities within this cross-section is symmetric, the swiftest
threads of the current being in the center and the slowest adjacent
to the banks. If now curvature be introduced in the course of
the channel, centrifugal force is developed. This centrifugal force
is measured by the square of the velocity, and is therefore much
greater for the swift central threads of the current than for the
slow lateral threads. The central threads, tendiog the more strongly
toward the outer bank, displace the slower threads at that bank,
and the symmetry of the distribution of velocities is thus destroyed.
As pointed out by Thomson and others, this redistribution of velo-
cities determines the erosion of the outer bank and the simultaneous
deposition of detritus along the inner bank.
It has been shown by Ferrel that the deflecting power of the
rotation of the earth upon a body moving on the surface is equiva-
lent to the centrifugal force which would be developed if the body
followed a circular course with radius of curvature (/>) equal to
v
k r,- In this expression v is the velocity of the body, n the
Zi 'ih COS. '*
angular velocity of the earth's rotation, and 9 the polar distance of
the locality.
The effect of rotation on a stream being equivalent to a centri-
fugal force is identical in kind with the effect of curvature of
channel,* and this identity renders a quasi-quantitative comparison
possible. Humphreys and Abbott found during flood a mean
velocity of the Mississippi river at Columbus of 8.4 feet per second.
The value of p corresponding to this velocity and the polar dis-
tance of the locality is about 20 miles. The actual bends of the
channel in the same region, which depend for their features on the
velocity and volume of the river at flood stage, have a radius of
* The author has since seen reason to modify this statement. The two
effects are not strictly identical in kind, because the effect of rotation varies
with the first power of the velocity, while the effect of curvature of channel
varies with the second power. For this reason the selective power of curva-
ture is, for the same deflective force, double the selective power of rotation.
The introduction of this consideration would modify the numerical results
derived from the Mississippi river, but would not impair the qualitative
conclusion. A modified treatment of the subject will be found in the Ameri-
can Journal of Science for June, 1884; Vol. XXVII, pp. 427-432.
GENERAL MEETING. 23
curvature of about H miles. Centrifugal force being a simple in-
verse function of radius of curvature, it follows that the deflective
force by which the river is impelled toward its right bank by virtue
of rotation is proportioned to the force by which it is impelled
toward its outer bank on acute bends in the ratio of li to 20. That
is to say, in this particular instance the rotational deflective force
is 1\ per cent, of the deflective force from curvature of channel.
The process of lateral corrasion is so complex that it is impossible
to convert this result into terms of erosion and consequent deflec-
tion of stream channel, but a consideration of the manner in which
the two deflective forces are combined sufficiently indicates that that
due to rotation cannot be ignored. Wherever the stream bends
toward the left the centrifugal force developed by the curvature is
augmented by the rotational force; wherever the stream turns to-
ward the right the centrifugal force is diminished by the amount of
the rotational force ; so that the tendency of the swiftest threads of
current to approach the outer bank must be notably greater in one
set of bends than in the other.
If this analysis of the subject is legitimate, the rotation of the
earth ought surely to modify the courses of rivers to such extent
that the modifications are observable phenomena. Exception should
however be made of two important cases : first, rivers which are
rapidly deepening their channels are by that fact held rigidly to
their original courses, and are not deflected either by rotation or
by any other cause ; second, those parts of rivers whose function
is deposition instead of erosion, should theoretically, under the
influence of rotation, built their alluvial plains higher on the right
hand side than on the left, and having established an inclination
of the alluvial plain toward the left, should thereafter meander
over the plain with equal facility in all directions. It is only in
the. middle courses of streams, where the work performed by the
water is chiefly that of transportation, that the discovery of the
effects of rotation should be expected.
Mr. Ward remarked that in the regions especially discussed the
river courses are, in general, southerly, while the prevailing winds
are westerly, so that the influence of the winds is opposed to what-
ever influence may be exerted by rotation. Mr. Abbe said that
the tendency of driftwood toward certain river banks, cited by
24 PHILOSOPHICAL SOCIETY OF WASHINGTON.
von Baer, had been plausibly explained as due to prevailing winds,
but such action is purely or chiefly superficial, and.a less important
factor in erosion than the behavior of the* main current, which is
comparatively little influenced by winds. Nevertheless, he was
surprised that the rotational influence admitted of so large a quan-
titative expression.
Mr. Dall said that the northward-flowing rivers entering the
Arctic ocean afforded at their mouths no evidence of the effect of
rotation. The summer winds of Arctic regions are from the north-
east and east, and these produce on the north coast of America a
shore-current, which drifts the beach sand and shingle westward,
and deflects the river-mouths in the same direction. All the rivers
from the Mackenzie to Point Barrow illustrate this tendency. On
the coast of Siberia the fresh water discharged by the large rivers
has been observed to turn eastward, although the winds would
tend to throw it the opposite way. The Arctic ocean is there
deeper ; and it is believed that its principal currents are controlled
by the northeasterly set of the general currents of the North
Atlantic.
Mr. Robinson spoke of the indirect influence of wind on river
channels, through drifting sand. ' Mr. Hazen pointed out that the
influence of wind might be eliminated from the problem by study-
ing the streams running east or Avest. Mr. Boutelle suggested
that the course of the Mississippi did not indicate any result of
rotational influence. Mr. E. Farquhar inquired Avhether the
behavior of the Gulf Stream and other ocean currents was in accord-
ance with the theory of rotational influence ; and Mr. Dall re-
sponded that in the discussion of ocean currents this cause had lately
dropped out of sight, the determination of courses being ascribed
to the winds.
Mr. Mussey inquired whether the acuteness of continental
masses toward the south admitted of an explanation based on the
effect of terrestrial rotation ; and Mr. Dutton responded by saying
that the mass of speculation in regard to the recurrence of certain
forms of continental outline had never really accomplished more
than the statement of the fact. The fact itself is an accident,
dependent on the volume of the ocean and the general laws govern-
ing the formation of mountain chains. If the ocean were five
hundred feet deeper, or five hundred feet shallower, the forms of
GENERAL MEETING. 25
continents would be so far different that all the existing resem-
blances would disappear. The pointed extremities of some conti-
nents are merely expressions of the fact that mountain chains are
more or less linear, and do not hold the same height throughout
their whole extent.
Mr. G. E. Curtis read a paper on
THE RELATIONS BETWEEN NORTHERS AND MAGNETIC DISTURB-
ANCES AT HAVANA,
upon which remarks were made by Messrs. Abbe and Coffin.
[It will be published by the Army Signal Office as fiiynal Service
Note No. XIII.']
Mr. Gilbert recurred to the subject of Mr. Russell's paper of
the preceding meeting, and dissented from the view advanced by
Mr. Antisell in regard to the origin of pumice. Mr. Antisell
announced that he would discuss the matter more fully at some
future meeting.
250th Meeting. March 29, 1884.
Vice-President Mallery in the Chair.
Forty-two members present.
The Chair announced the election to membership of Messrs.
Basil Norris and William Stebbins Barnard.
Mr. J. S. Billings spoke briefly on
composite photography applied to craniology,
exhibiting several composite photographs of skulls. Adult male
skulls of the same race were selected for composition and were
photographed in sets of from 7 to 18—front, side, and back views
being separately taken. The composition was directly from the
skulls and not from the photographs.
Incidental mention was made of the uncertainty of measure-
ments of cranial capacity by means of shot. Not only did differ-
26 PHILOSOPHICAL SOCIETY OF WASHINGTON.
ent observers obtain widely different determinations from the same
skull, but the same observer was not able to obtain«closely approxi-
mate results in successive determinations.
Mr. G. Brown Goode made a communication on
FISHERIES EXHIBITIONS,
giving a list of all international exhibitions and describing es-
pecially those of Berlin (1880) and London (1883). The adminis-
trative systems of these two national exhibits were contrasted, and
the social and economic results of the London exhibit were ex-
plained. [The substance of the paper will be published in the ex-
ecutive report on the London and Berlin exhibitions.]
Mr. M. H. Doolittle began a communication on
MUSIC AND THE CHEMICAL ELEMENTS,
but was unable to complete it before the hour for adjournment.
The remaining portion was postponed until the next meeting.
By unanimous consent adjournment was deferred for a few
minutes in order to afford Mr. Antisell an opportunity to reply to
a criticism made at the previous meeting in regard to his views on
the origin of pumice.
251st Meeting. April 12, 1884.
The President in the Chair.
Forty-one members and guests present.
Announcement was made of the election to membership of
James Arran Maher, John Belknap Marcou, John Milton
Gregory, Francis Tiffany Bowles, and William Eimbeck.
GENERAL MEETING. 27
Mr. M. H. Doolittle made a communication on
MUSIC AND THE CHEMICAL ELEMENTS.
[Abstract.]
The mathematical theory of music requires the satisfaction of
/ 3 \ y
the equation 2X = I ~tt ) nearly; in which, for equal temperament,
x = the number of equal intervals in the octave, and y =-= the
number of these intervals that correspond to a nearly perfect fifth
;
and, for untempered music, x = the number of approximately
equal intervals in the octave, and y = the number corresponding
to a perfect fifth.
The above equation gives
log JL
x 2 . 176091
,j = ioj2 nearly = mm nearly;
and by the method of continued fractions we obtain the succession
, .
'
. 3 7 24 31
ot approximations—» —> — , — > &1F
5 12 41 53 ac-
For scales appropriate to major thirds, but disregarding fifths,
5 3
we may substitute — for —- in the above equations, and obtain
4 2
1 9 19
the approximations — > -—, — , &c. For the chord having the
o 28 59
vibration ratio 7 : 4 (called by Ellis the subminor seventh), we may
4 21
obtain in like manner the approximations -f-» kt?' &c.
Since -q~ sa= jn' the first two series of approximate fractions
include a common scale of twelve intervals to the octave, of which
seven intervals give the fifth, and four give the major third. The
first and the third of these series include a scale of five intervals
to the octave, of which three constitute the major third, and four
constitute the subminor seventh. There is some reason to believe
that this is the scale of Japanese music, with the intervals
7 8 9 ^ 8 TT II. -n -i J
-£->
-s-'
-o-» ~n" ~y r lve-tone scales have universally prevailed
in early music; but it is questionable whether the vibration ratios
28 PHILOSOPHICAL SOCIETY OF WASHINGTON.
have in any case involved the prime number seven. It would be
interesting to know what scale best represents the songs of wild
birds.
There is much reason to believe that simple mathematical princi-
ples underlie the phenomena of chemistry. It is not, a priori,
absurd to suppose that matter in some way conforms to the prop-
erties of the primes 2, 3, and 5 ; in which case such derivative
numbers might be expected prominently to appear as prominently
7
occur in the science of music. The fraction rg might reasonably
be expected.
If all the keys of a piano should be arranged seven consecutive
keys in a line, the next seven in the next line, and so on, the columns
give successions of fifths. It has been shown that if the chemical
elements are arranged in the order of their atomic weights in lines
of seven, the columns contain elements remarkably similar to each
other. We seem to have a chemical scale remarkably analogous
to the ordinary musical scale. If the piano keys be arranged in
lines of twelve, the columns give octaves ; bwt nothing is devel-
oped from a similar arrangement of the chemical elements, whence
it may be inferred that the observed analogies are accidental, and
have no true logical basis.
If the intervals of the chemical scale could be supposed to cor-
respond to the seven intervals of the diatonic scale, the non-appear-
ance of the twelve-fold relation would be accounted for ; but, while
the diatonic scale may have some claim to be called natural, it is
not directly established by algebraic investigation of the relations
of prime numbers. Until the discovery of chemical flats and
sharps, there will be insufficient reason to regard the present chem-
ical scale as diatonic.
Mr. Lefavour illustrated the connection between tone and
wave-length by means of a logarithmic spiral of base 2, the har-
monic notes having radii vectores equal to multiples of the principal
note.
Mr. Elliott said he had learned from Mr. Poole that he had
endeavored, in his euharmonic organ, to produce perfect chords in
all keys without temperament.
Mr. Kummell remarked that in modern music the intervals of
the major and minor thirds are the most important, because with-
GENERAL MEETING. 29
out them there is no harmony. This is also apparent from the well-
known rule in thorough-bass that a third with its fundamental
note is to be treated as a complete chord. Now it happens, in
dividing the octave by equal temperament into 12 equal parts,
that a major third is nearly 4 and the minor third nearly 3 of
these, and thus we obtain not only tolerable fifths, but also tolerable
thirds, and the requirement of thirds for harmony is approximately
fulfilled. They are still better fulfilled, of course, if we divide the
octave into 41 or 53 parts, as Mr. Doolittle has shown. As to the
seventh harmonic, Poole and Helmholtz rightly hold that it should
be and is used by instruments which can temper. It is obviously
the fourth element of the chord of the dominant G, B, D, F, the F
being the seventh harmonic to the G two octaves below (nearly
so in equal temperament and exactly in natural harmony), and
this chord in modern music forms the opposing harmony to the
tonic chord C, E, G, in major, and C, E fiat, G, in minor. Instru-
ments with fixed tones like the piano-forte have to use equal tem-
perament, and thus virtually reject all natural harmony except the
octave. This defect is generally inappreciable in very slow move-
ments, but may be noticed by a very cultivated ear.
Other remarks were made by Messrs. Clarke, Mussey, and
Harkness.
Mr. H. Farquhar read a
REVIEW OF THE THEORETICAL DISCUSSION IN PROF. P. G. TAIT's
" ENCYCLOPEDIA BRITANNICA " ARTICLE ON MECHANICS.
[Abstract.]
This article covers seventy-four quarto pages in the last edition
of the Encyclopsedia, and gives a thorough mathematical treatment
of the subject. No innovations calling for comment—unless an
extended use of the " fluxional " notation for derivative functions
be so regarded—appear until near the end, where two and a half
pages are devoted to a disproof of the objective reality of force,
and an advocacy of the disuse of the term in scientific writing.
The character of the publication, and the eminence of the author
in mathematics and physics, entitle his arguments to a careful
examination.
30 PHILOSOPHICAL SOCIETY OF WASHINGTON.
In the first place, Prof. Tait infers that force can have no such
reality as matter has, because it is to be reckoned positively and
negatively—an action being opposed by reaction—while matter or
mass is signless. This suggests two comments: (1), the author
never questions the objective reality of space and time, of which
realities it is an essential feature that to every direction or interval
A-B, an equal direction or interval B-A, of opposite sign, corres-
ponds
; (2), the idea of a negative mass is not a self-contradictory
one, and was once generally accepted. The element phlogiston was
given up not because of any absurdity in ascribing levity to ma-
terial substance, but because a form of matter with positive mass
(oxygen), capable of explaining all the phenomena, had been actually
separated and identified.
Prof. Tait's next criterion of objective reality is quantitative
indestructibility, an attribute shared by time, space and matter, to
which he adds energy. But the evidence of the indestructibility
of energy is not of the same nature as that of the indestructibility
of matter ; for the latter in all its forms may be localized, and its
density or elasticity measured ; while the former, when stored up
or " potential," cannot be shown to possess any of the properties of
energy kinetic, or any existence in space, or any objective character
whatever. Prof. Tait admits this difficulty virtualty, and awaits
for its solution the discovery of some evidence "as yet unexplained,
or rather unimagined." All strains and other actions of a clock-
weight on its supports are obviously precisely the same—or impalp-
ably somewhat stronger—with the weight wound up an inch, as with
it wound up a yard; and the existence of a greater "potential
energy " in the latter case is to be found not in the clock, but in
the mind, which requires this expression as a form in which to put
its conviction that a certain greater amount of work can be obtained.
Even though it be admitted that there are no other intelligible
terms in which this conviction can be stated, it is clear that the
indestructibility of energy is an ideal and subjective truth, and
cannot, therefore, be relied on as evidence of a reality distinctively
"objective."
A third point made by Prof. Tait against force is that its nume-
rical expression is that of two ratios : " the space-rate of the trans-
formation of energy" and "the time-rate of the generation of
momentum." These results are obtained by simple division, in an
GENERAL MEETING. 31
equation which expresses the fact that the work done by a body in
falling the distance h is just that required to lift it through h against
gravity. The fallacy involved in treating the numerical expression
for force as force itself, has been well exposed by Mr. W. R. Browne
(in a criticism of the same article, L. E. D. Phil. Mag. for Novem-
ber, 1883) ; and the assumption that ratios are necessarily non-
existent is even more fallacious. Were it trustworthy, Prof. Tait's
deductions would not be the only ones admissible. His equations
would lead quite as conclusively to proofs of the non-objectivity
of space and time (the former becoming the rate of work-units,
the latter of motion-units, per unit of force), and so to a confirma-
tion of the celebrated German view, that that which is universal
and necessary in thought, belongs to the Subject ; or they might
even give mass in the form of a ratio, and hence suggest the non-
objectivity of matter.
Not the least of the Professor's objections against force, it would
appear, is that it is " sense-suggested." It is a mere truism to say
that no other suggestor is possible, within the domain of science.
It is, perhaps, better worth while to call attention to the indubitable
fact that the real, if not the avowed, ground of the objection
against " action at a distance," entertained by many physicists, is
that such action is not directly suggested by sense-impressions. This
is what they must mean by calling it " occult ; " actions as our con-
sciousness knows them, and as we can produce them, being gene-
rally characterized by proximity undistinguishable from actual
contact. Further, if there is any reproach in this epithet, energy
is quite as open to it as any function of energy can be. In fact,
our senses directly report work, in the form of nerve-disturbance,
and nothing else. Force is no more truly an inference from nerve-
reports testifying of energy exerted, than is matter. In fact, the
inference of the independent existence of matter is the less direct
and more questionable of the two. The view advocated by Mr.
Browne, following Boscovich, that matter is but "an assemblage
of central forces, which vary with distance and not with time " or
with direction, is one of great simplicity as well as suitability to
analytic treatment, and one of which no disproof is possible.
The paper was discussed by Messrs. Doolittle and Elliott.
32 PHILOSOPHICAL SOCIETY OF WASHINGTON.
252d Meeting. April 26, 1884.
Mr. Harkness in the Chair.
Thirty-eight members and guests present.
Announcement was made of the election to membership of
Messrs. David Porter Heap and Thomas Mayhew Woodruff.
Mr. J. R. Eastman made a communication on
A NEW METEORITE.
[Abstract.]
A mass of meteoric iron weighing 113 pounds was accccidently
discovered in the making of an excavation at Grand Rapids, Mich-
igan, and was examined by the speaker in 1883. One face shows
evidence of fracture, and the greater part of the remaining surface,
of fusion. A very small sample submitted to Mr. F. W. Taylor
for chemical examination had a specific gravity of 7.53 and a com-
position :
Iron .... 94.54
Nickel .... 3.81
Cobalt .... .40
Insoluble (about) . . .12
The stone is supposed by its holders to consist of gold and silver,
and to be the buried treasure of a miser. This delusion has caused
it to form the subject of a lawsuit.
The communication was discussed by Messrs. Bates and F. W.
Clarke.
Mr. "W. H. Dall read a paper on
CERTAIN APPENDAGES OF THE MOLLUSCA.*
* Published in tbe American Naturalist, Vol. XVIII, pp. 776-778.
GENERAL MEETING. 66
Mr. J. S. Diller made a communication on
THE VOLCANIC SAND WHICH FELL AT UNALASHKA OCTOBER 20,
1883, AND SOME CONSIDERATIONS CONCERNING ITS
COMPOSITION.
[Abstract.]
The sand is composed chiefly of crystal fragments of feldspar,
augite, hornblende, and magnetite, with a considerable proportion
of microlitic groundmass and a very few splinters of volcanic glass.
Its mineralogical composition is that of a hornblende andesite ; but
the chemical analysis by Mr. Chatard shows it to contain only
52.48 per cent, of silica,—which is much more basic than the average
for that group. The character of the minerals, as well as the gen-
eral composition of the sand, indicated so clearly that the crater
from which it must have issued was erupting hornblende-andesite,
that I was led to seek an explanation for its paucity in silica.
With this purpose in view, a number of volcanic sands and dusts
from various parts of the world were examined and compared with
the lavas to which they belong. First and most important among
these is a sand from Shastina, a crater named by Captain Dutton,
upon the northwestern flank of Mt. Shasta, in northern California.
This sand, like that from Unalashka, is composed chiefly of crystal
fragments of feldspar, augit#, hornblende, and magnetite, with
fragments of microlitic groundmass. Besides these, there are many
pieces of hypersthene crystals and pumiceous glass. The sand con-
tains 60.92 per cent, of silica, while the hornblende-andesite lava
(rich in hypersthene) of Shastina, to which the sand belongs, con-
tains 64.10 per cent, of silica.
From these and other examples it may be stated as generally
true that volcanic sand is composed essentially of crystalline frag-
ments, and contains less silica than the lava to which it belongs.
With volcanic dust, however, the case is different. Microscopical
examination shows that it is composed chiefly of volcanic glass
particles ; and as far as chemical analyses have been made, they
indicate that volcanic dust is more silicious than the lava to which
it belongs.
That volcanic sand should be crystalline and basic, and the
accompanying dust vitreous and acidic, as compared with the lava
34 PHILOSOPHICAL SOCIETY OF WASHINGTON.
to which they belong, is not merely determined by accidental cir-
cumstances, but has its inception in the magma before the eruption
takes place. By the process of crystallization magmas are fre-
quently divided into a crystalline solid portion, and an amorphous
more or less fluent portion. Basic minerals are the first to crys-
tallize, so that as the process advances the amorphous remnant of
the magma becomes more and more silicious. The crystals are
generally thoroughly intermingled with the amorphous magma, and
in the latter are accumulated nearly all of the absorbed gases
under great tension, so that when the pressure is relieved it may
be blown to fine silicious dust, which may be carried by the wind
many miles from its source, while the solid crystalline portion will
contribute chiefly to the formation of sand, and be precipitated
comparatively near the crater from which it issued.
In cases where no previous crystallization has taken place in the
magma before it comes to violent eruption, the volcanic dust then
formed will have about the same chemical composition as the lava
to which it belongs. Mr. Russell has recently described an inter-
esting case of this kind in the western part of the Great Basin.
It appears to be generally true that if other conditions are favor-
able the difference in chemical composition between volcanic sand
and dust is directly proportional to the amount of crystallization
in the magma before its ejection.
The basic character of the Unalaahka sand may be explained by
supposing that the silicious portion of the magma was carried away
in the form of dust.
The source of this sand is supposed by the collector, Mr. Apple-
gate, the Signal Service Observer at Unalashka, to have been the
new crater formed last autumn, near the Island of Bogosloff, about
sixty miles away.
Mr. Dutton spoke in commendation and amplification of Mr.
Diller's contribution to geologic philosophy. Mr. Dall described
the geographic relations of the volcano from which the Unalashkan
dust was presumably derived, showing the improbability of the
eruption having been directly observed. He spoke also of the dis-
tribution of the Aleutian volcanoes and the lithologic characters
of their ejectamenta.
There ensued a general discussion of the nature and properties
GENERAL MEETING. 35
of volcanic dust and of the theory which ascribes recent meteo-
rologic phenomena to the dust ejected by Krakatoa. In this Messrs.
Duttox, Paul, W. B. Taylor, Diller, Robinson, and Ward
participated. Mr. Dutton pointed out that their process of for-
mation tends to give volcanic dust particles a quasi-definite size,
and probably does not produce a large amount of dust fine enough
for indefinite suspension. The greatest distance to which volcanic
dust has been definitely ascertained to travel is eight hundred miles.
Mr. Paul argued from the violence of the Krakatoan explosion
its competence to charge the atmosphere at very great altitudes,
and considered the fineness of the dust a sufficient explanation of
its indefinite suspension.
Mr. Taylor said the phenomenon to be accounted for was
specially remarkable, first, for the unusual elevation of the finely-
divided smoke or dust extending far above the highest cirrus clouds,
or probably to twenty or thirty miles above the earth's surface (as
shown by its twilight duration) ; secondly, for its wide diffusion
(covering a large fraction of the terrestrial atmosphere) ; and
thirdly, for the long continuance of its suspension in the air (ex-
tending over many months). Mr. Lockyer and Mr. Preece had
suggested an electrical condition of the matter as favoring both its
extraordinary diffusion and its equally extraordinary suspension.
This hypothesis seemed to the speaker very plausible. Electricity
is a phenomenon of volcanic eruption, and dust particles charged
with electricity in the same sense with the earth would be repelled
not only by one another, but by the earth. At thirty miles above
the ground the air is not only very rare, but is practically anhydrous,
and the discharge of electricity is impossible.
Mr. Diller, in response to a question by Mr. Paul, said that the
microscope reveals no limit to the fineness of Krakatoan dust. The
higher the magnifying power applied, the greater the number of
particles visible ; and this relation extends to the limits afforded by
the capacity of the instrument. To more powerful microscopes,
yet finer particles would presumably be visible.
36 PHILOSOPHICAL SOCIETY OF WASHINGTON.
253d Meeting. . May 10, 1884.
The President in the Chair.
Fifty-four members and guests present.
Announcement was made of the election to membership of
Messrs. John Murdoch, Romyn Hitchcock, "William Smith
Yeates, George Perkins Merrill, and Frederic Perkins
Dewey.
It was announced that a vacancy in the General Committee,
occasioned by the resignation of Mr. J. J. Knox, had been filled
by the election of Mr. F. W. Clarke.
By invitation, Mr. G. H. Williams, of Baltimore, Maryland,
addressed the Society on
THE METHODS OF MODERN PETROGRAPHY,
first, defining the field of petrography, and second, discussing the
methods of petrographic investigation. These methods are: (1),
chemical; (2), mechanical ; (3), optical; (4), thermal. The chem-
ical methods are quantitative and qualitative. The mechanical
methods include the separation of the constituent minerals of rocks
by precipitation in heavy solutions and by the use of electro-mag-
nets. The optical methods include the preparation of thin sections,
their examination by transmitted ordinary light, and their exam-
ination by polarized light, for the determination of crystallographic
system, pleochroism, and angles of extinction. The thermal methods
are chiefly synthetic, consisting in the artificial production of min-
eral aggregates for the purpose of determining the processes of their
natural production. By the regulation of temperatures in fusion
and refrigeration all varieties and all structures of basic rocks are
reproduced. Acidic rocks have not been thus reproduced^ and it
is believed that great pressure is a condition of their genesis.
Mr. Dutton spoke of the bearing of modern petrographic in-
vestigations on some of the greater problems of geology.
GENERAL MEETING. 37
There followed a symposium on the question
WHAT IS A GLACIER?
[Abstract.]
Mr. I. C. Russell: In framing a definition of a glacier it is
evident that we must include both alpine and continental types,
and also take account of the secondary phenomena that are com-
monly present. With this preamble we may define a glacier as an
ice-body, originating from the consolidation of snow in regions
where the secular accumulation exceeds the loss by melting and
evaporation, i. e., above the snow-line, and flowing to regions where
loss exceeds supply, i. e., below the snow-line.
Accompanying these primary conditions, many secondary phe-
nomena dependent upon environment, as crevasses, moraines, lami-
nation, dirt-bands, glacier-tables, ice-pyramids, etc., may or may
not be present.
Mr. S. F. Emmons: The glacier is a river of ice, possessed, like
the aqueous river, of movement and of plasticity. In virtue of
the latter quality it adapts itself, though more slowly, to the form
of the bed in which it flows. The neve field is the reservoir, from
which it derives not only its supply of ice, but the impulse which
gives it its first movement. The nev6 is formed by the snows which
accumulate in relatively wide basins above the snow-line from
year to year, living through the heat of summer. Its mass may be
more or less compact, according as it is thicker or thinner, and it
may have a certain movement, which will be greater or less, accord-
ing to the greater or less inclination of the basin ; but until it moves
from its wide and shallow bed into a narrower and deeper one, and
thus gives outward proof of the plasticity of the ice of which it is
composed, it does not become a glacier. It may be crevassed.
Often a long crevasse at its upper edge gives definite proof of its
movement ; and this movement may cause a cracking or crevassing
in other points, resulting from the unevenness of its bed. It may
or may not carry blocks of rock on its surface, but these would be
rare, and never in the well-defined moraine ridges that are formed
upon the glacier proper. Not, however, until its form had essen-
tially changed to fit the bed in which it flows should it be considered
to constitute a glacier proper.
21
38 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. "W J McGee: The phenomena of glacier ice and neve ice
appear to belong to a graduating series; and in consequence the
two phases can only be arbitrarily discriminated. Any classifica-
tion depending upon coincidence of the loci of apparent transition
from the first phase to the second with loci of sudden constriction
or abrupt acclivity in the valley is artificial and incompetent,
since such coincidence is fortuitous; the classification depending
upon the ability of the second phase to sustain bowlders upon its
surface is superficial and incompetent (provided such ability be due
to density of the ice), since the sub-surface density of the neve,
being determined by its age and the pressure of the superincumbent
mass, must, in some portions, equal the surface density of the gla-
cier; and the classification depending upon rate of motion is equally
incompetent, since motion is common to the entire ice-mass, and
abruptly varies only where conditions of glacier-bed are suddenly
variant. Arbitrary diagnostic characters may and should be, how-
ever, agreed upon by consense among glacialists. Perhaps the
most satisfactory line of demarkation detectable is the snow-line,
above which superficial debris is buried by precipitation, and below
which it is exposed by ablation.
Mr. W. H. Dale: It is proper to discriminate masses of ice
moving in a definite direction from the immense fields of ice which
are practically stationary. The term " glacier " should be restricted
to the former. A glacier is a mass of ice with definite lateral
limits, with motion in a definite direction, and originating from
the compacting of snow by pressure. Moraines are not diagnostic
;
and the definition should not include those masses of arctic ice
which, by reason of their low temperature, are fixed in position.
Mr. T. C. Chamberlin: Nomenclature is a matter of conveni-
ence. When subjects rise into familiar thought and frequent
reference brevity of expression calls for specific names. But terms
arising thus from a natural demand are not closely discriminative.
Hard and fast lines of demarcation do not prevail in nature, but
rather gradations of character. Were it otherwise names of sharply-
defined application could be more freely used. The terms neve and
glacier doubtless originated to satisfy the convenience of guides and
travelers, aud were without strict scientific application. In attempt-
ing to give them scientific definition, I think we shall fail of satis-
faction by making them structural terms. The better distinction
GENERAL MEETING. 39
is genetic. There is an area of growth and an area of waste to
every glacier, and the distinct recognition of the two in quaternary
glaciers is likely to rise to some importance. Superficially the area
of growth coincides with the n6ve ; the area of waste is that of the
glacier proper. From every annual snow-fall there remains, at the
time of maximum summer melting, a remnant that feeds the gla-
cier. This is the neve for that year. The area may be greater or
less in different seasons. The neve-field is accurately shown only
on the day of maximum waste.
A contribution of much value, bearing upon the property of ice
which permits glacier motion, has recently been made by Petterson,
who has demonstrated, by refined experimentation, that ice, es-
pecially if impure, shrinks as it approaches the melting point and
becomes plastic.
Mr. C. E. Dutton desired to reiterate the remarks of Mr.
Chamberlin to the effect that definitions can rarely or never be
made rigorous. Glaciers, no doubt, vary in their characteristics like
almost all other groups of phenomena. There is little difficulty in
recognizing a glacier when all those features which characterize it
are present, and when the conditions are of the ordinary nature.
But exceptional cases arise. The lower parts are sometimes want-
ing and the neve alone remains, or the portion where the neve*
passes into the glacial stream may constitute the termination. In
the latter case those who desire to be extremely precise in their
phraseology might hesitate. It should seem best, whenever an
occurrence is modified or defective, to use the term " glacier," with
a qualification which shall express the particular circumstancs.
Remarks were also made by Messrs. Gilbert and Elliott.
254th Meeting. May 24, 1884.
The President in the Chair.
Twenty-six members and guests present.
It was announced from the General Committee that after the
255th meeting, Juue 7, the Society would take a vacation until
October 11.
40 PHILOSOPHICAL SOCIETY OF WASHINGTON.
A request on behalf of the coming Electrical Exhibition at Phil-
adelphia for instruments and books was communicated to the Society.
Mr. H. H. Bates read the following paper on
THE PHYSICAL BASIS OF PHENOMENA.
If there is anything entirely disheartening, it is to see the few
landmarks of human achievement disappear before the shifting
current of opinion, as headlands disappear under the ceaseless
buffeting of the ocean. It is no doubt a matter of poignant regret
to the cherisher of ardent theological convictions to see the bulwarks
of faith slowly undermined by controversy. So, also, to him Avho
has built his convictions on supposed demonstrable and irrefragable
fact, to find nothing unassailable, not even the axioms and postu-
lates conceded for ages as first principles, on which the fabric of
science was reared, nor the sublime inductions of Galileo and
Newton, on which the modern philosophy called natural—the only
fruitful philosophy which man has produced—has been founded.
But the course of criticism shows that there are no first princi-
ples. Nothing is unquestionable. Even the mathematic joins
hands with the metaphysic. I propose briefly to examine the fun-
damental grounds of mechanical philosophy, in view of the wide
divergence of basal hypotheses in recent years, and especially on
account of the importance conferred upon certain speculations by
their admission into works of standard reference and authority.*
To do this aright it is necessary to go behind the mere sub-science
of mechanics to the essence and substance of things, as did the
eighteenth-century philosophers succeeding Newton. The obser-
vational data which have accumulated since that time by the splen-
did efforts of the molecular physicists enable us to review and recast,
with some promise, the primary dogmas regarding the physical basis
of phenomena. It is legitimate to frame hypotheses on subjects
which are still unfathomed, but which confessedly do not belong to
the domain of the unknowable. The distinguished example of the
authors of the vortex atom would alone justify such a conclusion.
No entirely satisfactory hypothesis of the atom has yet been
* Encyclopaedia Britannica, 9th Ed., Articles " Mechanics," "Measure-
ment," etc.
GENERAL MEETING. 41
fouud. I do not design to discuss the vortex atom here at length
;
for, although it is the most successful form of the Cartesian doctrine
of vortical substance, it has not been perfected, and is generally-
regarded rather as an example of remarkable speculative and math-
ematical ingenuity, than as a discovery, corresponding with any
facts of objective physics. It has insuperable difficulties, some of
which have been pointed out by Clifford, and others by Clerk-
Maxwell. Moreover, unparticled or continuous substance, the
necessary postulate in this hypothesis, is something we not only
have no experience of, but find full of inconsistencies with ex-
perience, when we gain a clear conception of what it implies. Such
a conception fulfills Hegel's paradox that being and non-being are
the same, since it forbids all mobility, all differentiation, as was
perceived by the followers of Democritus. It simply affords an
inviting basis for analytical discussion, on account of the elimina-
tion of the very conditions of objective existence which make the
mathematical difficulty.
There are some postulates regarding substance which we may
probably be permitted to assume at the outset. We may postulate
its objectivity, and also its discontinuity. I have no space to review
here the time-worn controversy between continuous and discontin-
uous substance. The arguments, which are exhaustive from the
metaphysical side, are as old at least as Democritus and Anaxa-
goras. Suffice it to say that modern experiential philosophy has
decided the battle experimentally in favor of the discontinuity of
matter. The dispute only lingers in the region of the atom, where
observation cannot penetrate or has not penetrated. The inability
to conceive which attaches to all non-experiential affairs is encoun-
tered here, coupled with the too great facility of conceiving what
is superficially observed, but will not bear analysis. Thus our first
impressions of substance are in favor of its continuity. It is only
after much reflection that we get the idea of necessary discontinu-
ity, as bound up with the exhibition of existing phenomena. But
the wonderful development of the Cartesian mathematics, in con-
junction with the infinitesimal calculus, and its great facility in
dealing with geometrical continuities, has tacitly revived the Car-
tesian idea regarding the nature of matter, as synonymous with
space relations, which never reached intelligible development at the
hands of its author, and wholly declined and disappeared after the
42 PHILOSOPHICAL SOCIETY OF WASHINGTON.
establishment of the Newtonian philosophy, and the discovery of
the discrete character of substance.
In point of fact, experience would point to extreme porosity or
discreteness as characteristic of substance, rather than to its oppo-
site
—
perfect continuity. The infinite divisibility of space has
nothing in the world to do with the question, though this is a con-
fusion often fallen into. On the contrary, there is an infinite dis-
tinction between the infinitesimal discrete units of substance, occu-
pying extension by their interactivity, and the passive infinitesimal
resolvability of space continuity. This is the antipodean difference
between the Epicurean and the Cartesian conceptions ; the former
admitting of the operations of force, the free exhibition of motion,
the organization of material phenomena, which are phenomena of
mobility ; the latter constituting a plenum, with only ideal divisions,
and phenomenally as necessarily barren a negation as space itself.
Substance is purely experiential. In its essence it is still incom-
prehensible, because experience has not yet reached down to those
recesses. We know nothing of substance except by its manifesta-
tions. These manifestations are cognized by us through sense im-
pressions, weighed, compared, adjusted, and analyzed in the mys-
terious alembic of the mind. First impressions have enormous
predominance, and are intensified by heredity of cerebral predis-
position and function.
"We cognize substance only in bulk by direct perception, and
these vast aggregations stand in thought for matter. A drop of
water contains incomparably more molecules than the ocean con-
tains drops ; a grain of sand more particles than the earth contains
grains ; and it is this vast mesh of complicated forces that forms
the integrated concept of matter to our apprehension. The child,
before he can walk, encounters obstacles to movement, reaction to
his every muscular effort, of equal measure to his own ; and thus
his first and profoundest convictions of objective existence are asso-
ciated with resistance, opposition, repulsion. This impression of
matter is so early that it remains with us as its most natural and
obvious characteristic.
The idea of weight is also one of the earliest experiences. This
idea would not be conceivable to a denizen of the deep sea, for
our first ancestor who emerged from the water gained the experience
at the cost of great struggle and enterprise. By the natural devel-
GENERAL MEETING. 43
opment of muscle and function the child rears itself very early
against the constant pull of our pedestal, triumphs over it with
new-found energies, dances on tiptoe, and spurns the ground, but
is soon content to draw the battle, to wander around a few weary
years on equal terms, at length to call in the aid of a stick or
crutch, and, finally, to resign the unequal contest, and sink, van-
quished and satisfied, to rest in its bosom. Weight thus seemed a
natural characteristic of matter until identified and generalized by
Newton as a universal and especially a reciprocal property. This
generalization transferred the property, in conception, from the
naturally heavy body to a cause outside thereof, namely, the earth
itself. Here the human mind relucted, for, unlike repulsion, attrac-
tion is not an observational fact. All forms of tension, stress,
constraint—by whatever name called—are attended in the child's
experience with an intermediary connection. The string is neces-
sary to pull the cart, and the action of the magnet upon the iron
particles is viewed with astonishment and awe. The sense of mys-
tery does not proceed so far in his case as to contemplate the equally
mysterious power which makes his string differ from a rope of sand.
The most profound attention of the human mind has not yet
fathomed this mystery.
Inertia or mass is a less obvious property, being in early obser-
vation and in common apprehension bound up with weight. It
was not recognized in philosophy till Galileo's time, nor is it now
by the common perception, except after training. A lady makes
no scruple of asking to have a loaded car or train or vessel stopped
at a given point on the instant, and reinvested with motion any
number of times ; and would-be inventors often contrive theoretical
machines having numerous heavy reciprocating parts timed to
velocities impossible of execution. With beings under other con-
ditions it is wholly different. The sword-fish, e. </., can have no
conception of gravity, as he has no perception of it, but his appre-
hension of inertia is finely cultivated, through the muscular sense,
in setting up and modifying the rapid movements in which his
existence delights, as well as through his vivid realization of mo-
mentum, in the piercing of a whale or a vessel, by which his
function is so powerfully exhibited. When once realized by human
perception, however, inertia becomes identified with substance as
its most primary characteristic.
44 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The old scholastic property of impenetrability, also, is one of
the superficial notions of experience, gained in the same way as
that of repulsion. It seems to pertain to solids—the typical mat-
ter—with approximate accuracy, though calcined plaster of Paris
and water, e. g., will occupy a good share of each other's volume,
and still form a highly porous solid. But a quart receiver full of
hydrogen can have a quart of carbonic acid gas deftly introduced
into it as into a void space; and so can a quart of water, at ordinary
temperature and pressure, according to Gmelin, without increase of
volume, although water is the type of material continuity. As to
impenetrability in the molecule we can predicate nothing. The
evolution of heat in chemical combinations indicates penetration of
volume, with reorganization of the molecule in less space ; and there
is no reason, except a scholastic one, why two or more molecules,
or even atoms, should not occupy the same place, as admitted by
the highest authority—James Clerk-Maxwell.
Dimension ia also a common notion, derived similarly from supe-
ficial and early experience. Solids alone have figure and assign-
able dimension, though liquids have fixed volume, and gases variable
volume, in inverse ratio to constraint; but even solids are of vary-
ing and fluctuating dimensions, according to temperature, density,
etc. Solidity and liquidity are, it is well known, but mere transi-
tory conditions of material aggregation, for all matter is capable,
by sufficient accession of molecular motion, of assuming that hyper-
bolic or expansive condition which we call gaseous, and in this
state dimension and impenetrability are meaningless terms. Con-
cerning dimension as a necessary attribute of the unit of mass,
Clerk-Maxwell says (Encyclopaedia Britannica, 9th Ed., Vol. 3, p.
37): "Many persons cannot get rid of the opinion that all matter
is extended in length, breadth, and depth. This is a prejudice
* * * arising from our experience of bodies consisting of im-
mense multitudes of atoms." That there is no necessary relation
between mass and volume as there is, e. g., between mass and weight
is shown to common experience by the notably different masses of
a buck-shot and a pith-ball of the same dimensions, or of a cannon-
ball and a child's hydrogen balloon. A pellet of iridium equiva-
lent in mass to the pith-ball might be microscopic, and, by extreme
supposition, infinitesimal. We are not forced, however, to deny to
GENERAL MEETING. 45
the unit of mass finite magnitude, as this would be an experiential
fact when ascertained.
The remaining so-called properties of matter are too obviously
transitory, accidental, or derivative to require attention. Color,
luminosity, opacity, transparency, sapidity, sonority, odor, texture,
temperature, diathermancy, plasticity, hardness, brittleness, density,
compressibility, conductivity, malleability, fusibility, solubility, and
many others, are too clearly but conditions of aggregation, or else
mere subjective states due to the way the complicated interactions
of the primary qualities affect our senses. What are the primary
qualities ?
Here is where the modern method of philosophy flags, by the
disappearance one by one of the experimental means of approach,
as we eliminate the non-essentials. But though the substance is
thus elusory, we cannot yet believe it to be illusory.
Chemical and molecular physics have already gone marvellously
beyond the ordinary range of sense-perception, by strictly scientific
methods. Not only is the discrete character of matter established,
but many data of the differentia and organization of the molecule
are discovered. Here is a vast field of science in itself. From the
ideal molecule, or simple couple, up through the 70 actual organized
molecules of our provisional elements, then the chemical molecules
of their combinations in vast numbers, discovered and undiscovered,
and, lastly, the enormously complex organic molecule in infinite
variety, the domain transcends in area for classification that of
biologic science. The simple molecule has not yet been discovered,
much less the molecular constituent, the atom, or the indivisible.
It is evident, however, that the properties of matter which are
essential, not differential, must reside in the atom. The philoso-
phers succeeding Newton treated the atom and the elementary
molecule as one, from lack of sufficient chemical knowledge. We
are on a higher plane of information, but their method is not nec-
essarily vitiated by such lack of distinction.
We cannot, as before said, attribute a priori to the atom dimen-
sion or figure, though we postulate it to aid conception. As the
atom is an absolute unit, there is incongruity in finally assigning to
it such relative attributes, which are but matters of comparison
and degree. There are properties, however, which are inseparable
from an absolute essence. These are the properties by which the
46 PHILOSOPHICAL SOCIETY OF "WASHINGTON.
essence is manifested to us. We know them provisionally as forces,
in the Newtonian nomenclature. Had gaseous matter neither
weight nor mass, we could not know of its existence. But these
attributes are so constant in matter that we estimate its quantity
in terms of them and have no other exact terms. Weight is the
statical measure ; mass the dynamical measure. And since weight
and mass correspond for all substances, under all transformations,
we judge that the correspondence identifies them alike with the
essence. They cannot be the mere result of organization. They
must belong to the ultimate atom.
At this point it would seem proper to attend to a question of defi-
nition. Definitions are essential to clearness, on the one hand, and
a source of entanglement on the other, if we fall into the scholastic
error of regarding a mere word as the coextensive symbol of an
idea. Words are evolved during the imperfection of ideas, and
language is still a most imperfect medium of expression. Hence,
logic is not a science in the sense that mathematics is. I have used
the term force. This is a word of much ambiguity of meaning.
We may use it as a convenient mathematical expression for a mere
rate of change of momentum, or we may go farther and define it,
as that which changes a body's state of rest or of uniform motion
in a straight line ; either of which uses restricts it to only a portion
of phenomena, and ignores the whole science of statics, dealing with
forces in equilibrium and the phenomena of balanced stress. If we
give it a more general signification, as that which changes or tends
to change, or conserve, the state of motion of particles, or systems
of such, either in quantity or direction, we embrace statics as well
as kinematics, and get a measurably philosophical definition, if we
bear in mind the proviso that we do not thereby postulate force as
an entity apart from substance.
And since the compound variable space and time condition which
we call motion (of which rest is but a phase) is the sensible result-
ant of the interaction of such discrete substance by constant rear-
rangement where readjustment is free, or the potential resultant
where confined, we may admit that the observed tension and per-
sistence, of whatever form, is that which effects the phenomenon
(though masked by infinite variety and composition), and always
across the discontinuity: not as separate entities, but as modes of
manifestation of the interacting and pervasive substance itself and
GENERAL MEETING. 47
its only manifestations. This we call force—the inscrutable agent
of phenomena—and this I take to be the true Newtonian concep-
tion, as evinced by his maturest conclusions, expressed in query 31
appended to his Optics. (B. 3, 2d Ed., 1717.)
So far as weight goes, it was generalized by Newton to be a
reciprocal force or stress, operative without limit on the law which
inheres in radial space relations—the inverse square of the dis-
tance. The term operative means effective upon mass, namely,
bridging the discontinuity. Gravity is the typical attractive force
—
vis centripeta. The relation is mutual by the law of action and
reaction, and amounts to a universal tension among particles, con-
trolling all matter everywhere into orderly movements and relations.
This is what we postulate from observation, on the Newtonian plan
of naming simply what we see. The notion, however, of action at
a distance has encountered a metaphysical difficulty in many minds,
from the preconception derived from ordinary experience that all
affections or stresses must proceed through an intermediary connec-
tion, deemed continuous. Even Newton made concession to this
prejudice in his oft-quoted letter to Bentley. That there is really
no such continuity in any mode of connection known is demonstra-
ble, and the notion itself that the fancied continuity of some rare
effluvium could in any way aid the mechanics of the problem is
chimerical. Clerk-Maxwell, moreover, has shown (Nature, Vol. 7,
p. 324; Encyclopaedia Britannica, Vol. 3, p. 63) that action at a
distance is as necessarily implied in repulsion as in attraction, so
that theories of repulsion do not aid conception. Ability or ina-
bility to conceive, furthermore, is not held even by the metaphysi-
cians to be a criterion of objective truth. Such truths exist inde-
pendent of the conceiving mind. The conceiving organ was evolved
by experience, and conception develops with attention. The first
law of motion was wholly inconceivable to the contemporaries of
Galileo, and we find such instances even now. Thus, while plain
truths are inconceivable until established, some utter absurdities
have been deemed conceivable, as, for instance, vacuity of two
dimensions. State of mind, then, is no measure of external truth.*
* In this connection, to illustrate how entirely a matter of opinion or pre-
judice or culture is this notion of conceivahility, I quote from a letter
48 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The second force or manifestation of the atom, inertia,—or mass,
—
unlike gravity, is not unlimited in range of action. As to this
property matter is discrete. Mass has both a locus and a limit
(being apparently dependent for dimension on multiplicity), and
amounts to that incomprehensible property by which conservation
of motion is maintained. Under gravity, quantity of motion varies
according to relations of contiguity, but under inertia motion is
conserved in direction and quantity, is modified in direction and
quantity by interaction of mass with gravity, and is redistributed
by interaction with repulsive force upon an indefinitely near ap-
proach of particles, upon conservative principles. Its discreteness
gives matter its numerical and finite character, and admits of that
interplay which constitutes phenomena* Its reality and primary
written by Faraday to Dr. Playfair, in response to some inquiries of the
latter about bis atomic opinions
:
* * * " I believe in matter and its atoms as freely as most people—at
least, I think so. As to the little solid particles which are by some supposed
to exist independent of the forces of matter, and which in different sub-
stances are imagined to have different amounts of these forces associated
with or conferred upon them, * * * as I cannot form any idea of them
apart from the forces, so I neither admit nor deny them. They do not
afford me the least help in my endeavor to form an idea of a particle of
matter. On the contrary, they greatly embarrass me ; for, after taking an
account of all the properties of matter, and allowing in my consideration for
them, then these nuclei remain on the mind, and I cannot tell what to do
with them. The notion of a solid nucleus without properties is a natural
figure or stepping-stone to the mind at its first entrance on the consideration
of natural phenomena; but when it has become instructed, the like notion
of a solid nucleus apart from the repulsion, which gives our only notion of
solidity, or the gravity, which gives our notion of weight, is to me too dif-
ficult for comprehension ; and so the notion becomes to me hypothetical,
and, what is more, a very clumsy hypothesis." (Playfair's works, Vol. 4,
p. 84.)
Here we see a difficulty opposite to that usually encountered, for, while
many people profess an infirmity of conception of the forces apart from the
imaginary vehicle, Faraday finds the vehicle of no use as a carrier of the
properties, but a positive impediment.
* This property has a multiplicity of names in the Newtonian nomencla-
ture, according to the varying aspect of its function. Thus, in the aspect
of persistence of mass in state of rest or of motion uniform in direction
GENERAL MEETING. 49
character, when once apprehended, have proved more acceptable
to the imagination than has the conception of central force,
and under appulsion hypotheses (with the aid of that other readily
accepted property, repulsion, and certain highly artificial hypo-
thetical media), it has been made to do duty in providing so-called
explanations of gravity, under its form of vis viva.
It has always seemed to me that the mode of approach adopted
by Boscovich Avas the most philosophical and rigorous of any. He
viewed matter for the purposes of mathematical treatment and for
investigation of its essentials, as divested of accidental and fugitive
properties ; and as the analytical calculus had not then become so
developed as to wholly fascinate the attention of geometers with ab-
.
stract and ideal relations, he proceeded from prime physical data.
He thus identified matter by those apparently general and charac-
teristic properties recognized by Newton as the basis of mechanical
philosophy in conjunction with the laws of motion. These proper-
ties are, as before said, gravity, inertia, and repulsion ; or, as char-
acterized by function, attraction, conservation, distribution. In
this view matter consists of certain lod of central forces, mutually
attractive by the first property according to a variable law in the
duplicate inverse ratio of distance without limit, but restricted in
manifestation as to the second property to the infinitesimal locus,
thereby excluding unitary dimension. Contemplating matter un-
der this aspect alone, a dilemma arose. For gravity waxing by
the law of inverse squares of the distance up to the focus or origin
involves the consideration of infinite force and apparently of infi-
nite velocity in the limit, in the supposable case of rectilinear ap-
and quantity, i. e., of resistance to change of state except in conformity
with motion impressed, the property is called vis insita, which may be vis
insita activa (momentum), or vis insita passiva (vis inertias, of mass.) In
its aspect of acquirement of a new state of motion by interaction with other
forces or masses, Newton called the new state thus superposed vis impressa;
which, when the operation of acquirement has ceased, becomes again vis
insita. In its aspect of persistence of mass towards uniform direction of
motion under the constant deflective stress of vector central force, it is
called vis centrifuga. And in its active form, conditioned by motion ac-
quired, its capacity for furnishing motion from its store, either for impressing
motion upon other mass, with consequent loss, or for supplying the poten-
tial fund under the drain of adverse central force, is called vis viva (energy.)
50 PHILOSOPHICAL SOCIETY OF WASHINGTON.
proach, at which point the equations become unexplainable. While
Enler and La Place differ in their interpretations of the result,
Boscovich sought to solve the apparent absurdity and inconceiva-
bility by the invention of his ingenious and complex system of
alternate spheres of attraction and repulsion, or change of sign,
on a very near approach, with infinite repulsion at the focus, which
so loaded down and vitiated his hypothesis as to cause its rejection.
This result was similar to that of Le Sage's speculations and those
of the Ptolemaic astronomers, each thus working out the falsity of
his respective scheme by superadded complications to readjust the
theory to the progress of criticism or of observed fact.
By attributing finite magnitude to the atomic mass, however,
Boscovich's difficulty disappears, as I had the honor of pointing
out before this Society some ten years ago. This may be deemed a
violent hypothesis in regard to a positive discrete simple absolute,
as the atom is presumed to be, but parallel difficulties inhere in any
other finite supposition, as, e. g., a sphere of repulsion. Under my
provisional assumption, the way out follows from an elementary
proposition of Newton's, and it does not demand the gratuitous
change of law or of continuity involved in the resort of Boscovich.
The movement of a gravitating particle under stress of a center of
gravitative force would be in all respects as the great 18th century
mathematicians have demonstrated, until the margin of the par-
ticle reached the attracting center, where, if we suppose the attrac-
tive virtue to prevade the particle equally throughout a certain
finite volume of mass, however minute, as gravity does the mass of
a sphere, the maximum of attractive force would be attained ; for,
as Newton has shown, homogeneous spheres are controlled under
gravity by a law of force varying directly as the mass and inversely
as the squai'es of the distance between their center of mass and the
attracting center, at all points beyond the surface, and directly as
the distance between the said centers within the surface ; so that,
after passing the surface, the attractive center must proceed on-
wards to the gravitating center of mass (relatively), not by a force
increasing to infinity, but by a force decreasing to zero, after pass-
ing the maximum, since it is balanced at the center by opposing
stresses.*
*Let M be an exaggerated particle of mass and Cn fixed center of gravi-
tation external thereto. Newton proved that for all positions outside of a
GENERAL MEETING. 51
A similar law of attraction prevails between two gravitative par-
ticles when both are similarly endowed with finite spherical volume
and mass, excluding the idea of impenetrability (which is not a
necessary attribute of mass), the Newtonian law being the product
(J\lm\ *
~JT ) ^or
outside positions.
gravitating homogeneous spherical mass the stress is precisely as though the
whole mass thereof were concentrated at the center of said sphere, and
varies directly as the mass and inversely as the square of the distance be-
tween the said center and the fixed center of gravitation ; i. e., G ^*—«. M
(P.
The maximum of gravitating force will here be at the surface, where d is
minimum. He also proved that at all points within a homogeneous gravi-
tating spherical concentric shell a gravitating particle is uniformly affected
by balanced attractions. Hence, the stress for any smaller concentric sphere is
g '^^^ m m being the smaller spherical mass and r the reduced radius.
But since homogeneous and similar masses are as the volumes, and similar
volumes are as the cubes of the homologous dimensions,
The maximum of gravitating force is here also at the surface, where r is
maximum.
* I write the formula this way because it is possible that we have been in
error all along in regarding the denominator as a radial space relation, as
implied when we write it —
—
m
In discussing the deflection of the particle
under gravity, Newton, for mathematical simplicity, treated it as governed
by a fixed attracting central force, and in testing various relations found that
the radial space relation gave the true path of the planetary bodies under
the immense preponderating influence of the sun's mass. The fixed center
of attraction is, however, a mathematical, not a physical, condition, and can
only be realized by making M = oo, when we get a form of expression
which does not give a law of force. I think it possible that the relation is
a mere reciprocal distance relation, since the stress is mutual for the masses
and each is equally distant from the other. The inverse form of the relation,
moreover, may arise from our subjective way of viewing distance, as meas-
ured outwardly from ourselves, since we have to go from here to yonder.
It is possible to look upon the relation as really one of contiguity or near-
ness, and by placing —. = c we get the cosmical law of gravitation as
Memc. This, however, would not be a useful formula, since we are not ac-
customed to expressions which attain maximum value with minimum mag-
nitude.
52 PHILOSOPHICAL SOCIETY OP WASHINGTON.
For positions of encroachment the law is more complicated, and
forms an interesting field for mathematical discussion. Where three
or more atoms are superimposed the problem becomes too complex
for discussion. It is noted, however, that such compound atom, if
quiescent from extreme abstraction of heat, would be in a condition
of elastic equilibrium, ready to respond like a bell to the slightest
disturbances. In all these cases of interpenetration the law of stress
would be finite and diminishing, and if the line of encounter should
chance to be a right line through their centers (a condition infi-
nitely rare in actual occurrence), they would continue on or repeat
according to energy of approach ; while upon any other lines of
approach orbital relations would supervene, in modified curves of
the second order, either hyperbolic, parabolic, or elliptic, according
to velocity, and with or without partial penetration, according to
nearness of approach.
Boscovich, however, did not adopt this solution, although within
his reach. The problem of the action of a gravitative particle as
controlled by an attractive center has several aspects of statement,
which may be confined to four, for practical investigation. In the
first, where the particle is assumed to be without mass, no discus-
sion is possible, for the two suppositious points instantly assume the
same locality, and end the relation. In the second, where the par-
ticle is endowed with inertia but not magnitude (and the attractive
locus fixed by postulate), the element of motion enters, but infinite
terms appear in the equations in the limit, forbidding interpretation.
Thirdly, when we attribute finite magnitude to the gravitative par-
ticle for gravitative pervasion, as in actual spherical masses, no in-
finite terms appear, and we get an intelligible mathematical discus-
sion, with planetary results for exterior positions, and pendulum
results for interior positions, as I have heretofore demonstrated
:
and lastly, when both the gravitating loci are invested with similar
attributes of volume and of mass (excluding extraneous notions of
ordinary collision and repulsion from the problem), the results are
similar to those of the third hypothesis. I do not introduce any
of the mathematical discussions here, as the dynamics of the par-
ticle have been fully treated by mathematicians, though I am not
aware that any of them have pursued it to physical conclusions.
It is not likely, however, that there is any matter so simple as
this modified Boscovichian atom; that is, which can be identified.
GENERAL MEETING. 53
All the matter we know of is already compounded and highly or-
ganized. The ideal simple molecule would consist of a single pair
of such atoms, bound to each other in orbital relations of more or
less eccentricity, including the extreme rectilineal form of simple
pendulum-like oscillation through one another's centers ; and it is
a most significant fact that spectroscopic observation of all incan-
descent matter shows atomic matter to be in this state of transverse
or orbital oscillation with inconceivable but synchronous rapidity
without regard to range, according to the pendulum law of stress
varying directly as the range of oscillation, discovered by Galileo.
Any theory of the simple molecule must take cognizance of this
observed fact. Another cognate fact is that the law of elastic
cohesion manifest in all elastic tensile action
—
"id tensio sic vis"—
is a parallel law of stress, as illustrated in the spring balance weigh-
ing scale, the spring dynamometer, the isochronous spring governor,
etc., and is a function of molecular and ultimately of atomic force
and distance.
If the atom is really thus characterized, the repulsion or resistant
property experienced in matter becomes worthy of investigation,
since it drops.out as the primitive affection or disaffection postulated
by Boscovich. I have shown that it is not necessary to oscillatory
motion. We must admit that the notion of rebound or recoil, in
the ordinary sense, between simple atoms possesses difficulties. No
less does the idea of plasticity or destruction of momenta. Con-
sider what is involved in the hypothesis of two absolutely hard,
rigid, unparticled, homogeneous spherical bodies of any magnitude
at all, if possessed of mass, meeting on a rectilineal central line of
motion. We know what would haj^pen in case of ordinary spherical
elastic masses or aggregations of molecules. Such merely undergo,
first, apparent contact, then compression, deformation, strain, accu-
mulation of stress, retardation of velocity, momentary arrest, accel-
eration on new lines of departure, relief of strain, recovery of form,
redistribution of momenta, and final resumption of uniform veloci-
ties, with relative motion inverted and aggregate energy of motion
unimpaired, unless permanent distortion and heat have absorbed a
portion. All this complex action is involved in the term elasticity.
None of this could take place with simple undifferentiated particles,
unless we invent for them a mystic atmosphere or cushion of repul-
sive capacity surrounding the locus, as Boscovich was forced to do
22
54 PHILOSOPHICAL SOCIETY OF WASHINGTON.
by logical conclusions. Without this, contact would be absolute
and instantaneous at first impact. As hardness .involves impen-
etrability, absolute destruction of motion on the instant must ensue
;
that is, motion and no motion at consecutive instants of time; a
discontinuity unknown to experience, and known to be inconsistent
with the nature of motion and of time. This argument from breach
of continuity is due to Leibnitz. Conversion into heat motion is
excluded, heat being a mode of motion of the entire atom. More-
over, the destroyed motion has to be recreated instantaneously in
new directions, for destruction of energy cannot be postulated.
This geometrically angular motion is also unknown to experience,
for all deflected bodies pass by continuity from motion in one direc-
tion into a new direction, and, so far as we can see, must do so.
These discontinuities in translator)7 relations are therefore put aside,
not because they are inconceivable, but as illogical and non-experi-
ential. Simple repulsion by contact without occult intervention is
a false suggestion, and we find that we get the pseudo-conception
from our false observation of what occurs in the collision of sensible
masses, somewhat as we make a false observation and generalization
about material continuity, or about tension, from a superficial per-
ception of matter ; thus creating concepts from supposed experi-
ence which can have no true objective counterparts. I shall recur
later to a possible derivative basis for repulsion.
It is remarkable that to Newton we owe the final establishment
of the majority of those fundamental and universal truths which by
simplicity and generality seem to touch the absolute ; that is, more
than to any and all other philosophers combined. Thus, of the six
ultimate generalizations, four were formulated and placed on an
impregnable basis by Newton : the three laws of motion and the
law of gravitation. All of these were inconceivable when first pro-
mulgated, were hotly controverted on the metaphysical plan, were
finally established experientially, and are now generally accepted
as axiomatic by the modern mind, except for sj>oradic reversions
which appear now and then to deny their actuality and reassert
their inconceivability. The remaining two universal inductions
are the collective group of axioms formulating the relations of ex-
tension—the only enduring remnant of the Greek philosophy—and
the law of the conservation and unity of energy, unperceived in
Newton's time in its generality, though taught as a dogma by the
GENERAL MEETING. 00
Cartesians. These also are still held to be inconceivable by certain
disciples of metaphysical methods and axiomatic by others. Sucn
mental attitudes should lead us to believe that simplicity has been
arrived at in all these cases and the boundaries of explainable
knowledge reached, where inconceivability necessarily begins.
It has been said that paradox is born either of confusion of
thought, or of knowledge, or confusion of statement arising out of
the imperfection or subtlety of the verbal vehicle of thought. Thus,
as Clerk-Maxwell points out, the celebrated arguments of Zeno of
Elea, establishing the inconceivability of motion, represented in
the paradox of Achilles and the tortoise, were unanswerable and un-
answered until Aristotle showed, some half century later, that du-
ration is continuous and incommensurable by numerical methods
in the same sense that extension is. The old logical dilemma of the
irresistible force encountering the immovable body was insoluble to
the Greek mind, both from lack of physical knowledge and lack of
verbal clearness of statement. The acute sophist knew not the
nature of force, the constitution of bodies, the conservation, trans-
formation, and dissipation of energy, and consequently knew not
the refuge and escape from the dilemma contained in the percep-
tion of the conversion of molar energy into heat energy, expansion,
and dissipation. The resources of verbal subtlety and of inner
consciousness failed, as they always do. Something of the same
difficulty remains in modern problems, where observation and strict
verification are, from the nature of the problem, inapplicable, or
where the confusion arises from the still-existing imperfection of
language, or, again, where generalizations, both clearly made
out and clearly formulated, have not passed into the instinctive
popular apprehension. The modern dilemma of the inconceiva-
bility of infinite or finite space is, I take it, due to the metaphysical
form of the statement. For when we reflect that the ideas of im-
mensity and of infinitesimal resolvability are but abstract generali-
zations of the merely relative continuities, extension, distance, and
dimension, which are in their turn but abstractions of the sense-
perceptions, form, translation, and volume, the statement becomes
intelligible and entirely conceivable, and I think, thouoh with
deference, saves geometry ; that is, the universality of that system
of inductive postulates regarding the relations of extension and
inferences therefrom, known as geometry to the Greek philosophy,
50 PHILOSOPHICAL SOCIETY OF WASHINGTON.
but now named Euclidean by certain analysts whose so-called
geometry is symbolic. Geometry is therefore able to deal with all
aspects of extension, without regard to limit, in spite of some in-
firmity in the Greek method, for scale cannot affect the generality
of extension relations, and abstract unconditioned space is not an
entity but a mere negation, concerning which relative propositions
are unintelligible. A false philosophy regarding space is at the
root of all modern heresies concerning geometry and mensuration,
founded in misapprehension of the Euclidean inductions or gene-
ralizations.*
The first law of motion is but the formulated recognition of in-
ertia, which is only manifest in conjunction with motion, actively
or passively. It was known to Galileo, and laid down by Descartes
as a law in his Principia. It is a cosmical truth, bound up with
the absolute nature of mass and the true relations of extension,
which correlates the whole fabric of dynamical knowledge with
rectilinear geometry, curvilinear motion being demonstrably not a
simple state of conservation under inertia, but a resultant of mul-
tiple forces. The simple action of mass under the first law of
motion, if undisturbed, furnishes the absolute unreturning recti-
lineal path which overthrows all speculation about possible ideal
spaces. I here recall a book written by a learned American of
Philadelphia—learned, that is, according to the mediaeval stand-
ard of the colleges—and jxiblished only during the past year, en-
* There are two opposite though similar forms of error in the assumptions
regarding space. The first is that space is a specific or perhaps generic en-
tity or ohjectivity per se, possessed of conditions and attributes, like sub-
stance, such as dimension (in several), differentia in localitj^, figure, as cur-
vature, etc. (hence necessarily finite), and only uncognizable by us simply
for lack of perceptive faculties to correspond. This is the fundamental
error, as it seems to me, of Eiemann and Lobatschewsky. The second is
that of the older Cartesians, who viewed space as but the mere attribute or
synonym of substance, and inconceivable apart from it, so that bodies sep-
arated by void space would be absolutely in contact without regard to dis-
tance. Both of these speculations are purely metaphysical, and non-exper-
iential, the latter resulting from the old scholastic method of syllogistic de-
duction from primary postulates of verbal definition, and the former from
similar inferences from the forms of the analytical logic of symbols, the use
of which is still in the scholastic stage. Like Zeno's paradox, these merely
intellectual difficulties should be removable by intellectual processes.
GENERAL MEETING. 57
titled "An Examination of the Philosophy of the Unknowable, as
expounded by Herbert Spencer," wherein he naively lays down the
first law of motion as unintelligible except by appulsion. Motion,
he says, in the absence of propulsion is inconceivable. I have no
space here to reproduce the explanation evolved out of consciousness
by this reasoner to account for the action of a ball struck by a bat
after leaving the bat. It resembles in ingenuity and gratuity some
of the inventions devised to explain gravity. The notable thing
about it is that here, at this date, is a mind of good caliber, informed
in the higher schools of learning, which is still of the mental period
of Aristotle ; a mind which has evidently never apprehended in-
ertia, nor heard of the great contributions to knowledge made by
Galileo and Newton, by which philosophy was entirely revolution-
ized.
The second law of motion, regarding the independence and co-
existence of motions, on which we occasionally see comments in
the metaphysical vein controverting its possibility, has long been
established experientially. Its early experimental proof is attrib-
uted to Galileo. Yet I recall a pamphlet written and published
only during the last year by a learned German at Leipzig, the
theme of which was that " the sun changes its position in space,
therefore it cannot be regarded as being in a condition of rest."
This, he concludes, overthrows the entire fabric of Copernicus, be-
cause the planetary orbits in such case cannot be closed.
The third law of motion is but formulated reciprocal stress, in
its modes of compulsion and repulsion, through which mass acts on
mass to redistribute motion by what appears to be necessarv law.
The stress is necessarily reciprocal, since there is no point cl'appui,
or fixed fulcrum, in the universe.
We have thus been brought to the boundary of the absolute,
where all is inconceivable until found out, and where the simple
data are unexplainable. All examination seems to continue to
point to mass and weight as the ineffable simple insignia of sub-
stance standing on this limit. "We must accept something as ele-
mentary fact ; what shall we find more elementary? Repulsion is
still debatable; for, if Ave make an issue between repulsion and
compulsion as contradictory primary attributes of the same essence,
or untenable in conjunction for artificiality, by far the greater dif-
ficulties attach to the former, some of which I have already alluded
58 PHILOSOPHICAL SOCIETY OF WASHINGTON.
to. The profound mind of Boscovich was forced to accept repul-
sion as a primal quality, but in deference to the physical hypotheses
of his time, he overloaded it with complication. This has been
weighed in the balance of philosophical judgment and found want-
ing. I have intimated that there are possible grounds for surmising
that it may not be a simple property of the atom, but a mere mode
of distribution of energy dependent on composition of motion of
atomic mass after change of sign, i. e., a mode of vis impressa after
exhaustion of the space relation ; for, mathematically, the hyperbolic
lines of approach and recession of two atoms under the high proper
motion characteristic of the atom, and on lines not directly central,
would be similar, at sensible distances, in their asymptotes (which
would be the practical paths), whether the deflection were due to
attractive or repulsive stress, though acceleration and retardation
at the passage of the infinitesimal focus would be inverted.*
* It is well known that for any finite system of two particles controlled
by gravity the lines of movement are closed curves of the second order, of
more or less eccentricity, about the common center of gravity, which, for
equal masses, would be midway. For an infinite system under the same
conditions the orbits are parabolic, but for a system to which the particles
enter by extraneous motion the lines of movement are hyperbolic, thus
:
Fig. 1.
Now, under repulsion, the lines of motion are seen to be similar, A B, D E,
Fig. 2, being asymptotes of the hyperbolas representing the two paths at
sensible distances
:
GENERAL MEETING. 59
It therefore seems to me immaterial to result which of the two
modes of passing the infinitesimal focus is the true one. In either
case the distance at passage is infinitesimal, and the force may be
as near infinity as the facts require it to be assigned. The normal
or rectilineal encounter is here excluded from supposition. In that
case, under repulsive stress, as postulated by Boscovich, the recoil
would be rectilineal and opposite, without breach of continuity.
Under attractive stress, with finite volume of the atomic mass,
penetration would ensue as before shown ; but without dimension
or repulsion we have an insoluble condition, although the occur-
rence would be infinitely rare. Only one pair of elements is here
considered. In all real encounters, whether of masses or molecules,
the effect is a vast resultant, but should not be different in kind
from that of the elements ; that is, hyperbolic or expansive between
alien systems under motion. As the number of elements ordinarily
engaged could not be represented by any numerical places of arabic
notation for which we have names, we see the hopelessness of stat-
ing the problem mathematically. I therefore do not presume to
This encounter represents only one element of the molecule, of which
myriads are engaged at every recoil of molecules, not to speak of solids.
It is thus seen that the mesh constituting the molecule is ordinarily impen-
etrable to other meshes. If the curve F G be allowed to represent the out-
line of the molecule, the limb of the solid to which it belongs, say a buck-
shot, will be represented by the Sierra Nevada, or the Andes, and its diam-
eter would be measurably represented by that of the earth, as approximately
shown by Sir Wm. Thompson in the case of a drop of water.
60 PHILOSOPHICAL SOCIETY OF WASHINGTON.
offer this as an explanation of repulsion, and I confess that to me
repulsion is in its mechanism incomprehensible. We know the re-
sult experimentally, and that is resistance to penetration, and reac-
tion at insensible distances on an undefined boundary which begins
prior to contact and increases in a high exponential ratio as approx-
imation progresses. The contact boundary of any solid—even the
smoothest and hardest—resembles the astronomical limb of Jupiter
in geometrical indefiniteness. The contact transmitter in the tele-
phone, the whole range of whose phenomena occurs under pressure
and so-called contact of varying degrees, illustrates how relative a
thing is contact. Under high velocities the distinction between
solids, liquids, and even seriforrn bodies entirely disappears in re-
spect to repulsive reaction, though this is the most sensible distinc-
tion between them under low velocities.
We may, therefore, adopt the conclusion that if any of the ap-
parently simple properties of the atom are to be thrown out as de-
rivative and secondary, presumption points to repulsion as the com-
plex one. We could possibly account for phenomena in a universe
bound together by purely tensile stress, but most of the sensible
phenomena of solids—cohesion, affinity, tenacity, etc., including
nearly all of statics—remain hopelessly unattackable problems un-
der a hypothesis of pure repulsion, like that of Le Sage, or Pres-
ton. It is to be noted that the kinetists who freely postulate repul-
sion and appulsion, without analysis, as a primordial fact, but re-
luct against compulsion or tension, are forced to the invention of
the most complicated and gratuitous mechanism and media to ex-
plain the phenomenon of gravity, and then without attainment of
result. Le Sage's atom is too complicated, even without his suppo-
sitious or extra-mundane operative machinery ; and the vortex
atom is but a mere analytical expression for an unproducible con-
dition in a figmentary mathematical plenum.
The thesis that conservation is the characteristic by which we
identify objective existence will not bear the test of examination
It is only in the most recent times that such a quality has been
known or imagined, and its establishment, both as to matter and
energy, is justly viewed as the triumph of modern philosophy. The
evocation of matter from nothing and its relegation to nothing.
even by the finite will of a wizard, was ever a common and universal
notion, which did not at all impair the belief in its present reality
GENERAL MEETING. 61
and substantiality. We have only to go to Apuleius for this, and
it is doubtful if even now the notion of the indestructibility of mat-
ter is anything but a scientific conviction, for do we not see num-
bers of our contemporary fellow-citizens meeting together frequently
in our midst to witness feats of materialization out of nonentity by
powers akin to those of the sorcerer, without an idea of incongruity ?
Nor has the essentially modern doctrine of the conservation of en-
ergy anything to do with the belief in its reality. Few peojile ap-
prehend it even now. No philosopher understood it a hundred
years ago. Its verity rests on a sufficiently general inductive basis,
from the refined and exhaustive experiments of Joule, and the the-
oretical conclusions of Mayer and Clausius, and it is accepted in
the same sense that the law of gravitation is accepted. But the
duality of matter and energy to the exclusion of force is a verbal
shift, the assumption of which removes no difficulty. Matter, the
object, remains unexplained; and energy, the phenomenon, becomes
segregated and unintelligible. Energy, in fact, is but mass in phe-
nomenal manifestation, being a product of triple factors, two of
which—translation and speed—are not things, but variable and
evanescent conditions, and, taken together, constitute motion. Mass
is the absolute or persistent factor, but the evanescent character
of the variable component—motion—would render the entire phe-
nomenon—energy—apparitional, were it not for the distance re-
lation involved in motion, which, under the same inscrutable agency
which modifies and saps the motion renders it potential upon change
of sign. This agency, the dynamical source of the manifestation,
being central to mass and likewise persistent and constant, renders
the positive and negative potentialities of movement constantly
equal, and the actual and potential energies consequently comple-
mentary, from which energy gets its character of conservation.
Energy cannot therefore be that other reality of existence (be-
sides matter), since force is clearly the one reality at the bottom of
the manifestation of both, to whose persistence and resistance to
change, except through transformation, the conservation of both is
due. This one reality is, in its triple aspect of causation, (1) at-
traction—the source and modifier of motion
; (2) inertia—the con-
server of motion ; and (3) repulsion—the distributer of motion ;
or, more correctly, in its aspect of quality: (1) vis centripeta—the
power of mutual control across distance ; (2) vis insita—the power
62 PHILOSOPHICAL SOCIETY OP WASHINGTON.
of persistence in state of motion impressed ; and (3) the distributive
power of imparting and acquiring motion by transfer, at minimum
distance, which may be called vis partitiva, the result of which is
Newton's vis impressa. Matter thus comes into the world of phe-
nomena by the simple presence of other matter, permitting the
exhibition of these comparisons and interactions, involving the
conditions of contiguity, distance, position, translation, direction,
succession or sequence, and time-rate for the continuous increments,
decrements, successions, and uniformities, all bound up in the com-
pound variable continuity—motion. With motion and distance
comes the dependent phenomenon—energy—active and potential,
which should be a constant, the numerical units of mass being con-
stant throughout immensity, provided the sum of the motions,
potential and actual, be constant. This the dynamical theory de-
duces from the fact of central force (for without force potential
motion is ridiculous), and the thesis of the conservation of energy
is a dynamical truth or nothing. It is therefore all the more ex-
traordinary that certain kinetists, who reluct against central force,
should have selected, out of all the manifestations of the universe,
the variable and conditional product—energy—to be the one reality
or objectivity, aside from the undefined hypostasis—matter—as a
primordial simple fact at the basis of phenomena. It has been
mathematically demonstrated by Mr. Walter R. Browne (London
Edinburgh and Dublin Philosophical Magazine, January, 1883, p.
35) that the conservation of energy is true if the material system
is a system of central forces, and is not true if the system is any-
thing but a system of central forces. In fact, the ordinary theo-
retical proof of the principle of the conservation of energy assumes
the forces acting to be central forces, i. e., reciprocal stresses between
units of mass, as recognized by Clausius in his Mechanical Theory
of Heat. Moreover, the entire body of kinetists, who have aimed
to supersede gravity or central force, have freely assumed an extra-
mundane supply of motion and energy without regard to conser-
vation, and it is notable that every hypothesis for this purpose yet
broached involves the constant expenditure of work without re-
covery, and postulates the accession of energy in infinite influx
from some occult source, of which only a small portion relatively
is available or manifest in observable phenomena, thus violating all
three of the canons of philosophical ascription—true cause, sufficient
GENERAL MEETING. 63
cause, and least cause. Such is the power of conception of the un-
known in endeavor to explain the inconceivable known.
If the dynamic hypothesis of perpetual transformation of energy
could be established as a universal induction, with as much gen-
erality, e. g., as the statement of the law of gravitation, it would
establish and confirm that law, by Mr. Browne's demonstration, as
something more than a law, to wit, the necessary constitution of
matter as a system of central forces and nothing more, substan-
tially as conceived by Newton and elaborated by Boscovich. At
present it is but a dynamic induction, but the theory of gravity is
no more. Our appliances are material, and we can deal with mo-
lar forces, but only indirectly and inferentially with those which
are atomic. Conservation is indubitably true of energy in the me-
chanical and molar sense, under the laws of dynamics and the per-
sistence of force. It is, also, experimentally true, so far as we can
trace it, of those less understood forms of energy which are mole-
cular or atomic, the establishment of which was the great glory of
Benjamin Thompson, Clausius, and Joule as to heat, and of a mul-
titude of observers as to electrical energy. We infer it as a gen-
eral truth of these energies (formerly known as imponderables,
since they are not manifestations of matter in the concrete), from
the fact of their convertibility with other modes of energy which
are undoubtedly dynamical, and also from the intimate connection
of electrical energy with one of the specific exhibitions of central
atomic force—magnetism. Such clews create a warrantable pre-
sumption that the phenomena in question will all ultimately be
classified among the modes of atomic mass and motion, inductively
as well as hypothetically. Possibly in the investigation of these
evanescent modes of energy the missing simple particle may come
to light. Provisionally, we are entitled to rank them among the
mechanical modes of energy, as products of the same material
forces, assuming, until the contrary is proved, that some form of
matter is concerned in manifestations so correlated by conservation
with undoubted material activities.
In including the imponderables within the general dynamical
law of conservation, we have to take account of the phenomenon
of dissipation, first pointed out by Sir William Thompson. It is
true that heat (as well as electrical energy) is strictly correlated
with and interconvertible with energy of mass motion, as before
64 PHILOSOPHICAL SOCIETY OF WASHINGTON.
stated, but in its final form energy seems to take leave of matter
altogether, so far as our perceptions can follow it, and disappear
as a material phenomenon (though liable to reappear wherever
matter is encountered whose particles are deficient in a like
species of atomic motion with that which disappeared ; which fact
indicates that atomic mass is still a factor, with its inherent prop-
erty of persistence and transference). The earth and all upon it
is radiating heat energy away into space at the constant rate of
500° F. of absolute temperature, more or less ; the sun and the
visible stars at the rate of many millions of degrees. Much energy
also passes off in the luminous form. Of electrical and actinic
energies we know less, and of some we doubtless know nothing.
This amounts to a constant drain of the dynamical supply of
energy. These final forms, the radiant energies, have a remark-
able specific high cosmical velocity of their own, which is a func-
tion of something not material, or at least not molar. It is sup-
posable that, in addition to the dynamical source of motion from
central forces, and the contraction of systems in dimension which
supplies dissipation, there may be an inherent and primordial store
of atomic motion. The high proper motion of some of the stars,
beyond what can be accounted for on dynamical principles, and the
inexhaustible and enormous supply of radiant energy from the
visible stars, have afforded grounds for such a surmise, but these
speculations do not belong to the domain of mechanics.
And here we must bear in mind that the dynamical theory, in plac-
ing these assumed agencies and modes of interaction in causal relation
to phenomenal motion, by no means predicates or can predicate any-
thing concerning absolute motion or its cause. The lack of this dis-
tinction may have proved a stumbling block to some in comprehend-
ing the idea of force. Were it not for the observed dissipation of
energy no system could become contracted in dimensions a particle
by the interactions of material forces, nor is there now any known
way by which the material system can be expanded in dimensions
except by the accession of motion from extra-mundane sources,
which there is no scientific mode of ascertaining. The sum of mo-
tions under the action of forces remains the same, and any change
would imply creation or annihilation, which is not ascribable to a
material agency. Primordial dimension remains as inscrutable
a fact as ever, and primordial motion an unsolved problem.
GENERAL MEETING. 65
In conclusion, I know nothing of force except as a manifestation
of matter, and nothing of matter except through its manifesta-
tions. It is substance that interacts with substance, so far as we
know, always reciprocally, and force is but the convenient transla-
tion of the terminology invented by Newton to designate these
several species or modes of action, in the word vis, with its appro-
priate adjective. He was arraigned by the Cartesians (and virtu-
ally is by their modern representatives) as the reintroducer of oc-
cult qualities into philosophy, but his statement was "hypotheses
non jingo" and to a similar charge brought against him by Leib-
nitz he pertinently replied that it was a misuse of words to call
those things occult qualities whose causes are occult though the
qualities themselves be manifest.
I have adopted gravity as the type of central inherent force
—
vis centripeta—but I would not thereby be understood as excluding
from the category of material forces any and all other modes of
tensile or constraining force which may be hereafter made out as
specific, by the elucidation of such phenomena as affinity, cohesion,
tenacity, elasticity, ductility, viscosity, capillarity, polarity, mag-
netism, etc., now so little understood, any more than I would ex-
clude any form or mode of energy which may be observed, from
the category of material phenomena. The Newtonian doctrine of
force would not be impaired by such discovery, and its strength
lies in the fact that it as readily includes static phenomena—that
despair of the kinetist, who has no imaginable hypothesis by which
to range them under a form of motion—as it does kinematical phe-
nomena. Statical force (Newton's vis mortua) cannot be ignored
in a theory of force. The straw that breaks the camel's back
the very lightning that crashes through the sky—are familiar ex-
amples of its power made manifest. Its reality may be exemplified
by suspending two heavy balls of equal weight at equal heights
one by an elastic cord, and the other by a tense string. The dif-
ference of effort required to displace the two vertically upwards,
which can be measured, makes sensible the difference between the
two forms of balanced statical forces. In the one case the antago-
nizing force is suddenly withdrawn, and in the other gradually.
Wherever strain exists—and it is everywhere—there force is as
certainly present as when it becomes manifested in a stress relieved
by motion and measurable in terms of energy.
G6 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Let us, then, give up the standard of a priori conceivability,
in view of its many historical failures, and adopt as possible that
which is provisionally ascertained. The " ego " and the ." cogito "
—
(
'artesian starting points—-have proved barren and irrelevant in
Philosophy. True Philosophy is concerned with objectivity. The
data of consciousness, mainly acquired in infancy or in the womb,
are blind guides. Many an ego, whose brain Avas his cosmos, has
run through his brief subjectivity, but the order of nature endures.
The same facts are continually observed, verified, recorded, and
rectified, but the observers change. Their intelligent observations
add to the sum of knowledge. This is all the proof we need of
objectivity, and all we will get. The insoluble difficulties of Phi-
losophy have disappeared one by one since the happy thought of
eliminating them by observation entered. The immortals are those
who have successfully applied this method. It is only where ob-
servation fails that the insolubility lingers. Beyond the sphere of
the knowable it will continue, in spite of introspection. How mas-
terful is fact in the presence of the most intricate mental subtle-
ties. The ball leaves the bat, in spite of the inconceivability.
Galileo's plummet dropped from the moving mast strikes the deck
and not the water, in spite of the inconceivability. The Earth re-
turns in its orbit, to the second, in spite of the sun's rapid fall
through space, and of the inconceivability. Two opposed horses
can pull no more than one, in spite of the inconceivability. The
guinea and the feather dropped in the exhausted receiver strike
the plate together, in spite of the inconceivability. The isochro-
nous pendulum swings through the widest arc in the same time as
through the smallest, in spite of the inconceivability. The minute
hand overtakes the hour hand, in spite of the inconceivability. The
masnet draws the iron with undiminished force through all pos-
sible interpositions, in spite of the inconceivability. Could an ex-
ception be found, the perpetual-motion "crank" would work a
greater inconceivability, by the instant contrivance of a power-
generating machine.
We need not aspire, therefore, to remove any of the inconceiva-
bilities of the external world. We must accept them as natural to
the finite comprehension, as necessary to faculties which act by
comparison, and above all as evidences of objectivity. On the
other hand we should avoid that opposite error of the introspective
GENERAL MEETING. 67
school, of deeming that probable, or in any way connected with
fact, which merely seems conceivable. I have shown that while
the simplest truths have generally proved inconceivable until found
out and established by genius, the greatest absurdities have had
ready currency without a doubt of their conceivability. This all
mythology shows. Such rubbish as " a thing cannot act where it
is not," and "a body cannot move where it is not," or "a cause
cannot precede its effect "—mere metaphysical assertions or subtle-
ties in face of everyday fact—Avere stumbling blocks for ages.
Such assumptions formed the basis of deduction in lieu of observa-
tion, and blocked the possibility of advance. And even yet, rigid
deduction from the most hare-brained premiss, if the chain of de-
duction is sufficiently intricate, seems to possess fascinations over a
verifiable induction, with many minds.
And now, ifany ask, " cui bono " to the scientist, these philosophical
inquiries and intricacies when he has the vast field of unexplored data
still before him to occupy him, I answer, the queries of Philosophy
are not only the main-spring and final cause of science (her first
fruitful daughter and handmaid), but they, consciously or uncon-
sciously, dominate the methods and results of science herself.
Each investigator, even though in the domain of the most abstract of
the sciences, postulates more philosophy than he is aware of; and with
so much the more danger to final accomplishment if he assumes his
philosophical basis without examination. It is the errors of giant
minds that are dangerous, by their ponderosity. The infallibility
of the master, Aristotle, seemed to make investigation useless,
until the rise of parallel giants, like Galileo and Copernicus, stim-
ulated a new conflict of opinion. And Descartes, though harm-
less from all his productions within the metaphysical domain, is
dangerous by his very eminence and originality in science,
which gives vogue and currency to his monumental errors.
Although acquainted with the true law of motion, his scheme
of matter evolved from consciousness would forbid all exhibi-
tion thereof. A grand geometer, he erected a scaffold for
scaling immensity, and with unparalleled penetration perceived
how a purely ideal logic, if general, would represent truth in a
wholly dissimilar realm of deduction, if equally general. Strange
to say, this grand and useful discovery has become the engine, in
nihilistic hands, for overthrowing all the positive knowledge we
68 PHILOSOPHICAL SOCIETY OF WASHINGTON.
possess—the achievements of two thousand years of human effort.
Not only geometry—all that has survived to us of philosophical
value from the antique world—but the basis of positive dynamics,
as handed down from Galileo and Newton and Boscovich and
Dalton, are apparently undermined, for all that gives them intel-
lectual value—their certainty—unless an effort be made in the
neglected field of philosophy. With strange inconsistency these
advocates par excellence of the experiential origin of knowledge
are found in the same breath promulgating as possible truth mat-
ters not only non-experiential, but not representable in ideas de-
rived from or verifiable by experience, and avowedly originating
not from inductive generalizations—the only source of knowledge
—
but in purely deductive processes in the old scholastic way, from
logical premises of bald assumption. In a similar way, in the
hands of the Greek sophist, language, a good servant, became a
vicious master, and made a chaos of all ethical achievement. A
remnant of knowledge, fortunately expressed, not in verbal, but
diagrammatic logic
—
geometry—was left, but only to fall now by
the hands of similar iconoclasts, armed with more potent destruc-
tiveness, in its full flower and fruit of twenty centuries of unmo-
lested growth.
It is time, therefore, to get back to Baconian ground, and while
using for its legitimate jjurposes the magnificent modern machinery
of analytical investigation in the field of abstract continuity—ex-
tension, motion, duration—not attempt to conjure with it as a source
of objective revelation, which no mere machinery can be. A scaf-
fold of n dimensions is as useless to the geometer as to the archi-
tect. To assume matter as continuous, simply because of the posses-
sion of a potent engine for the investigation of continuities, is to re-
peat the practice of certain quack specialists, who are prone to diag-
nose nearly every form of disease as a variety of their own peculiar
specialty. And to interview the symbols of a mathematical logic
for the prime definition of a fundamental objectivity, like force, is
to revert to a barren source of knowledge, by an obsolete process
in philosophy, and bar all progress in anything but abstract tech-
nique.
The paper was discussed by Mr. W. B. Taylor and Mr. Kum*
mell.
GENERAL MEETING. 69
Mr. T. Robinson made a communication on
THE STRATA EXPOSED IN THE EAST SHAFT OF THE WATER-WORKS
EXTENSION.
[Abstract.]
The shaft (23' square in the clear) was begun in the bottom of
an old sand-pit at a level of 131.5' above tide. This sand-pit was
excavated in the side of a hill ; and recent cuttings have exposed
the strata from the hill-top to the level of the top of the shaft.
Thus we have a vertical section of 188.5', extending from 171.5'
above tide (or 40' above the top of the shaft) to 17' below tide.
1. About 6" of surface soil.
2. A layer of gravel in red clay, about 4' thick, containing isolated
bowlders from a foot to two feet in their longest diameters.
3. About 24' of a mixed material, consisting mainly of sand and
kaolin. The two are sometimes uniformly mixed ; at other
times they lie in separate masses of two or three feet in
thickness at one point, and run down to as many inches
at another. In short, the whole bed is a sort of " pell-mell
"
of sand and clay.
4. A bed of sand, about 10' thick, generally sharp and clean, but
varying from coarse to fine grains, and streaked with iron
oxides, with pebbles near bottom of stratum.
5. A thin stratum of clay, about 2' thick, varying in color from blue
to red, and containing in spots fragments of lignite.
6. 2.5' of sharp, coarse, clean sand.
7. 32.5' of red clay, mottled with blue and gray, showing no lami-
nation.
8. 5' of sandy clay, mottled as above. Between this stratum and the
clay above, there Avas no dividing line; the two beds blended
gradually along their line of union.
9. A bed of gray, clayey sand, 6' thick. In this bed occurred, on
one side of the shaft, some masses of sandstone, somewhat
more ferruginous than the surrounding sand, and on the
other side a tongue of clean, red clay.
70 PHILOSOPHICAL SOCIETY OF WASHINGTON.
10. A bed of sand with its upper
surface horizontal, having a
thickness of about V at one
side of the shaft and 4' on the
other.
11. A stratum, about 2' thick, of
sandy mud, containing lignite.
The laminse of this bed were
horizontal, while its upper sur-
face fell from north to south
at the rate of about one in
eight.
12. 6' of sand containing nodules of
iron pyrites, isolated masses
of lignite, and pockets of red
clay.
13. A bed of fine, clean sand, con-
taining here and there a little
clay. This bed was 9' thick,
and gradually gave way to the
succeeding bed.
14. A bed of sandy kaolin, 6' thick,
very wet and difficult to work.
It was a regular mortar-bed
in consistence.
15. A layer, 2" to 4" thick, of hard,
ferruginous conglomerate.
16. 9' of blue-grey clay, hard, com-
pact, and possessing a very
unctuous feel. This bed con-
tained a bunch of rootlets, the
first trace of organic remains
below the lignite of No. 11.
17. A bed of clayey sand, streaked
with red, blue, and grey, T
thick, and gradually running
into the subjacent stratum.
lrflSP
S40
OStM&tiL,
GENERAL MEETING. 71
18. A bed of clean, white, sharp sand, about 2' thick. (These last
nine feet were difficult to work. The material could not be
shovelled, and was too sandy to pump.)
19. A layer of red sand about V thick, containing on one side of
the shaft a clayey sediment with lignite, and on the other a
ferruginous conglomerate.
20. 5' of blue-black, hard clay, running into a sandy sediment,
and this, in turn, into the next stratum.
21. 3.5' of clean, white sand.
22. 2' of dark green, compacted sand, containing pebbles and
lignite.
23. 1.5' of fine, sharp sand, almost apple-green in color. Beneath
this lay the irregular surface of No. 24.
24. Dark, coarse-grained, soft, chloritic rock. This rock could be
easily removed by the pick to a depth of three feet, where
blasting was begun at about twenty-six feet above mean
tide. The rock grew harder as the depth increased for about
ten feet, when it became a chloritic gneiss, and in general
remained of that nature through about thirty feet to the
bottom of the tunnel grade, or seventeen feet below mean
tide.
255th meeting. June 7, 1884.
Vice-President Billings in the Chair.
Thirty-five members and guests present.
Mr. G. K. Gilbert presented a
PLAN FOR THE SUBJECT BIBLIOGRAPHY OF NORTH AMERICAN
GEOLOGIC LITERATURE.
Mr. J. W. Powell presented a slightly different plan for the
same purpose.
These plans proposed to establish at the outset a limited number
of divisions of the subject-matter of the literature and to simul-
taneously prepare a bibliography of each.
72 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. J. S. Billings criticised the plans at length and advocated
that which has been adopted for the indexing o£ the Library of
the Army Medical Museum.
Other remarks were made by Messrs. Antisell, Norms, Goode,
E. Farquhar, F. W. Clarke, Harkness, Toner and Ward.
The meeting announced for October 11 was informally ad-
journed, to enable members to attend a meeting of the Anthropo-
logical Society, and listen to an address by Dr. E. B. Tylor, of
Oxford, England.
256th Meeting. October 25, 1884.
The President in the Chair.
Forty members and guests present.
The Chair announced the death, since the last meeting, of Dr.
Joseph Janvier Woodward, a former President of the Society,
Gen. Orville Elias Babcock, and Gen. Benjamin Alvord.
Announcement was also made of the election to membership
of Messrs. Washington Matthews, Stimson Joseph Brown,
Tarleton Hoffman Bean, and Robert Edward Earll.
Mr. S. M. Burnett read a paper entitled
—
ARE THERE SEPARATE CENTRES FOR LIGHT-, FORM-, AND
COLOR-PERCEPTION ?
controverting the theory which gives an affirmative answer to
the question, and maintaining, first, that there is no white-light
sensation that cannot be resolved into its constituent elements of
color sensation ; and, second, that the sense of form is an expres-
sion of the idea of extension as represented by the dimensions
of the area of the retina impressed. The idea of form is not
a purely visual sensation, but is based also on information derived
from other sources.
[The paper is published in the Archives of Medicine, Vol. XII,
No. 2, October, 1884.]
GENERAL MEETING. 73
Mr. T. Robinson read a paper entitled
—
WAS THE EARTHQUAKE OF SEPTEMBER 19TH FELT TN THE
DISTRICT OF COLUMBIA?
[Abstract.]
At 3.20 p. m. of September 19 1 noticed a peculiar vibration of
the floor, table, and chair. I saw my ink shaking and heard the
door of the room rattling. The table and chair rocked in a north
and south direction. The sounds made by the door were at regular
intervals of something less than a second each. My room is on the
second floor of the Howard University building.
Immediately after the occurrence I inquired if other persons had
noticed anything unusual at that time. One had heard a rum-
bling, another had felt the shock, and a third had both felt and
heard it. The miners in the water-works' tunnel also heard a rum-
bling noise at about the same hour.
From the motion of my table and chair and the continued thump-
ings of the door I judge that the shock passed in the direction of
the meridian, and continued from ten to fifteen seconds.
There was no local cause for the phenomenon, and I concluded
that it was in some way connected with the earthquake that oc-
curred in the West at about the same time.
Mr. Paul remarked that the direction of the motion communi-
cated to buildings by a slight earthquake shock is not a reliable
index of the direction of the earth tremor. The azimuth, ampli-
tude, and period of vibration of the buildings are functions of their
structure rather than of the azimuth, amplitude, and period of the
earth vibration.
Other remarks were made by Mr. H. A. Hazen and Mr. Elliott.
Mr. J. S. Billings exhibited a collection of microscopes illus-
trating the evolution of the mechanical stage. The collection will
be sent by the Army Medical Museum to the New Orleans Ex-
hibition.
Mr. Billings read a paper by Mr. Washington Matthews on
NATURAL NATURALISTS.
[Abstract.]
It is easy to understand that a savage may be well versed in the
knowledge of animals and plants which contribute to his wants,
74 PHILOSOPHICAL SOCIETY OF WASHINGTON.
but it is a matter of surprise that with equal care he acquires and
disseminates information about creatures which he .does not use. I
have never yet failed to get from an Indian a good and satisfactory-
name for any species of mammal, bird or reptile inhabiting his
country; and I have found their knowledge of plants equally com-
prehensive. It is true that not all Indians are equally well in-
formed in this respect, but, as a class, they are incomparably supe-
rior to the average white man or to the white man who has not
made zoology or botany a subject of study.
There is a prevalent impression that Indians are unable to gen-
eralize ; and a paragraph goes the rounds of ethnological treatises
to the effect that the Chatas have no general term for oak tree,
but only specific names for the white oak, the black oak, the red
oak, etc. This impression is entirely erroneous. The Indian is as
good a generalizer and classifier as his Caucasian brother. His
system of classification does not fully coincide with that of the white
naturalist, because his system of philosophy leads him to base his
groups upon a different series of resemblances, but his arrangement
is nevertheless the result of a process of generalization.
Mr. Ward remarked that his own experience fully sustained the
statements of the paper in regard to the botanical ignorance of
white men, but less fully in regard to the accuracy of Indian ob-
servations. When collecting plants in Utah, he had found that
Piute boys and girls gave names to nearly all his specimens, dis-
criminating allied species; but in collating the Indian botanical
names recorded by others, he had been led to suspect that certain
discrepancies arose from failure to recognize the same species in
different stages of development.
Mr. Mason said it is a canon of anthropology that things seem
marvellous to us only when we do not understand them, every
human phenomenon being governed by law. Our ignorance in re-
gard to wild animals and plants is to be explained by the fact that
our activities do not bring us into close relation with them, whereas
the savage is dependent on them for sustenance. The market-
women who bring herbs to Washington have names for them all,
and ignorant mechanics handle technical terms of their craft with
great familiarity.
Mr. Dutton said that his own acquaintance with the Navajos
GENERAL MEETING. 75
made him prone to believe that they diagnose species of plants, but
lie questioned their powers of generalization.
In illustration of Mr. Mason's remark that familiarity is con-
ditioned by contact, he related that rural rambles had made him
when a boy so familiar with the fauna and flora of his district that
he knew a name for every prominent species. As a man, he had
been occupied with other and different matters, and had lost this
familiarity.
Mr. Welling admitted that the Indian was an acute observer,
but questioned the propriety of calling him a naturalist. As illus-
trated by the paper, his methods of interpretation are metaphysical,
not scientific.
Other remarks were made by Mr. Hilgard.
257th Meeting. November 8, 1884.
Vice-President Billings in the Chair.
Forty-eight members and guests present.
Mr. Billings, on behalf of the General Committee, reported the
following resolutions
:
Resolved, That this Society receives with deep regret the an-
nouncement of the the death, on the 17th of August last, of Dr.
Joseph Janvier Woodward, an ex-president of this Society and
one of its original founders.
Resolved, That this untimely death has deprived science of one
of its most energetic, patient, and skilful workers and this Society
of one of its most efficient and distinguished members.
Resolved, That in our sorrow for this affliction we have some
consolation in the knowledge that his long and great suffering is at
last ended and that the fruits of his unceasing labors for the last
twenty-five years remain for the benefit of the world and as an en-
during monument to his memory.
Resolved, That a copy of these resolutions, duly authenticated,
be forwarded to his bereaved family.
In presenting these resolutions, Mr. Billings spoke briefly of
Dr. Woodward's work and his characteristics as a scientific man,
76 PHILOSOPHICAL SOCIETY OF WASHINGTON.
eulogizing his accuracy of observation, his delicacy of manipula-
tion, his conservatism as a theorist and as a crkic of new ideas?
and alluding to his delight in teaching and his interest in, and
affection for, the Philosophical Society.
Mr. Powell spoke of his remarkable acumen and his conspicu-
ous mental integrity. Mr. Gihon spoke of his boyhood ; Mr. Toner
of his ability as a practitioner ; and Mr. E. Farquhar of the im-
pression of great force conveyed by his presence and conversation.
The resolutions were unanimously adopted.
Mr. C. E. Dutton made a communication on
THE VOLCANOES AND LAVA FIELDS OF NEW MEXICO,
his remarks being illustrated by photographic lantern views, and
by a map exhibiting the boundaries of the region usually termed
the Plateau country.
[Abstract.]
Beginning at the north, the boundary of the Plateau country
runs along the southern base of the Uinta Range to the junction
of the latter with the Wasatch ; following the eastern base of the
Wasatch southward it strikes off towards the southwestern corner
of Utah ; thence turning due south it crosses the Colorado river,
and gradually shifts its course to the southeastward, preserving this
direction for nearly 400 miles and far into New Mexico ; here it
rapidly turns north northeastward, reaching into the Valley of the
Rio Grande, and follows the western bank of that river nearly or
quite into Southern Colorado ; here the course of the boundary ,is
somewhat indeterminate, but is, in a general way, first northwest-
ward, then northward to the place of beginning. The western and
southern border of the Plateau province is usually sharply defined
;
the plateaus end generally in great cliffs suddenly terminating the
horizontal strata, and the profiles drop down upon the rough, irreg-
ular topography of a type peculiar to the Great Basin. The
eastern border of the Plateau province is by no means so definite
the features peculiar to it pass rather by gradual transition into
those characterizing the Rocky Mountains of Colorado.
Among the many geological features of this wonderful region,
the volcanic masses are not the least interesting. Volcanic action
has prevailed there upon a grand scale, and it may be first noted
GENERAL MEETING. 77
that volcanic rocks predominate around the borders of the
province. The interior spaces, while not wholly devoid of them,
show but a very small amount. The region of the High Plateaus
of Utah, which lies upon the western or northwestern border,
discloses a very large mass of lavas, erupted chiefly during
tertiary time, and representing almost continuous activity from the
eocene to the quaternary. Proceeding southward, we are never out
of sight of eruptive masses, and in the Unkarets, on the border of
the Grand Canon, we find many scores of old and young cinder-
cones and some considerable lava-fields. In the San Francisco
Mountains we also have a vast field of volcanic rocks, and thence
southeastward they augment in volume and area until at the
southernmost extension of the Plateau country they become indeed
immense. Still following the boundary northward into the Valley
of the Rio Grande they are found abundant, and a singularly
interesting field is presented in the neighborhood of Mt. Taylor.
The speaker was engaged during the past summer in the geological
examination of the Mt. Taylor district, and it is of the striking
features there presented that he designs especially to speak.
Mt. Taylor is an old volcano long since extinct. Its altitude is
about 11,400 feet above the sea. It stands upon a high mesa, from
the summit of which it rises as an ordinary volcanic cone of con-
siderable magnitude—much larger than Vesuvius, much smaller
than iEtna. Its lavas are rather monotonous in type, so far as ex-
ternal appearances are concerned, consisting probably of basalts
and andesites. The mesa upon which it stands is of great extent,
being 40 miles long and 25 miles wide. It is composed of nearly
horizontal cretaceous strata, capped everywhere with basalt or an-
desite, ranging from 200 to 400 feet in thickness. To the north-
east and to the south of it are similar high mesas, also capped by
basalt and andesite, but presenting no great volcanic pile like Mt.
Taylor. The only features which indicate volcanic vents are barely
noticeable hillocks, which scarcely affect the evenness of the hori-
zontal surfaces and which are wholly incommensurate, apparently,
with the vast lava caps upon which they occur.
These lavas are all of tertiary age. It would be difficult to say
to what divisions of tertiary time their activity should be assigned,
"but it cannot have been very late tertiary and it is reasonably
certain that it cannot have been very old tertiary. In a general
78 PHILOSOPHICAL SOCIETY OP WASHINGTON.
way their activity is inferred to have prevailed in a period not far
from middle tertiary time
—
possibly in the miocene. The large
amount of erosion which has occurred since their eruptions ceased
forbids a much later period, and the still larger amount of tertiary
erosion which preceded this activity equally forbids a much earlier
one.
Upon the summits of the mesas no recent eruptive rocks occur.
But in the broad valleys which lie between them and around them
are lavas of quite another age. These valley lavas are all recent.
Indeed the most superficial observer is at once impressed with the
freshness of their aspect, and critical examination confirms the
view that none of them have any geologic antiquity, while some of
them are so modern that it seems as if half a dozen centuries were
a large estimate of the time which separates us from their outflow.
These recent eruptions are basalts of normal type. The external
aspects of the fields of young lava resemble those of the Hawaiian
Islands. The two forms of solidified lava are well presented, viz
:
the viscous or ropy, and the rough clinker fields.
A striking characteristic of both old and young lavas—those
upon the mesa summits and those in the valleys below—is the usual
though not universal absence of cinder cones or piles of fragmental
matter built up around the orifices from which the lavas were ex-
truded. The eruptions, with the exception of those of Mt. Taylor,
belonged to the quiet order which are typified among volcanoes
now active, by Mauna Loa and Kilauea.
But the volcanic remnants which appeal most strongly to the im-
agination of the observer, remain to be described. In the broad
valleys which separate the lava-capped mesas are seen many con-
spicuous objects rising as sharp peaks or aiguilles of rock to great
altitudes. They are very black in color, and contrast powerfully
with the bright tints of the sedimentary beds around them. These
peaks, which range in altitude above the valley plains from
700 or 800 feet to 2,000 feet, consist of columnar basalt. They
are, in fact, the ancient lavas which congealed in the volcanic
pipes, while the sedimentary strata which formerly inclosed them
have been swept away in the great erosion of the country. In that
long-continued and great denudation these " necks," by their more
adamantine character, have resisted the general decay, and remain
to attest the former extension of the strata over the valleys and the
GENERAL MEETING. 79
existence, prior to their denudation, of volcanic extravasations
which probably covered them wholly or in part. In the mesa walls
and on their slopes may be seen numerous instances of partially
excavated necks, while in others the necks are just beginning to be
exhumed. In the latter cases remnants of the old cinder-cones
Avhich were piled up over their summits are still preserved, so that
natural sections of the whole apparatus are exhibited. There are
many scores of these necks, and the effects of erosion in unearthing
them are exhibited in all stages. Wherever the true neck or core
is disclosed the basalt is seen to be columnar, and the columns are
often arranged in beautiful fashions.
No more striking illustration and proof of a great erosion could
be mentioned than is here disclosed, and the region must become
a classic one, to be referred to by future geologists as an excellent
example of some of the grandest laws and - processes with which
their science deals.
Mr. Powell spoke of the distribution of eruptions. They are
apt to occur on the faces of acclivities undergoing erosion, but not
on acclivities due to displacement. Near a fault they break through
the uplifted block rather than the thrown. They do not occur in
the bottoms of canons.
In mapping the Plateaus he had thrown the boundary farther
north than Captain Dutton, so as to include a large area north of
the Uinta Mountains.
The peculiarly favorable conditions under which geology is
studied in the plateau region enable its features to be comprehended
without the doubts and the laborious compilation of details else-
where necessary. It results that while the structure of the Plateau
country is as well known as that of any equal area in the world,
the literature of its geology is exceedingly small.
Other remarks were made by Messrs. White and Gilbert.
258th Meeting. November 22, 1884.
The President in the Chair.
Forty-nine members and guests present.
80 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. E. B. Elliott made a communication on
ELECTRIC LIGHTING,
which was discussed by Messrs. Hilgard, Welling, Mussey,
Paul, and Powell.
Mr. H. Allen Hazen made a communication on
THERMOMETER EXPOSURE.
[Abstract.]
In recent experiments for determining the relative values of tem-
peratures in city and country, it has been found that ordinarily, on
clear days, in the early morning, at 6 feet above ground, in the
country, temperatures are 4 to 5 degrees lower than in the city, and
also that the air is always nearly saturated in the country, but not
as nearly in the city. This is due more to intense radiation from
grass in the country, this cooling the air to the dew point, than to
the heating and drying from pavements and walls or chimneys of
houses.
To obtain a standard air temperature it is proposed to use bright
and black bulb thermometers joined together and swung over grass
ground under an umbrella, with no shade from trees or buildings,
in the day time. Under such circumstances the two thermometers
can be brought within 0.5° of each other, and the true air tempera-
ture may be taken as about as much lower than the bright-bulb as
that is lower than the black.
Recent experiments with six different thermometer shelters indi-
cate a general agreement, except in the case of the Wild shelter.
The peculiar condition effected by the Wild shelter is inferior ven-
tilation, and the experiments indicate the practical sufficiency of
the single-louvred shelter. To determine the humidity with the
psychrometer in still air, the employment of artificial ventilation
is recommended.
Remarks were made by Mr. Paul.
259th Meeting. December 6, 1884.
By courtesy of the officers of the Columbian University, the
meeting was held in the lecture hall of the University building.
GENERAL MEETING. 81
Members of the Anthropological, Biological, and Chemical Societies
and their friends were present by invitation.
Mr. J. W. Powell, by request of the President, occupied the
Chair.
Present, one hundred and four members and guests.
The business of the evening was the presentation of the Annual
Address of the President, Mr. J. C. Welling. In introducing
him to the audience, the Chairman sketched the history of the
Society, describing the socio-scientific club of which it was the
offspring, and referring to the younger scientific societies of Wash-
ington, of which it might be regarded as the parent.
The President then read an address on
THE ATOMIC PHILOSOPHY, PHYSICAL AND METAPHYSICAL.
[Printed in full on pp. xxix-lix.]
On motion of Mr. Gregory, the Society tendered its President
a vote of thanks for his efficient administration and instructive
address.
260th Meeting. December 20, 1884.
the fourteenth annual meeting.
The President in the chair.
The Chair announced the death, since the last meeting, of Mr.
Henry Wayne Blair.
The Chair announced the election to membership of Mr. Robert
Edwards Carter Stearns.
It was announced that the Mathematical Section would, in the
future, hold its meetings in the mathematical class room of the
Columbian University, the use of that room having been tendered
by the officers of the University.
The order of business was then read, and afterward the minutes
of the last annual meeting.
82 PHILOSOPHICAL SOCIETY OP WASHINGTON.
The report of the Secretaries were read and accepted. (Printed
on page xxiii.)
The report of the Treasurer was read, received, and referred to
an Auditing Committee, consisting of Messrs. H. C. Yarrow, Mar-
cus Baker, and W. C. Winlock. (The report is printed on pages
xxiv and xxv.)
The minutes of the 258th and 259th meetings were read and ap-
proved.
The officers of the ensuing year were then elected. (The list is
printed on page xv.)
The rough minutes of the meeting were read, and the meeting
adjourned.
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON
MATHEMATICAL SECTION.
*3

STANDING RULES
MATHEMATICAL SECTION,
1. The object of this Section is the consideration and discussion
of papers relating to pure or applied mathematics.
2. The special officers of the Section shall be a Chairman and a
Secretary, who shall be elected at the first meeting of the Section
in each year, and discharge the duties usually attaching to those
offices.
3. To bring a paper regularly before the Section it must be sub-
mitted to the Standing Committee on Communications for the
stated meetings of the Society, with the statement that it is for the
Mathematical Section.
4. Meetings shall be called by the Standing Committee on Com-
munications whenever the extent or importance of the papers sub-
mitted and approved appear to justify it.
5. All members of the Philosophical Society who wish to do so
may take part in the meetings of this Section.
6. To every member who shall have notified the Secretary of the
General Committee of his desire to receive them, announcements
of the meetings of the Section shall be sent by mail.
7. The Section shall have power to adopt such rules of procedure
as it may find expedient.
24 8s
OFFICERS
MATHEMATICAL SECTION FOR 1884.
Chairman, Asaph Hall. Secretary, Henry Farquhar.
LIST OF MEMBERS WHO RECEIVE ANNOUNCEMENT OF THE
MEETINGS.
Abbe, C.
Avery, R. S.
Baker, M.
Bates, H. H.
Billings, J. S.
Burgess, E. S.
Christie, A. S.
Coffin, J. H. C.
Curtis, G. E.
DeLand, T. L.
Doolittle, M. H.
Eastman, J. R.
ElMBECK, W.
Elliott, E. B.
Farquhar, H.
Flint, A. S.
Gilbert, G. K.
Gore, J. H.
Green, B. R.
Hall A.
Harkness, W.
Hazen, H. A.
HlLGARD, J. E.
Hill, G. W.
King, A. F. A.
Kummell, C. H.
McGee, W J
Newcomb, S.
Paul, H. M.
Lefavour, E. B.
Peirce, C. S.
Ritter, W. F. M'K.
Smiley, C. W.
Taylor, W. B.
Upton, W. W.
Walling, H. F.
WlNLOCK, W. C.
Woodward, R. S.
86
BULLETIN
MATHEMATICAL SECTION.
10th Meeting. January 30, 1884.
The Chairman presided.
Seventeen members and guests present.
The Section proceeded, under Rule 2, to the election of a Chair-
man and a Secretary for the year 1884. On motion of Mr.
Elliott, the rules governing the elections of the Society were
adopted. The officers for 1883—Mr. Hall, as Chairman, and Mr.
H. Farquhar, as Secretary—were re-elected, after each had briefly
expressed a desire that the choice might fall on some one else.
Mr. Kummell read an extract from a letter lately received from
Mr. Artemas Martin, of Erie, Pennsylvania, in which the forma-
tion of an American Mathematical Society was recommended.
After some informal discussion, Mr. Winlock moved the appoint-
ment of a special committee, with instructions to report on the
advisability of taking steps for the formation of such a society.
On motion of Mr. Elliott, the matter was postponed.
Mr. Kummell then made a communication on
CURVES SIMILAR TO THEIR EVOLUTES,
in which he made use of the intrinsic equation, and showed this prop-
erty to belong to a whole class, of which the logarithmic spiral
is at one extreme and the cycloids are at the other.*
* Prof. Benjamin Peirce solved a problem almost identical with this one,
in Gill's Mathematical Miscellany for May, 1839, by essentially the same
methods. This solution, which had not been seen by Mr. Kummell at the
time of reading his paper, is believed to contain the first use of what has
since become known as the "intrinsic equation."
87
88 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Remarks on this communication were made by Messrs. Christie
and Hill.
Mr. G. K. Gilbert made a communication on
THE PROBLEM OF THE KNIGHT'S TOUR.
[Abstract.]
The ordinary problem, requiring the knight to traverse the chess-
board and return to his original position in sixty-four moves, is
susceptible of very numerous solutions, and is not difficult. Its
interest is increased by extending it so as to include fields of other
form and size.
It is readily shown that a perfect tour is impossible on any field
containing an odd number of squares.
A symmetric tour is one divisible into two or more similar parts.
A tour has bilateral symmetry when one-half, being turned face
downward upon the other, coincides with it. A tour has biradial
symmetry when one-half, being rotated through 180° about the cen-
ter of figure, coincides with the other half. A tour has quadri-
radial symmetry when its fourth part, being rotated through 90°
about the center of figure, coincides with the adjacent quarter.
A tour having bilateral symmetry cannot be devised on a field
containing a number of squares divisible by four.
A tour having biradial symmetry cannot be devised on a field
whose number of squares is divisible by two and not by four.
A tour having quadriradial symmetry cannot be devised on a
field whose number of squares is divisible by eight.
It follows that on square fields the tour is impossible if the num-
ber of spots on a side is odd ; bilateral symmetry is never possible
;
quadri-radial symmetry is possible only when the number of squares
on a side is the double of an odd number. The only symmetry
possible on a chess-board is biradial.
The above conclusions are deductive. It is determined empiri-
cally that the smallest square field on which the tour can be exe-
cuted is that with 36 spots. Upon this field the number of possible
tours with biradial symmetry is twenty-one, of which five have
also quadriradial symmetry.
Remarks on this communication were made by Messrs. Elliott
and Hall, who called attention to previous work on the subject.
mathematical section. 89
11th Meeting. February 20, 1884.
The Chairman presided.
Eighteen members and guests present.
Mr. H. Farquhar made a communication on
EMPIRICAL FORMUL2E FOR THE DIMINUTION OF AMPLITUDE OF
A FREELY-OSCILLATING PENDULUM.
[Abstract.]
The theoretical formulae usually employed are obtained by in-
tegration from an expression for the diminution of the amplitude
in terms of the amplitude itself. The most important term in this
expression is one involving the first power of the amplitude, indi-
cating a resistance proportional to the velocity of the pendulum's
motion. A term containing the square of the velocity (or ampli-
tude) also enters; and, to allow for the friction of the pendulum
knife-edge on its support, a term independent of the velocity would
have to be added. Atmospheric resistance to very high velocities
is found, moreover, to be proportional to a higher power than the
square of the velocity. There are thus more than three terms the-
oretically required to express the resistance, and these must be
calculated, such is the uncertainty of the subject and the complex-
ity of the conditions on which the different resistances depend, from
the observations themselves. Since these observations must also
be depended on for an additional constant (the amplitude at some
initial time or the time of some standard amplitude), and since
they are not complete or exact enough to furnish more than three
constants, or four in a few exceptional cases, it is obvious that a
good approximation to theory must content us in practice.
Two convenient methods of representing amplitude in terms of
time are suggested by imposing arbitrary conditions. First, taking
three terms to express the diminution (the amplitude being ^), thus:
a -\- b<p
-f- c?
2
,
suppose the square of half the middle co-efficient equal to the
product of the other two. This expression has then the form
:
7 (f + V-
90 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Integrating this value of — Dt<p, and supplying a constant, we
have:
O + V) (t— e) = a,
in which the constants a-\- be, e and — b, are easy to calculate by
least squares.
To show the agreement of this formula with observation, take
Mr. Pierce's " mean swing " at three European stations (U. S. Coast
Survey Report for 1876, appendix 15, pages 232, 271) and apply
b = 29'.2, e = —7632s, a = 756847, in calculating <p from t. Hence
the following table
:
t.
MATHEMATICAL SECTION. 91
A ?=- Ya {& + 6) 2 ~ 4ac + (? + 6) l/(^ + 6) 2-4ac}
The correction to the time of oscillation ( jn D
t ^ ) involves
the logarithm of t — e, and is not very simple in practical applica-
tion.
The second convenient method is the one by which the residuals
in the last column of the table above given were calculated. In
this the rate of diminution is supposed proportional to <p x + n, n be-
ing a proper fraction. Hence,
2
, n »
2~ n
n , . ,. , _. — l 2 na nay
9 (t — e) = a, and D t <P = 2
—
(2-n)(<-e)n * 2 — n
This formula is very simple, and the table shows its agreement
with observation to be fair for the larger amplitudes—those of chief
importance. In this calculation n = £, e = — 10716s , and a=
89400. Better results would have been obtained by using a slightly
smaller value of n, say 0.44 ; but in practice the nearest tenth or
reciprocal of a whole number is sufficient. In reducing the obser-
vations given by Prof. Oppolzer, n was taken equal to 0.28 ; but
one of the residuals exceeded V, though two others were as high as
0'.9. The observations at low pressures, above referred to, indi-
cated a much smaller n. By using the value 0.04, however, the
agreement of formula and observation was perfect, n thus appears
to be nearly proportional to the square root of the atmospheric
pressure; but when very small, it may be supposed to vanish, and
<p
n replaced by the logarithm of <p. In this case e will of course
be the time of unit-amplitude, instead of that of infinite amplitude
as in former cases.
No two observations of the diminution of amplitude of the same
pendulum will in general be found to be copies of each other, for
differences in atmospheric conditions and in friction on the support,
imperceptible otherwise, will manifest themselves in a changed rate
of diminution. Even in calculating the correction for different
parts of one extended swing, it is advisable to adopt different values
of one or other of the constants found. By so varying the quan-
92 PHILOSOPHICAL SOCIETY OF WASHINGTON.
tity e, in the formula last given, all disadvantages from its want of
exact accordance with observation disappear, and the results are
brought far within the needful limits of accuracy.
Mr. Gilbert then stated
A CONCRETE PROBLEM IN HYDROSTATICS,
suggested by the fact that the shore-line of a quaternary lake in
the Great Basin is shown by levels to be more than a hundred feet
higher on elevated land, that once formed islands near its middle
part, than on the margin of the lake. This inland sea, known as
Lake Bonneville, was one hundred and twenty miles across. Among
the possible explanations of the present difference of level, the
effect of the removal of a large body of water in changing the form
of level surfaces in its basin had been suggested, and the problem
was to find how great an effect was due to this cause.
In the discussion that followed, Mr. Paul called attention to the
complexity of the calculation of equipotential surfaces.
Mr. Woodward had formerly made a somewhat similar compu-
tation to ascertain the deflection of the plumb-line caused by un-
equal local attraction to eastward and to westward at the eastern
end of Lake Ontario; from which it appeared to result that the
effect due to this cause was insignificant in comparison with that
required by the problem.
Other remarks were made by Messrs. Doolittle, Hill, H. F \r-
quhar, and S. J. Brown.
At the request of the Chairman, a communication promised by
him was postponed until next meeting.
mathematical section. 93
12th Meeting. March 5, 1884.
The Chairman presided.
' Fifteen members present.
Mr. A. Hall read the following paper on
THE FORMULAE FOR COMPUTING THE POSITION OF A SATELLITE.
The method of rectangular co-ordinates in space furnishes a very-
simple and at the same time a general method of treating many
questions in astronomy. This method was introduced into practical
astronomy by Lagrange in his memoir on the Transit of Venus,
June 3, 1769 (Berlin Academy Memoirs, 1766). Whenever we
have to consider the relations of three points in space, we may take
the origin of co-ordinates at one of the points, and then forming
the values of the rectangular co-ordinates of the other points in
terms of the polar co-ordinates, the sum or difference of two of the
x co-ordinates being equal to the third x co-ordinate, we have an
equation between the three polar co-ordinates. Similar relations
hold for the axes of y and z, and hence result three equations be-
tween the two angles and the distance that are required to be
found. This method is extremely useful, and can be applied to a
great number of questions in parallax, aberration, eclipses, and to
those that occur in nearly every part of spherical astronomy. A
great recommendation of this method is its simplicity, and the fact
that it is so closely connected with first principles that it can be
applied with the greatest ease. After the equations are formed
they have only to be transformed by known rules, and the whole
work is thus reduced to algebraic and trigonometric transformations
which can be safely made. These advantages are so great that it
is not surprising that this method of treating astronomical ques-
tions has come so largely into use, and the generality and elegance
of the process are in marked contrast with the old methods which
proceed by spherical trigonometry. . Perhaps a disadvantage of the
new method is that it is too mechanical, and one is apt to forget or
never know the meaning of the quantities that are employed. The
old geometrical methods have therefore their value in calling to
mind a more exact knowledge of the quantities that are used in
the solution of a problem.
94 PHILOSOPHICAL SOCIETY OP WASHINGTON.
In the method which Bessel has employed for computing the
position of a satellite, he has derived his formuke by Lagrange's
method. Thus if a- and d be the apparent right ascension and
declination of the planet at any instant, a', <5' the same quantities
for the satellite, and if p and p' be their distances from the earth,
and if r be the radius vector of the satellite, and a and d its right
ascension and declination seen from the planet, we have, by the
method of rectangular co-ordinates,
(f COS o COS a' s= p cos d cos a -f r cos d cos a
p' cos d* sin a! = p cos <5 sin a -f- r cos d sin a (1)
p' gin & = p sin <S +r sin d
If p and s are the angle of position and distance of the satellite
with respect to the center of the planet, the spherical triangle
formed by the pole of the equator, the planet, and the satellite
gives us the following equations
:
cos s = sin d sin o*
-f- cos 3 cos & cos (a! — a)
sin s cos p = cos 8 sin 3' — sin d cos & cos (</ — a) (2)
sin s sin p = cos ^ sin (a' — a)
IfN and J" be the longitude of the node of the orbit of the sat-
ellite on the equator, and its inclination to the equator, and u the
distance of the satellite from the node counted on its orbit, we have
cos d sin (a — N) = sin u cos J
cos d cos (a — N) = cos u (3)
sin d = sin u sin J
These three sets of equations are fundamental, and are sufficient
for the complete solution of the problem—Given the orbit of a sat-
ellite to determine its apparent angle of position and distance. We
have only to transform these equations, and, in order to ease the
computation, to introduce, as Bessel has done, certain auxiliary
quantities which depend on the position of the planet in the heavens,
and the position of the orbit of the satellite with respect to the
equator. These auxiliary quantities will of course vary with the
position of the planet, and also from the slow changes that the node
and inclination of the orbit undergo, but they can be tabulated
easily. So far
:
therefore, as the practical solution of this question
is concerned there is not much more to be desired, but it is interest-
MATHEMATICAL SECTION. 95
ing to look at the problem from another point of view, and one
that will lead us to consider more closely its geometry.
Imagine a set of rectangular axes in space, the origin being at
the center of the planet, and denote by X, Y, Z the points on the
celestial sphere made by the intersections of these axes. Let S be
the point where the prolongation of the radius vector of the satel-
lite strikes the sphere ; then we have for the co-ordinates of the
satellite
x = r. cos SX
y = r. cos SY
z = r. cos SZ
We can express these cosines by means of six auxiliary quanti-
ties similar to those that Gauss has used for computing the position
of a planet. Take the prolongation of the right line drawn from
the earth to the planet as the axis of Z, the axis of Y in the plane of
the declination circle that passes through Z, and the axis ofX at
right angles to this plane and in the direction of increasing right
ascensions. Let be the pole of the equator and T the positive
pole of the orbit of the satellite. Introduce the following notation,
which is the same as Bessel's
:
arc TX = /, angle OTX= F
" TY=g, " OTY= G
" TZ —h, " OTZ = H
Since the arc TS= 90°, the spherical triangles STX, STY, and
STZ give
cos SX= sin / cos STX
cos SY— sing cos STY
cos SZ = sin h cos STZ
The distance of the satellite in its orbit from the node being u,
and the angle OTN being 90°, we have
STX= 90° -(F+ u)
STY= 90° — (G+ it)
STZ = 90° - (R+ u)
And the values of the co-ordinates are therefore
:
x = r. sin / sin (F
-f w)
y = r. sin g sin ( G + u) (4)
z = r. sin h sin (H -f u)
96 PHILOSOPHICAL SOCIETY OP WASHINGTON.
These are the values at which Bessel arrives by the analytical
method. The arcs/, g, h are always less than 180°, and the only
difficulty is in counting the angles F, G, H. In the purely ana-
lytical process we merely substitute so as to satisfy the equations,
and the result is right if we pay attention to the algebraic signs
;
but in the preceding quasi-geometrical method we must be careful
to count the angles F, G, H in the direction of increasing right
ascensions from 0° to 360°. The formulae for computing the six
auxiliary quantities can be found from the spherical triangles
TOX, TOY, TOZ. In these triangles the angles at are
TOX=180°-(a-JV)
TOY= 90 -(a- JV)
TOZ =. 90 + (a - JV)
Hence, we have
cos / = — sin J cos (a — N)
sin / sin F = — sin (a — JV)
sin /cos F = cos J cos (a — JV)
cos g = cos 8 cos J -f sin ^ sin J sm (a — -^0
sin g sin G = — sin 8 cos (a — N) (5)
sin g cos G = cos 8 sin J — sin 8 cos J sin (a — N)
cos h = sin 8 cos J — cos 8 sin J sin (a — JV)
sin h sin H = cos «5 cos (a — 2V)
sin h cos H = sin 5 sin J" -(- cos <5 cos J" sin (a — JV)
The computation of these formulae may be changed by introduc-
ing other auxiliary quantities, as is commonly done, but nothing is
gained by such a change if the computer is accustomed to the use
of addition and subtraction logarithms.
By means of the spherical triaugles we can find a number of
elegant relations among the quantities / g, h, F, G, H. But we
have first
cos/2 + cos g* + cos h* = 1,
or these are the direction cosines of the line drawn from the planet
to the pole of the orbit of the satellite.
The triangle XTY gives
cos XY = cos XT cos YT + sin XT sin YT-cos XTY,
and we have XY = 90°, XTY = F - G,
MATHEMATICAL SECTION. 97
hence the values of cos XY, cos YZ, cos ZX furnish the equations
cos (jF — G ) = — cotg / cotg g
cos ( G — H) = — cotg g cotg h (6)
cos (H— F) = — cotg h cotg /
Again the triangle XTY gives
cos/= sin g cos TYX,
and from the triangle TYX
sin h sin FTZ=sin TYZ,
but TFX- 2TZ= 90°,
and YTZ=-{G-H),
hence these equations and similar ones give
cos/i
sin (F- G) =
sin/ sin g
sin (£-#)= C°S/, (7)v J sin g sin /i v y
. ,,-r ^ cos q
sin (H—F)= . j . ,v y sin /i sin /
By combining equations (6) and (7), we have
cotang (i^- GO = -~^^
cos 9 cos h
cotang (G — H) = —
cotang (H—F) = —
cos/
cos h cos/
COS(f
cos/2 = cotg CF- (?) cotg {H— F)
cos $r
2
= cotg (G— H) cotg (jP — G)
cos /t
2 = cotg (H— F) cotg (G — jff)
• « cos(g-g)
sin J - - sin ^_ qj gin (fi-_ F)
• ^_
cosCff- J)sm - -
sin ( (?
_jgr)sin ( jp_ Qi)
• !•_ cosQF- (?)sin n --
sin (£r_j?) sin ( (? _j3-)
98 PHILOSOPHICAL SOCIETY OP WASHINGTON.
These six auxiliary quantities are therefore strictly analogous to
those which Gauss introduced for computing *the position of a
planet. For controlling the computation, we have
sin g sin h sin (H— G)
tanSJ= sin/ cos F '
an equation in which each of the six auxiliaries enters into the
value of J.
If we introduce another auxiliary quantity, and put the angle
TZO = 180° - k,
it follows, from the manner adopted for counting an angle of
position, that
TZO = 180°
-O- k).
Denoting the angle between the radius vector and the axis of
Z by <t, the spherical triangle TZS gives
sin a sin (p — k) = cos (U -f- it)
sin <r cos (p — k) = sin (H+ u) cos h (8)
cos a = sin (H
-f- w) sin h
But we have also
p' sin s — r sin a
p' cos s= r cos a -\- p,
and by uniting these equations with (8), we can find s and p. This
method of finding the distance and the angle of position is due to
Marth, and as it is in constant use by him for the very convenient
ephemerides of satellites which he publishes, it may be well to con-
sider it further. If we multiply equations (8) by r, and then sub-
stitute the values of r sin a and r cos <* from the last equations,
we have
p' sin s sin (p — k) = r cos (-ET+ u)
p' sin s cos (p — k) = r sin (-0"+ u) cos h (9)
p' cos s = r sin (H -f- u) sin h -\- p
Instead of these exact equations we may use in nearly all known
cases of satellites the first two equations and put p for p' and s for
sin s. The equations for use are then
r
s sin (p — k) = — cos (H-\- u) (10)
r
s cos (p — k) = — sin (H+ u) cos h
MATHEMATICAL SECTION. 99
If we express s and r in seconds of arc, and assume that the orbit
T
is circular, — will be the semi-major axis of the apparent ellipse
P
T
described by the satellite, and — cos h will be the semi-minor axis.
T T
The quantities — , — cos h, H and k can be tabulated, and equa-
tions (10) furnish the easy method of computing s and p which is
employed by Marth (Monthly Notices, Royal Astronomical Society.)
For computing k we have from the triangle TZO
sin h sin k = cos (a — N) sin J
sin h cos k = — sin (a — iV) sin J sin 8 — cos J" cos 8 (11)
and, also, sin h sin k = — cos/
sin h cos k = — cos g
In what precedes it is assumed that the orbit of the satellite is
known. If this orbit is not known the easiest method of proceed-
ing seems to be the following : First, we assume the orbit of the
satellite to be a circle, and from the observed angles of position
and the observed distances determine the major and minor axes of
the apparent ellipse described by the satellite around the planet,
and the angle of position of the minor axis. Generally these
quantities can be found by a graphical method. The preceding
angle k is the angle of position of the minor axis, and cos h is found
from the ratio of the two axes. Then from the triangle TOZ we
have the equations
sin J cos (N— a) = sin h sin k
sin J" sin (JV— a) = cos h cos 8
-f sin h sin 8 cos k (12)
cos J = cos h sin 8 — sin h cos 8 cos k
With the approximate values of J andN found from these equa-
tions we can compute the auxiliary quantities depending on the
position of the plane of the orbit and the position of the planet,
and can determine the elements belonging to the plane of the orbit.
These approximate elements can afterwards be corrected by equa-
tions of condition or by other methods.
In work of this kind it is more convenient to have the inclination
and node of the orbit referred to the equator, and since these ele-
ments are commonly given with respect to the ecliptic we have to
transfer them to the equator. If n and i are the node and inclina-
100 PHILOSOPHICAL SOCIETY OF WASHINGTON.
tion referred to the ecliptic, e the obliquity of the equator, and w
the distance from the ecliptic to the equator counted on the orbit..
we have the following equations for finding J, N, and w. These
equations come from the triangle between the equator, the ecliptic,
and the orbit of the satellite. They are similar to those given in
the Theoria Mot., Art. 55,
xo — N n . e + i
sin £ J cos—n— = cos — sin
sin \ J" sin
cos \ J cos
cos h J sin
w — N
2"
w + N
2
w + N
2
= sin tt sin
= COS TT COS
= sin 17 cos
2
e — i
e -{- i
2
e — i
For the inverse problem of finding i, N, and w from J, N, and
e, we have from the same triangle
COS \ I cos
n — w N J
cos £ % sin 2~
= cos o~ cos
,
N
= sin o* cos
2
2
J- en -\- w N
.
sin J i cos —k— = cos ^- sin —
s
sin * t sin
w -)- w N . J +
= sin ^- sin
POSITION OF A SATELLITE.
MATHEMATICAL SECTION. 101
TX = f, OTX = F,OT = J, STZ = 90° — (H+ u)
TY=g, OTY= G, OY= 8, TZO = 180° - k
TZ = h, OTZ = H, OZ= 90° - d, TZS = 180° — (p — h)
NS— u, NOZ=a-N, TOZ= 90°+ (a— N), SZO =f= 360° -p
TOX= TOY + 90 = 180° — (a — N)
iVis the pole of OT, :. NOT = NTO = 90°
In response to a question, Mr. Hall said that in computations
of orbits of double stars, as little reliance should be placed upon
measures of distance as possible. Variations of angular velocity
are far safer.
Mr. G. W. Hill made a communication on
A FORMULA FOR THE LENGTH OF A SECONDS-PENDULUM,
which is published in full m the Astronomical Papers of the
American Ephemeris, Vol. Ill, Part 2, Chapter V.
13th Meeting. March 26, 1884.
The Chairman presided.
Fourteen members present.
Mr. Alex. S. Christie made a communication on
A FORM OF THE MULTINOMIAL THEOREM.
This communication is reserved by the author. Remarks were
made by Mr. Hill.
Mr. R. S. Woodward gave a
DISCUSSION OF A CONCRETE PROBLEM IN HYDROSTATICS
PROPOSED BY MR. G. K. GILBERT.
Remarks on this communication were made by Mr. Gilbert.
Mr. C. H. Kummell gave the first part of a communication on
THE QUADRIC TRANSFORMATION OF ELLIPTIC INTEGRALS,
which was unfinished when the hour of adjournment arrived.
25
102 philosophical society of washington.
14th Meeting. May 7, 1884
The Chairman presided.
Nine members present.
In the absence of the Secretary, the minutes were read by Mr.
Christie.
Mr. Kummell finished the paper begun by him at last meeting on
THE QUADRIC TRANSFORMATION OF ELLIPTIC INTEGRALS,
COMBINED WITH THE ALGORITHM OF THE
ARITHMETICO-GEOMETRIC MEAN.
[Abstract.]
The algorithm of the arithmetico-geometric mean, so remarkable
for its symmetry and convenience, was first used by Gauss many
years before the brilliant era of Abel and Jacobi. The form which
the theory of elliptic functions assumed under the hands of these
eminent geometers, though extremely beautiful, might be improved
from a practical point of view by a combination with the Gaussian
algorithm. In the attempt to do this, the defects of the usual nota-
tion became very annoying, and gradually the new, simple, and
consistent system of notations, as used in the following, resulted
:
I assume for the type of an integral of the first species,
ad<p f ad<p/adcp /•
|
l/V — & sin V J i/V cos 2 <P + b2 sin V
d<p- f dcpC r C a< ,- (i)
J l/l - f sin V J l/cos V + /52 sin V
o o
For the inverse of this I write xi—y = <p. (2)
By (1) we have the modulus y = - and the complementary modu-
lus /?= - . The letters y and /? are used throughout as symbols for
c b
- and - , respectively, and are expressed in a, b, and c whenever
required.
MATHEMATICAL SECTION. 103
In the theory of elliptic functions, sin arm*, cos artm, A amw
(Jacobi's notation) or snw, cnu, dnw (Gudermann's notation), the
elliptic quadrant K (Jacobi) is the numerical unit of their period.
Consistency requires the use of the quadrant as a unit for trig-
onometric functions also. Let
_J denote a circular quadrant (ordi-
narily denoted -77-) ; then we have, by the notation just explained,
J
_\y(=K of Jacobi). (3)/y'\ — f sin V
The complementary integral then
J
'
VTJ f^; =J (-JP of Jacobi). (4)/;
If n is an integer, then, and only then, (n |)y= n \y. (5)
Thus we should be careful in distinguishing between integrals
such as
(i
J
V « f » , , and i Ay = 1 f ,, ^ . ,' J 1/ 1 — ^ sin V J 1/1 — ^ sin V
o o
According to the system of notation just explained, it is unneces-
sary to use the Jacobian am or the Gudermannian n, neither of
which define the functional relation completely, and we write simply
sin <p = sin xi—y (= sin amw of Jacobi or
snw of Gudermann)
cos <p = cos u—y (= cos amu of Jacobi or
cnu of Gudermann)
j/l — f sin V = A <? = A u-7 (= A am?« of Jacobi or
dmt of Gudermann) (6)
I remark that none of the usual notations indicate the modulus,
and a grave objection to Gudermann's is that it is apt to give the
impression that smt and enw are not an ordinary sine and cosine.
I shall now give in this notation a number of well-known relations,
of which use will be made hereafter. The theorem of addition is,
if u and v are two integrals to the modulus y,
104 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Sill (it ± V)—y = sin it_y COS V—y A V
—y ± sin Vry COS U—y A it_y
-s- 1 — f
2
sin 2w
_y sin v
—y
COS (it ±v)—y= COS W—y COS V—y + sin U—y A W_y sin V—y A V_y
-T- 1 — r
2
sin 2w_y sin i>_y
A (it ± i>)_y = A it_y Al)_y+f sin it_y COS it_y sin V—y COS i>_y
-f- 1 — f' sin
2it_y sin v—y (7)
We have sin (±
_J) = ± 1
cos (± J) =
A (± J) - fi (8)
therefore, replacing v by
_Jy, we have
COS U-y
A it_y
sin u—y
sin (tt ±
_Jy) =
cos (it ±
_Jy) = dz /5
'
A (it ±
_\y) =
A U—y
(9)A W_y
Replacing in these it by it d=
_]y, we have
sin (u ± 2 ]y) = — sin u—y
COS (it ± 2 \y) = — COS U—y
A (l* ± 2
_Jy) = A 1t_y (10)
It follows, replacing in these it by it -}- 2 |y, that 4 _]y is the
complete period of the elliptic sine and cosine and 2 \y that of the
delta.
Placing u = v, we have the duplication formulae
:
sin (2m)
—y = 2 sin u—y cos u-y a w_y -e- 1 — y2 sin 4W_y
COS (2lt) _y = COS 2M_y— sin 2W_y A 2it_y ~- 1 y2 sin *U—y
A (2it)
_y = a 2w_y—
y
2
sin 2it_y cos 2it_y -f- 1 — f~ sin Hl—y (11)
Replacing in these u by £ it and solving, we have the dimidia-
tion formulae
:
sin2 f
-jj-
J
-y = 1 — COS U-y -r- 1 + A W_y
COS2 (-^-J_y = A 1«_y -f" COS it_y -r- 1 -J- A it_
y
A 2 (jA-Y = A2 + A it_y+ y2 COSit_y -fl + A it_y (12)
MATHEMATICAL SECTION. 105
Jacobi's imaginary transformation consists in assuming
sin <p = i tan <p
1
or cos <p =
or
then
cos 4>
cos <p
v r D* ™ cos ^
A
«• - ^1 1/1 " ^ sin '<* -^ A W-r (13>
A<£>
"' J l/l— /
or
106 PHILOSOPHICAL SOCIETY OF WASHINGTON.
therefore, replacing in (16) v by
_J/j, we have
sin (u ± 1/3 i).Q = —
:
—
v
—
iH J H y sin u.y
A (w db
_J/3 i)_/3 = =i= t cot W_y (18)
Placing in these w ±
_J/3 -i for u, we have
sin (rt ± 2
_|/3 i)-y = sin u.y
cos (w db 2
_J/3 i)-y = — COS U.y
i(«±2J i)-7 = — A u.y (19)
It follows, replacing in these u by u ± 2
_J/3 i, that 4
_J/3 1 is
the imaginary period of the elliptic cosine and delta and 2
_)/3 i
that of the sine. We have then, if m and fi are integers,
sin (u -\- 4 m
_Jy + 2 // _J/3 i)-7 = sin w-7
cos (u + 4 m
_]y -j- 4 fi _J/3 t)_y = cos w_y
a (m + 2 m
_\7 + 4 /j _J/3 »)_7 = a «_y (20)
The general problem of transformation may be stated thus
:
Assuming
<P <f'
J yV - t sin V
=
J • *" - # sin V or7 *" rf y y (21)
o o
then it is required to discover the relations between the given quan-
tities <p, a, y arid <p', a', /.
Before treating of the special subject of this paper (the quadric
transformation), a short exposition of some important points of the
general problem of transformation, slightly modified from Abel
(see Enneper's Elliptische Functionen, page 239-246), will be
given.
We have, by (21),
sin <p = sin [^ <p'y J _y =/(sin^')=/| sin y~ <p7J -y j (22)
where / denotes the unknown relation between sin <p and sin <p'.
MATHEMATICAL SECTION. 107
But we have, by (20),
sin OV + 4 m' _]/ + 2 // J// 0-y'
therefore,
Oy + 4 m Jy + 2 /-i J^ i) J _/
108 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Solving for <p, we have
a sin 2<p' a tan <p
f
tan 9 =
c -4- a cos 2/ = a'— 6' tan V (30)
2a sin y' cos <p' a sin ^' cos <p'
8m
*
=
i/a2 + 2ae cos 2/ + c2
=
a' A / ( ^
cos
c + a cos 2/ 1 / 6' \
*= 2a' a/ =TVaA *-^7; (32)
^=i(a'A/ +^) (33)
where we have placed
J(a + e) = a'; *(« — <D=&';
Vac = c' ; l/a'2 - c'2 sin V = a' A / (34)
From (32) and (33) follows
a' A $/ = h (a A fo + c cos ?) (35)
-
—
7 = £ (a a <p — c cos p) (36)
and (29) becomes 7TTZ = vTT7 (3 <0vy aA^aA^o v/
the integral is — <py= —} <p'y (38)
The first and third formula of (34) give the first step in the
algorithm of the arithmetico-geometric mean, and the first two fol-
low from (35) and (36) by placing <p = = <p', i. e., they are rela-
tions at the lower limit of the integrals, corresponding to (35)
and (36).
Assuming sin (2<p" — <p') = —7 sin <p' (28')
a" = h(a! + tf) ;b"=h (a' - c') ; c" = \/dl (34')
then we have — fy =—-, <p'y == -77 <p"y" (38')
Proceeding in this manner the amplitudes will very rapidly
reach a limit f^, while simultaneously a and c tend to become
equal to their common limit, the arithmetico-geometric mean of a
and c. Gauss, when investigating its functional properties, denotes
MATHEMATICAL SECTION. 109
this by M (a, c) ; elsewhere he uses the notation a(o°) or c(°°), which
is sufficiently distinct for our purpose.
At the limit we have a(°°) a ^(°°) = c(*) cos <p^°°\ therefore,
("/«-)t!r^) = ^> tan * <J + y(",)) (38M>
o
Let ? = J then ?'=_]'; 9" — J" . . . . ?<"> = _]<"> and111 1
_ I _
\r / ±_ |W // t I (00)
(=^)tanHJ + J(oo))) (39<->)
This transformation can be applied also to the more general form
:
9
Jdcp
—^f (sin 9, cos <p, a <p) (40)
o
for if, simultaneously to the above algorithm, we express sin <p, cos <p,
A <p in terms of sin <p', cos ¥>', A <p\ and these again in terms of
sin <p", cos ?>", A p", etc., by means of (31), (32), (33), we arrive,
after a few transformations, at the form
p(»)
J=/c(4osV> /(C0) <sin^ C0S^ <41)
o
which is an elementary form if / (sin <p, cos <p, A <p) is rational
with respect to sin <p, cos ^, A <p.
In tracing this process backwards, the quantities may be dis-
tinguished at the several steps by subprimes, so that we have, at
the first backward step,
sin (2<p — ?,) =
—
' sin <p
t
= ^j sin <p, (28,)
a = \ (a, + <0 ; 6 = i (a, — c,) ; c — j/o/ c, (34,)
Adding, and then also subtracting, sin <p
t
from (28,) and dividing
the difference by the sum, we have the following convenient for-
mula, also given by Legendre
:
tan (<p l — <p) = — tan <p (42)
110 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Solving (34,) for a/} bn c„ we have
a, = a 4- b ; b4 =2 }/ab ; c, = a — b
In order to have again the convenient algorithm of the arith-
metico-geometric mean, it is preferable to assume
a, = * a, = i (a + 6); 6 X = J 6, = l/o^ — i 0,= *(o— 6) (43)
For the second step assume
tan (>„ — ft) = -1 tan ?, (42x)
We have then — <py = <^- (?,)yi = ^ (?//)ya (44J
Continuing this process, which diminishes the modulus, and is
therefore called descending the scale of moduli, while the above is
called ascending, the a and b will rapidly approach their arithmetico-
geometric mean, a„ = b a , while ~nn <P{.n) tends towards a limit
which I shall denote </>„>. The limiting form of the integral is
S
d<p(<x,) <Pc
2°°&oo
—
6 C
o
and we have
\ r, -^4,^ = • • • • 2^r„ <*->. (-1: ^44(0O))
i i
If p = J then i ?, = -^ <p„ = . . . ^r ?(«) =...= _)
and we have
| J,- ^ Jr. -iJ»- i- J. (-£-> <"<->>
This remarkable value for the complete integral was discovered
by Gauss by means of a different transformation, known as Gauss'.
This may be deduced as follows : Assume in place of (44(°°)) the
following series of relations
\*t-\w* - \ to*= • • • • h (W° (= k ** (44 "}
MATHEMATICAL SECTION. Ill
To discover the relations for the first step we have to determine
<pt from the equations
(^1)71 =K^1 = JJfy (46)
Place in (12) u =(f>,)yv then & u = (^)n and u.7l = ?y ;^ J _7l
= ^1? and consequently
sin V'i = 1 — cos ^ -f- 1 + A <pt
COS Vi = A P/ + cos $pv -^ 1 -f A ^
a Vx = iV + a 9l + ril COS <p, H- 1 + ^ <P, (47)
From (32) and (33) we derive with due regard to (43)
o, A ^ = J (a A +
—J
<i A ?/ = i (a a 9 - —
)
(48)
and eliminating <p
t
from (47) by means of (48) there result the
relations
«i 1 — A P
sin Vi =— • i
—
r~i
—
T1
c
x
1 + A
2f
aA <p — b
COS
^-^(I + a,,)
a A (p -4- b
whence also
a sin <p,
sin <p = 1 ;—07-T
«
x + Cl Sln V^
a
a
cos 4\ A ^x
cos <p = —
;
=
—
rrT
a
x + ex sin Vx
a, — c, sin Vi ,_,^
This is Gauss' transformation. For practical use it is far less
convenient than that given above.
Instead of (46) we might have assumed -
m (^1)71 = n (^/)yi = 2w r~ <Py (jn, and n integers) (51)
For any special values of m and n we can express, by means of
112 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the addition theorem, the elliptic functions of {m C^)^} -yl in terms
of those of V and in the same manner those of -[w {?i)y\} -7i in
terms of those of <pr Since we know <p in terms of <p,, we can elimi-
nate <Pj and obtain a relation between 6X and <p, which would be a
new transformation. However, we need not expect to discover in
this manner any substitution sufficiently simple for practical use.
The substitutions given above may of course be applied also to
the complementary integral, and, since interesting relations will
be thus discovered, I place the different series of forms together for
comparison.
\ <?r - 7 fV = yfV = = ^j^(oo)
(-.§5yJtan*(J + ?<*>)
( Woo
-"i to/n-^to)*- -£(*->•
(
= ^ 0. (52y)
-j-^
—
^(ft)A"^to)A- =^ (^^
(
= r-/tan £ (J + 9»)
Woo
-s; fr-o^-yyCfJr.- =^ lim ^r
( c(°°) ^
4w = i-^v= =^)<".( "'a ^ a
(
=^(oo) (52/3)
i
i p > L i" " — - I (»>
MATHEMATICAL SECTION. 113
(
= ^tani(J + JO)
(
= r-/tani(J+ J.)Woo
—^JflT-^J^- =^J (53/5)
We easily deduce the symmetrical relations
?1(») (^X = ^oo 0(») (54)
Ji (fle) (J-)i« J2 (55)
This last equation is well known ; it appears here, however, as a
particular case of a more general relation. The quantity ^oo is the
argument of the functions and then usually denoted x\ ^>1 ( cc ) is
v v'
then denoted by x' ; Schellbach has -^ for ( loo)! and ~n for I/ 00),
while Hoiiel, in his Recueil de Tables, has p and p', respectively.
Other relations are
yt
(x)
_
<K ^2 _ ^ ^(cc)2 _ yi(00) ^ _ ^oo2 fKas
Jx(<B)~j ; J ~U«)i ; Jl«->" J "(J-X ^^
(M l (flB) fcOi_^_l fr-V (M^"» i''(oc)2 ™
CJ-X" J ' J ~ -Ji(0O); (J»)i"~ J "J-J ( 7)
The following expressions for the nome q can now be given
:
? = e
-2^J
=e -2(J„),
The first form is simply Jacobi's definition ; the second gives,
S1D.CG
(J K) 1 = hanHJ + J») (59)
g = cot
2
J (J + Joo) (60)
This is one of the best formulas for computing q, especially if the
modulus does not differ much from unity. The third form may be
114 PHILOSOPHICAL SOCIETY OF WASHINGTON.
used if b and c are not very different, for in that case the algorithm
of the arithmetico-geometric mean converges equally fast in both
directions. If either b or c is very near to a, the process may con-
verge in one direction so slowly that the formula becomes nearly
inapplicable.
The fourth form may be transformed to a new formula, which is
more convenient than any given. In (52/?) place <p = 2n _], then,
since
9X - 2"-' J j f, - 2—2 J ; <ps = 2«-3 j
9n=
_|; 9n + l = (2' i _J)n + l ....
we have
2 rt 2"- 1 2"~ 2
But we have by (28) sin (2(2„ j)„ + i — j)= — sin J
or 2 sin 2 (2" j)„ + i — 1 = —
(In
(61)
.•.sin(2»j)n + 1 =^j(i +M
If we suppose an= bn = b x within the precision of the compu-
tation, cn will be very small, yet not zero. We have then
5= J fin = ^T7"l ^2" J)" + l }fi» + 1
L_/ J 1 +sin(2w J)w + 1
"on + i \l-sin(2»' J)n + i
Ctn + 1
V 1+V*(*+£)
MATHEMATICAL SECTION. 115
1 +
1
I
M*+$)
Q>n + 1
*»*-£)
*- ' l/*(«»-6-) (sufficien% near>
_. _L j 2
2 y^ gn + t (
sufficiently near)
1 22 a,,
= r— / —
—
(sufficiently near) (62)
therefore we have by (61)
1 2~» . 22 an
or
6.
,
/22 a„\2-"
r-Jf-'A—
)
since cn = £ (a„_i — 6 n_i) = ?£—
ii Ctn
V C
z
n-2 / \ C„_2 /
if a„_i = i/a„ an-x
\ C n-3 / \ C„-3 /
if a„_2= y ' an_1 a#j_2
if «
2 = l/ a3 a2 (63)
if Cl = T/ a2 ^ (64)
116 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Using (63) in the fourth form of (58) we have
Cj a— b
and using (64) we have
«
- Gftr)' w
The norae of the complementary integral is denoted by Jacobi
and writers that follow him by q
1
. In our system this would be
the notation for the nome of the integral <p'y
;
q" that for <p"y", etc
;
also qx that of (^j)^ ; q2 of {<P^)y2 , etc. It is therefore better to
follow the example of Broch, who denotes the nome of the com-
plementary integral by p. We have then
-2-JjJ -2J X(») -2^Jp = e _J/S = e = e b<»
= cot2 J (J + J<«>) = |^rC= (^)
2
(67)
where o(**-1 ) = j/ aW a (n_1 )
a("-2) = j/ « n-i a n~2
a (»—3) = |/ a n-2 a »—
3
= l/ a'" a"
«' = i/ «" of (68)
By (55) and the second forms of (58) and (67) we have the
following relation between p and q
lp-'Alq-y2=_f (69)
or in Briggian logarithms
log { log p-V* log q-y*}= log (J log ej = 9.6678084 (69')
or logjlogp"1 log q-1 }= 0.2698684 (70)
By means of this relation we can always choose the shortest
route to either p or q. It is easy to see that the nomes and com-
MATHEMATICAL SECTION. 117
plementary nomes at the several steps of the modular scale are as
follows
2—2 2~1
<7n
2-n
q =q; tf = <f; f
= 9
»(») =
2"
(71)
2>n = i>
2"
^ ; p x =tf \ p=p; p =p*;p"
2-2
_M .2-»
i? j)<") = j>" (72)
We have then in this transformation the simplest possible case
of Abel's theorem (27) ; and because in ascending we pass to the
square of the nome, it is called the quadric transformation.
The ascending transformation is possible in real quantities if
c > a, for we have M{c, a) = M(a, c). Also if b > a we can use
the descending transformation ; and in either case we can, after
one transformation, proceed in either direction. This may be
symbolized by the following diagram
V > e"
«
118 PHILOSOPHICAL SOCIETY OF WASHINGTON.
CO CO
MATHEMATICAL SECTION. 119
T3
O
be
120 PHILOSOPHICAL SOCIETY OF WASHINGTON.
GO
a
o
to
O
o
be
.3
1=1
bO
t—I CO
-+1 o
CO CO
OS os
OO H
co ia
o OS
O
.
03
*» '
bC -
o S>-
bfl
o oO GO
o os'O iO
o -*O O)
oO iO
t- CO
&- s-
o
MATHEMATICAL SECTION. 121
H3
p
y*
I'l'l PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Hall spoke of the importance of the arithmetico-geometric
mean in astronomy.
Mr. W. B. Taylor made a communication on
A CASIO OF DISCONTINUITY IN ELLIPTIC ORBITS '
around an empty center of gravitative force. Diminution of the
minor axis of the attracted hody's path (the major axis being con-
stant) increases the ratio of distance at the two apses without limit,
the "periapsis" continually approaching the attractive center,
as long as the minor axis has a value, however small. But when
this axis is made to vanish, and the motion is directly to the center
of force, the body, instead of rebounding from it, as continuity
would require, will pass through it, and describe an equal path on
the opposite side, the orbit being at once doubled.
This paper was discussed by Messrs. Bates, Christie, Hall
and others, and brought out a wide diversity of view as to the
demeanor of a heavy point when coincident with an empty attract-
ing center.
15th Meeting. December 3, 1884.
The Chairman presided.
Nineteen members and guests present.
Mr. M. H. DOOLITTLE made a communication on
THE VERIFICATION OF PREDICTIONS.
[Abstract.]
Mr. G. K. Gilbert has published (American Meteorological
Journal, 8°, Detroit; September, 1884, pp. 160-172) a method of
estimating the ratio of skill in predictions of occurrences and non-
occurrences of a simple event. Adopting his notation, we have
8 = the sum or total number of cases,
o = the number of occurrences,
p = the number of predictions of occurrences,
MATHEMATICAL SECTION. 123
c = the number of coincidences or verifications,
i = the inference-ratio, or that part of the success which is due to
skill and not to chance, and which may be called the degree
of logical connection between event and prediction.
Since success is proportional to each of the two fractions
— and —
>
o p
it may be represented by their product
c?_
op'
The fraction — represents the ratio of random success, and
op
therefore — verifications out of p predictions are to be ascribed
to chance and must be subtracted throughout. The remainders,
op . op
o — — and p — —
»
S r 8
represent fields which chance leaves for science to conquer ; and
op
c —
—
s
represents the portion of each which science does conquer. Hence
op op
. £_ ^
* . Q — op)2
l
~
-?p v -?p
==
oP(s-oXs-py
s
F
s
By another method,
— = the probability that any single occurrence will be predicted
in some manner.
*—^2— = the probability that any single date of non-occurrence
will correspond to an unsuccessful prediction = the general
probability of unskillful prediction in any case.
Subtract from the probability that any single occurrence will be
predicted in some manner the general probability of unskillful
prediction, and we have
= the probability that any given occurrence will be
skillfully predicted.
124 PHILOSOPHICAL SOCIETY OF WASHINGTON.
In like manner
— = the probability that any single prediction will be fulfilled
in some manner.
"~— c
= the general probability of unpredicted occurrence; which,
in case of prediction, becomes probability of fortuitous ful-
fillment.
(* Q mmmm f
= the probability that any single prediction will be
fulfilled by reason of a logical connection.
Since the skillful predictions are mingled indistinguishably with
all the unskillful ones, and are vitiated accordingly, the value of
the vitiated probability of the skillful prediction of any single
occurrence may be represented by the product
f c p — c\ f c o — c\ (cs — op) 2
\ o ~ s — o) \p ~~ s— p) ~ op(s — o){8 — p)'
as before.
Prof. C. S. Peirce (in Science, 1884, Nov. 14, Vol. IV, page 453)
deduces the first of these factors as the unqualified value of i,
making no allowance for the vitiation, and tacitly assuming that
an assortment of predictions is the logical equivalent of a jumble
of the same predictions. He obtains his result by the aid of the
supposition that part of the predictions are made by an infallible
prophet, and the others by a man ignorant of the future. If Prof.
Peirce had called on omnipotence instead of omniscience, and sup-
posed the predictions to have been obtained from a Djinn careful to
fulfill a portion of them corresponding to the data, the remainder
of the occurrences being produced by an unknown Djinn at ran-
dom, he would have obtained by parallel reasoning the second
— —
—^—
J
. These Djinns represent, respectively, the
known and unknown forces of nature, and gauge the prophet's
knowledge with principal reference to the proportion of predictions
fulfilled. Prof. Peirce's test refers principally to the proportion of
occurrences predicted. His test eliminates sins of omission ; the
other, sins of commission ; and both are necessary to a proper
estimate of the prophet's comparative rectitude.
MATHEMATICAL SECTION. 125
In the data cited by Mr. Gilbert from Finley's tornado predic-
tions, s = 2803, o = 51, p = 100, and c = 28. By Mr. Gilbert's
formula,
cs — op
A H —
—
8 (° + p — c) -• °p
he obtains
Prof. Peirce obtains
I obtain
i = .216.
i = .523.
i = .142.
By making 8, o, and i constant, and imposing conditions on p and
c, we may obtain hypothetical data involving equal skill. Putting
c = p, I infer that Mr. Finley would have manifested equal skill if
he had made no false predictions of tornadoes, and, out of the 51,
had predicted 7.35. Mr. Gilbert's formula gives 11.18, and Prof
Peirce's 26.67. Putting c = o, I infer that he would also have
manifested equal skill if he had included all the 51 tornadoes by
making 323.7 predictions. Mr. Gilbert's formula gives 221.5, and
Prof. Peirce's 1364.
Mr. Finley's entire success in predicting tornadoes is
— =.154;
op '
and since the portion due to skill = .142, we may infer that .923
of this success is due to skill, and only .077 to chance. On the
other hand, of his success in predicting the non-occurrence of tor-
nadoes, only .147 is due to skill, and .853 is due to chance.
Prophecy and fulfillment are effects of a common cause. Neither
causes the other. The problem, broadly stated, requires a nume-
rical expression for the causal relation between two classes of phe-
nomena either in co-existence or in sequence, when the presence of
one corresponds sometimes to the presence and sometimes to the
absence of the other, and sometimes both are absent. In case of
sequence it is immaterial which is antecedent. The quantities de-
noted by o and p should therefore be interchangeable.
My formula responds properly to every test proposed by Mr.
Gilbert. The value of i increases rapidly with that of c, and
126 PHILOSOPHICAL SOCIETY OF WASHINGTON.
slowly with that of s, diminishes with increase of o or p, and varies
between the limits and 1. Skill in making false predictions is
indicated by a negative value of cs — op; but the same degree of
causal relation exists as when equal skill is employed in making
true predictions ; and a negative value of i can never occur. When
s = either p or o, i = -rp but the apparent indeterminateness van-
ishes when we consider that i is the product of two factors, of which
one = and the other is indeterminate within limits. And the
value of i is unaltered when predictions of non-occurrences are
substituted for those of occurrences, and vice versa. In the latter
case, write s — o for o, s — p for p, and s — o — p + c for c ; and
the formula reduces to its original form.
In addition to Mr. Gilbert's tests, two others may be considered.
In the case of predictions all falsely reported, we may write s — p
for p and o — c for c ; and the formula becomes
(op — cs) 2
op (s — o) (s — py
with a proper reversal of signs in the quantity under the exponent
and no change in the value of i.
If occurrences always appear whenever they are not predicted,
and never appear when they are predicted, we put e — and
p= s — o, with the result
i= l;
or the logical connection is perfect.
In order that the general formula shall be properly applicable,
care must be taken that the predictions are fairly homogeneous in
definiteness of time and space. For illustration : if predictions
that phenomena will occur in given months are examined indis-
criminately with those that they will occur on given days, the result
will be manifestly worthless.
It has been proposed to extend the problem so as to include three
or more classes of events of which one must happen and only one
can happen in any case. It seems clear to me that no single
numerical expression can be a proper solution of such a problem.
Suppose the three classes of events, A, B, and C. By the method
above given A and Not A may be examined ; and all instances
MATHEMATICAL SECTION. 127
involving either the prediction or occurrence of A may be excluded
and B and C separately investigated. Suppose it thus ascertained
that great skill has been shown in discriminating between A and
Not A, and little or none in discriminating between B and C. No
single numerical expression can properly comprehend these heter-
ogeneous results.
Mr. Curtis showed that some of the results given by Mr. Doo-
little could be independently deduced by another method.
Mr. Gilbert noted as a defect in the formula proposed by Prof.
Peirce, that it did not duly discourage positive predictions of rare
events ; and, while gratified with Mr. Doolittle's discussion of the
subject, he expressed a disappointment that no satisfactory decision
as to the treatment of cases of three or more alternatives had been
reached by him.
After some further discussion, a communication by Mr. M.
Baker was called, but postponed, on motion of Mr. H. Farquhar,
to allow time for the consideration of a testimonial to a late asso-
ciate, Mr. Alvord.
Mr. E. B. Elliott read the following tribute, prepared by Mr.
Baker and himself:
MEMOEIAL.
The Mathematical Section of the Philosophical Society of Wash-
ington, having suffered the loss by death, on October 16th, 1884, of
General Benjamin Alvord, one of its founders and active workers,
desires to place on record this testimonial to his worth and to the
loss to this Section and to science by his death.
Of his worth, one of America's greatest mathematicians has said
that he was a scientist of " real originality who had actually ex-
tended the boundaries of science."
The bent of General Alvord's mind and studies was early
directed towards a purely geometrical solution of the general prob-
lem of tangencies, and his reward, which it is our pleasure to
chronicle, was success.
Of his mathematical publications, the following is submitted as
a provisionally complete list
:
128 PHILOSOPHICAL SOCIETY OF WASHINGTON.
LIST OF MATHEMATICAL PUBLICATIONS BY GENERAL BENJAMIN
ALVORD.
1. The tangencies of circles and of spheres.
[In Smithsonian Contributions to Knowledge. 4°. Wash-
ington, 1856, Vol. 8, Article 4, 16 pp., 9 plates.]
Also issued separately.
2. On the interpretation of imaginary roots in questions of maxima
and minima.
[In The Mathematical Monthly. 4°. New York, 1860,
April, Vol. 2, No. 7, pp. 237-240.]
3. Tangencies.
[In Johnson's New Universal Cyclopaedia. 8°. New York,
1878, Vol. 4, pp. 723-4.]
4. Mortality in each year among the officers of the army for fifty
years, from 1824 to 1873, as derived from the army
registers.
[In Proceedings of the American Association for the Ad-
vancement of Science, 23d Meeting, Hartford, August,
1874. 8°. Salem, 1875, pp. 57-59.]
5. The intersection of circles and the intersection of spheres.
[In American Journal of Mathematics. 4°. Baltimore,
1882, March, Vol. 5, No. 1, pp. 25-44; 4 plates.]
6. Curious fallacy as to the theory of gravitation.
[In Bulletin of the Philosophical Society of Washington.
8°. Washington, 1883, Vol. 5, pp. 85-88.]
7. A special case in maxima and minima.
[In Bulletin of the Philosophical Society of Washington.
8°. Washington, 1884, Vol. 6, p. 149.]
Mr. M. Baker, in moving the adoption of this memorial by the
Section, said
:
General Alvord's entire life was that of the soldier, and his
routine of life work did not call him in the direction of mathemati-
cal study. Hence whatever he accomplished in mathematics or
literature was accomplished in military surroundings and with only
such facilities as barrack and camp life afford. If under these
MATHEMATICAL SECTION. 129
conditions the total of his contributions to science appears small,
we should bear in mind that any contribution under such circum-
stances is exceptional. And to have been able, therefore, to make
even a single contribution to human knowledge is to have done that
which few men in any generation do aud that of which any one of
us might well be proud.
General Alvord early became interested in the problem of tan-
gencies and intersections of circles, and his chief mathematical
work and fame rests on his complete and purely geometrical solu-
tion of the various problems relating to this subject. His chief
writings on this subject consist of the paper on Tangencies, in the
Smithsonian Contributions in 1856 ; the article on Tangencies, in
Johnson's New Universal Cyclopaedia ; and the paper on intersec-
tions, in the American Journal of Mathematics, March, 1882.
The memorial was adopted, and the Secretary was instructed to
send a copy of it to the family of the deceased.
Note.
The following members have assisted the Chairman and Secre-
tary in the examination of abstracts of communications to the
Mathematical Section
:
Title. Author. Third Member.
The Problem of the Knight's Tour. G. K. Gilbert. E. B. Elliott.
Formulas for Diminution of Ampli-
tude of a Pendulum H. Farquhae. A. S. Christie.
The Formulas for Computing the
Position of a Satellite A. Hall. C. H. Kummell.
The Quadric Transformation of El-
liptic Integrals C. H. Kummell. G. W. Hill.
The Verification of Predictions M. H. Doolittlb. M. Baker,

INDEX.
Page.
Abbe, Cleveland : remarks on deflection of
rivers 23
— report as Treasurer xxiv
Address of the President xxix, 81
Alaska river mouths 24
Alvord, Gen. Benjamin, Death of 72
— Memorial to 127
Antisell, Thomas: remarks on the chemical
elements 16
pumice 20, 26
Annual address xxix, 81
— meeting 81
Application of physical methods to intellec-
tual science 18
Are there separate centres for lipht- form-
and color-perception? 72
Aristotle, cited on atoms xxxii
Atomic philosophy 40
The, physical and metaphysical. ...xxix, 81
Auditing committee, Appointment of. 82
Report of 15
Babcock, Gen. O. E., Death of. 72
Bacon, cited on atoms xli
Baker, Blarcus: memorial to General Alvord.. 127
Barnard, W. S., Election to membership of.. 25
Bates, H. H. : communication on the physi-
cal basis of phenomena 40
Bean, T. H., Election to membership of. 72
Bibliography of North American geology 71
mathematical papers by Benjamin Al-
vord 128
Billings, J. S.: communication on compos-
ite photography applied to craniology... 25
— exhibition of microscopes 73
— remarks on bibliography 72
— resolutions on the death of Dr. Wood-
ward 75
Blair, H. \V., Death of. 81
— Election to membership of. 15
Bog-isloff, Volcanic dust from 34
Bout.elle, C. E., Election to membership of... 18
— remarks on the deflection of rivers 24
Bowles, F. T., Election to membership of..... 26
Boyle, Robert, cited on atoms xlvi
Brown, S. J., Election to membership of 72
Browne, W. R., cited on matter 31
Bulletin of the General Meeting 1, 3
Mathematical Section 83, 87
— Rules for publication of xiii
Page.
Buoys drifted by ocean currents 14
Burchard, H. C. : remarks on the irrigation
of the upper Missouri valley 20
Burnett, S. M. : communication on separate
centres for light- form- and color-percep-
tion 72
Why the eyes of animals shine in
the dark 13
Calendar xxii
Case of discontinuity in elliptic orbits 122
Chamberlin, T. C. : communication on What
is a glacier? 38
Chatard, T. M. : analysis of andesite 33
Chemical elements and music 27
Periodic law of 15
Cheyne, Dr. George, cited on heredity lv
Christie, A. S.: communication on a form of
the multinominal theorem 101
Clarke, F. W.: communication on the peri-
odic law of chemical elements.. 15
— election to Genera! Committee 36
Clerk-Maxwell, James, cited on properties
of matter 44, 47
vortex rings Hv
Clifford, Prof., cited on mind-stuff. liii
Columbian University affords the Society
facilities 80,81
Committee, Auditing 15, 82
— on communications, Duties of xii, 85
Membership of xiv, xv
publications, Duties of. xiii
Membership of. xiv, xv
Committees, Standing xii, xiv, xv
Composite photography applied to craniolo-
gy 25
Concrete problem in hydrostatics 92, 101
Constitution vii
Continents, Forms of 24
Craniology 25
Curtis, G. E : communication on the rela-
tions between northers and magnetic
disturbances at Havana 25
— election to membership 5
— remarks on the verification of predic-
tions 127
Curves similar to their evolutes 87
Dall, W. H. : communication on certain ap-
pendages of the mollusca 32
131
132 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Dall, W. H. : recent advances in our knowl-
edge of the limpets 4
What is a glacier ? 38
— remarks on Alaskan volcanoes 34
deflection of rivers 24
drifting of buoys 16
tornadoes 3
Dalton, John, contribution to atomic the-
ory xlvii, 1, lvi
Darwin, cited on gemmules liii
Death of Gen. Benjamin Alvord 72, 127
Gen. O. E. Babcock 72
H. W. Blair 81
Gen. Chas. Ewing xxiii
Gen. A. A. Humphreys 3, 4
Dr. J. J. Woodward 72
Resolutions concerning 75
Deceased members, List of. xxiii
Deflection of rivers 21
Deposits of volcanic dust in the Great Basin. 18
Dewey, P. P., Election to membership of..... 36
DiKer, J. S. : communication on the volcanic
sand which fell at UnalashkaOct. 20,1883,
and some considerations concerning its
composition .33, 35
— Election to membership of 21
Discontinuity in elliptic orbits 122
Discussion of a concrete problem in hydro-
statics proposed by Mr. G. K. Gilbert.-... 101
Diversion of water-courses by the rotation
of the earth 21
Doolittle, M. H.: communication on the
verification of predictions 122
music and the chemical elements.... 27
Dust, Volcanic 18,33
Dutton, C. E. : communication on the volca-
noes and lava fields of New Mexico 76
What is a glacier? 39
— remarks on the forms of continents 24
Navajos as scientific observers 74
r petrography 36
sun-glows 35
Earll, R. E., Election to membership of 72
Earthquake of Sept. 19 73
Eastman, J. R. : communication on a new
meteorite 32
the Rochester (Minn ) tornado 3
Eimbeck, William, Election to membership
of 26
Election of officers 82, 87
new members.... xi, 5, 10, 15, 18, 21, 25, 26, 32
36, 72, 81
Electric lighting 80
Elements, Periodic law of. 15
Elliott, E. B. : calendar for the use of the
society xxii
Page.
Elliott, E. B.: communication on electric
lighting 80
— memorial to General Alvord 127
— remarks on the euharmonic organ 28
irrigation of the upper Missouri
valley 20
sun-glows 17
tornadoes 3
Emmons, S. P.: communication on What is
a glacier? 37
— remarks on glaciers 9
Empirical formulae for the diminution of
amplitude of a freely-oscillating pendu-
lum 89
Entomology, Economic 10
Euharmonic organ 28
Ewing, Charles, Death of. xxiii
Existing glaciers of the High Sierra of Cali-
fornia 5
Eyes of animals, why they shine in the
dark 13
Faraday cited on the nature of matter 47
Farquhar, Edward : remarks on ocean cur-
rents 24
tornadoes 3
the late Dr. Woodward 76
Farquhar, Henry: communication on em-
pirical formulae for the diminution of
amplitude of a freely-oscillating pendu-
lum 89
the theoretical discussion in Prof. P.
G.Tait's Encyclopaedia Britannica article
on mechanics 29
— election as Secretary of the Mathemati-
cal Section 87
— remarks on drifting of buoys 15
— report as Secretary xxiii
Ferrel, William, cited on rotational deflec-
tion 22
Finley's tornado predictions 125
Fisheries exhibitions 26
Force, Reality of 30
Form of the multinominal theorem 101
Formula for the length of a seconds-pen-
dulum 101
Formulae for computing the position of a
satellite 93
General Meeting, Bulletin of 1, 3
Geological section of water-works shaft 69, 70
Gihon, A. L. : remarks on the late Dr. J. J.
Woodward 76
Gilbert, G. K. : communication on a concrete
problem in hydrostatics 92
the diversion of water-courses by the
rotation of the earth 21
INDEX. 133
Gilbert, G. K. : a plan for the subject biblio-
graphy of North American geologic lite-
rature 71
the problem of the knight's tour 88
— remarks on the origin of pumice 25
upper Missouri valley 20
verification of predictions 127
— report as secretary xxiii
Glacier tables 7
Glacier, What is a 37
Glaciers of the Coast Range 8
High Sierra 5
Rocky Mountains 8
Goode, G. Brown: communication on fish-
eries exhibitions 26
Gregory, J. M., Election to membership of... 26
Hall, Asaph : communication on the form-
ulae for computing the position of a
satellite 93
— election as chairman of the Mathemati-
cal Section 87
— remarks on the arithmetico-geometric
mean 122
Harkness, William : remarks on glaciers 9
the shining of eyes in the dark 13
Hazen, H. A.: communication on the sun-
glows 17
thermometer exposure 80
— remarks on the deflection of rivers 24
Heap, D. P., Election to membership of. 32
High Sierra, Glaciers of 5
Hill, G. W. : communication on a formula
for the length of a seconds-pendulum... 101
Hitchcock, Prof. C. H 4
Hitchcock, Romyn, Election to membership
of 36
Holmes, W. H. : remarks on glaciers 8
Humphreys, A. A., Death of. 3, 4
Ice pyramid 6, 7
Indians, Observation and generalization by. 73
Insecticides 10
Integrals, Transformation of elliptic 102
Intrinsic equation 87
Irrigation of the upper Missouri valley 20
Jenkins, T. A.: remarks on drifting of
buoys 15
Johnson, A. B. : communication on some
eccentricities of ocean currents 14
Johnson, W. D., Election to membership of... 18
Kauffmann, S. H., Election to membership
of 21
Kerr, W. C. : communication on the mica
mines of North Carolina 9
27
Page.
Kerr, M. B., Election to membership of. 21
— remarks on glaciers 8
Knight's tour 88
Knox, J. J. : resignation from General Com-
mittee 36
Kummell, C. H. : communication on curves
similar to their evolutes 87
the quadric transformation of ellip-
tic integrals, combined with the algo-
rithm of the arithmetieo-geometrical
mean 102
— remarks on musical intervals 28
Lake Bonneville 92
Lawrence, William, Election to member-
ship of. 21
Lefavour, E. B. : remarks on musical scales. 28
Leibnitz, cited on atoms xliii
Limpets 4
McGee, W J : communication on What is a
glacier ? 38
Maher, J. A.: Election to membership of 26
Marcou, J. B., Election to membership of.... 26
Martin, Artemas: letter to Mathematical
Section 87
Mason, O. T. : remarks on the conditions of
observation 74
Mathematical Section, Bulletin of 83, 87
Members of 86
Officers of. 86, 87
— society proposed 87
Matthews, Washington : communication on
natural naturalists 73
— election to membership 72
Members, List of xvi
deceased, xxiii
new '. xxiii
— of Mathematical Section 86
Memorial to General Alvord 127
Merrill, G. P., Election to membership of.... 36
Meteorite 32
Methods of modern petrography 36
Mica mines of North Carolina 9
More, Henry, cited on nature of matter xlii
Mount Taylor, Geology of. 77
Muir, John, cited on glaciers 8
Murdoch, John, Election to membership of. 36
Music and the chemical elements 27
Mussey, R. D. : communication on the appli-
cation of physical methods to intellec-
tual science .'. 18
— remarks on the forms of continents 24
Natural naturalists 73
Necks, Volcanic 78
Neve denned 37
134 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Page.
New members xxiii
— meteorite 32
— Mexico, Volcanoes of. 76
Newton, cited on atoms xliv
Norris, Basil, Election to membership of 25
North Carolina, Mica mines of 9
Ocean currents 14
Officers, Election of 82, 87
— List of. xiv, xv
— of the Mathematical Section 85, 86, 87
Ogden, H. G., Election to membership of..... 15
Paul, H. M. : remarks on earthquakes 73
equipotential surfaces 92
sun-glows 35
Peirce, Prof. Benjamin, cited on the intrinsic
equation 87
Peirce, C. S., cited on pendulum observa-
tions 90
the verification of predictions 124
Pendulum, Formula for diminution of am-
plitude of oscillation of. 89
Periodic law of chemical elements 15
Petrographic methods 36
Physical basis of phenomena 40
— and economic features of the upper Mis-
souri system 20
Plan for the subject bibliography of North
American geologic literature 71
Plateau country 76, 79
Powell, J. W. : communication on a plan for
the subject bibliography of North Amer-
ican geologic literature 71
— remarks on the distribution of eruptions. 79
glaciers 8
the history of the society 81
late Dr. Woodward 76
Predictions, Verification of 122
Presidential address xxix
Problem of the knight's tour 88
Pumice, Formation of. 20, 25, 26
Quadric transformation of elliptic integrals,
combined with the algorithm of the
arithmetico-geometric mean 102
Ray, P. H., Election to membership of 5
Recent advances in economic entomology... 10
our knowledge of the limpets 4
Relation between northers and magnetic
disturbances at Havana 25
Report of secretaries xxiii, 82
treasurer xxiv, 15,82
Review of the theoretical discussion of Prof.
P. G. Tait's Encyclepaedia Britannica
article on mechanics 29
Page.
Ricksecker, Eugene, Election to member-
ship of. 18
Riley, C. V.: communication on recent ad-
vances in economic entomology 10
— remarks on the irrigation of the upper
Missouri valley 20
Rivers, deflection of 21
Robinson, Thomas : communication entitled
Was the earthquake of Sept. 19 felt in
the District of Columbia? 73
on the strata exposed in the east shaft
of the water-works extension 69
— election to membership 10
— remarks on the deflection of rivers 24
Rochester (Minn.) tornado 3
Rotation and rivers 21
Rules for the publication of the Bulletin.... xiii
— of the General Committee xii
Mathematical Section 85
Society ix
Russell, I. C. : communication on deposits
of volcanic dust in the Great Basin 18
the existing glaciers of the High
Sierra of California 5
What is a glacier? 37
Sand, Volcanic 33
Satellite, Computation of position of a 93
Scales, Musical 27
Secretaries' report xxiii, 82
Sierra Nevada glaciers 5
Some eccentricities of ocean currents 14
Standing rules of the General Committee xii
Mathematical Section 85
Society ix
Stearns, R. E. C, Election to membership of. 81
Strata exposed in the east shaft of the
water-works extension, 69
Sun-glows 17, 35
Tait, Prof. P. G., on mechanics ; reviewed.... 29
Taylor, F. W. : analysis of meteorite 32
Taylor, W. B. : communication on a case of
discontinuity in elliptic orbits 122
— remarks on sun-glows 35
Thermometer exposure 80
Thompson, Gilbert, Election to member-
ship of. 18
— remarks on glaciers 8
Toner, J. M. : remarks on the late Dr. Wood-
ward ?6
Tornado at Rochester (Minn.) 3
Treasurer's report xxiv, 15, 82
Verification of predictions 122
Volcanic dust 18,33
INDEX. 135
Ward, L. F. : communication on some phys-
ical and economic features of the upper
Missouri system 20
— remarks on the deflection of rivers 23
Indians as botanic observers 74
Was the earthquake of Sept. 19 felt in the
District of Columbia? 73
Welling, J. C. : eulogy on Gen. Humphreys.. 4
— presidential address xxix, 81
— remarks on drifting of buoys 15
the Indian as a scientific observer... 75
Williams, G.H. : communication on methods
of modern petrography 36
What is a glacier? 37
Page.
White, C. H., Election to membership of..... 21
White, C. A. : report of auditing committee. 15
Why the eyes of animals shine in the
dark 13
Woodruff, T. M., Election to membership
of 32
Woodward, Dr. J. J., Death of. 72
— Resolutions on death of 75
Woodward, R. S.: discussion of a concrete
problem in hydrostatics proposed by
Mr. G. K. Gilbert 101
— remarks on deflection of plumb-line 92
Yeates, W. S., Election to membership of.... 36

BULLETIN
OF THE
PHILOSOPHICAL SOCIETY
OF
WASHINGTON.
VOL. VIII.
Containing the Minutes of the Society and of the Mathematical
Section for the year 1885.
PUBLISHED BY THE CO-OPERATION OF THE SMITHSONIAN INSTITUTION.
WASHINGTON :
1885

CONTENTS.
Page.
Constitution vil
Standing Rules of the Society ix
Standing Rules of the General Committee xn
Rules for the Publication of the Bulletin xiii
Officers elected December, 1884 xiv
Officers elected December, 1885 xv
List of Members xvi
List of deceased members xxv
Annual Report of the Secretaries • xxyii
Annual Report of the Treasurer xxviii
Calendar xxx
Annual Address of the President, Asaph Hall xxxin
Bulletin of the General Meeting 1
Report of the Auditing Committee 3
The vital statistics of the Tenth U. S. Cerisus, J. S. Billings,
(Title only) 4
Recent experiments on reaction time and the time sense, G.
Stanley Hall, (Title only) 4
Practical geology versus speculative physics, C. E. Dutton,
(Title only) 4, 5
Topaz from Stoneham, Maine, F. W. Clarke and J. S. Diller,
(Titleonly) 5
Two remarkable forms of mollusks, W. H. Dall 5
Geological and physical theories, "W. B. Taylor 6
Methods of verifying weather predictions, C. Abbe 8
Variations of latitude, A. Hall _. 10
Thunderstorms of 1884, H. A. Hazen 10
The Javal and Schiotz ophthalmometer, S. M. Burnett, (Title
only) 11
The difficulty in determining the direction of sound, A. B.
Johnson 11, 12
Mythological dry painting of the Navajos, W. Matthews 14
Comets II and III, 1884, W. C. Winlock 16
Problems connected with the physics of the earth's crust, H.
M. Paul, (Titleonly) 17, 18
Modern ideas of brain mechanism, F. Baker, (Title o?ily) 17
The flora of the Laramie group, L. F. Ward, (Title only) 17
The measurement of temperature at distant points, T. C. Men-
hall, (Titleonly) 18
The asteroids, G. L. Ravene, (Title only) 18
III
IV CONTENTS.
Page.
The mechanism of "clicks" and "clucks," A. G. Bell, {Title
only) «.. 18
The crumpling of the earth's crust, W. B. Taylor. 18
The columnar structure in the diahase of Orange mountain,
N. J., J. P. Iddings 19
The terraces of the Potomac valley, W J McGee, [Title only). 24
Anthropometric and reaction-time apparatus, J. S. Billings
and W. Matthews 25
The condensing hygrometer and sling psychrometer, H. A.
Hazen 25
A new volt-meter, T. C. Mendenhall 26
Flextures of transit instruments, W. Harkness 27
An attempt at a theory of odor, F. W. Clarke 27
The Flood Rock explosion, F. W. Clarke, C. F. Marvin, and
H. M. Paul 28
The systematic care of pamphlets, G. B. Goode and C. V. Biley 29
Germ cultures, J. S. Billings 30
Presentation of the annual address 30
Annual meeting 30
Bulletin of the Mathematical Section 33
Standing Rules of the Section 35
Officers of the Section 36
Example illustrating the use of a certain symbol in the calcu-
lus of affected quantity, E. B. Elliott, (Title only) 37
A collection of formula? for the area of a plane triangle, M.
Baker, (Title only) 37
Physical observations on Wolfs comet (1884, III), W. C.
Winlock 37
A slight modification of the Newtonian formula of gravitation,
W. B. Taylor : 39
An artifice sometimes useful for the adjustment of conditioned
observations, C. H. Kummell 41
The theory of Mercury, G. L. Ravene 41
A group of circles related to Feuerbach's circle, M. Baker 45
Distances on any spheroid, C. H. Kummell 52
On Grassman's system of geometry, A. Ziwet 53
Cause and chance in the concurrence of phenomena, M. H.
Doolittle, (Title only) 54
The asteroids, G. L. Ravene, (Title only) 54
Secular perturbations of Polyhymnia by Jupiter, W. F. McK.
Ritter 54
Some practical features of a field time determination with a
meridian transit, R. S. Woodward 55
Can the attraction of a finite mass be infinite ? C. H. Kum-
mell 58
Committees on mathematical communications t 68
Index 65
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
CONSTITUTION, RULES,
OFFICERS AND MEMBERS,
AND REPORTS OF
SECRETARIES AND TREASURER.

CONSTITUTION
THE PHILOSOPHICAL SOCIETY OF WASHINGTON.
Article I. The name of this Society shall be The Philosophi-
cal Society of Washington.
Article II. The officers of the Society shall be a President,
four Vice-Presidents, a Treasurer, and two Secretaries.
Article III. There shall be a General Committee, consisting of
the officers of the Society and nine other members.
Article IV. The officers of the Society and the other members
of the General Committee shall be elected annually by ballot ; they
shall hold office until their successors are elected, and shall have
power to fill vacancies.
Article V. It shall be the duty of the General Committee to
make rules for the government of the Society, and to transact all
its business.
Article VI. This constitution shall not be amended except by
a three-fourths vote of those present at an annual meeting for the
election of officers, and after notice of the proposed change shall
have been given in writing at a stated meeting of the Society at
least four weeks previously.
Yii

STANDING RULES
FOR THE GOVERNMENT OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON",
1. The Stated Meetings of the Society shall be held at 8 o'clock
p. m. on every alternate Saturday ; the place of meeting to be
designated by the General Committee.
2. Notice of the time and place of meeting shall be sent to each
member by one of the Secretaries.
When necessary, Special Meetings may be called by the President.
3. The Annual Meeting for the election of officers shall be the
last stated meeting in the month of December.
The order of proceedings (which shall be announced by the
Chair) shall be as follows
:
First, the reading of the minutes of the last Annual Meeting.
Second, the presentation of the annual reports of the Secretaries,
including the announcement of the names of members elected since
the last annual meeting.
Third, the presentation of the annual report of the Treasurer.
Fourth, the announcement of the names of members who, having
complied with Section 14 of the Standing Rules, are entitled to vote
on the election of officers.
Fifth, the election of President.
Sixth, the election of four Vice-Presidents.
Seventh, the election of Treasurer.
Eighth, the election of two Secretaries.
Ninth, the election of nine members of the General Committee.
Tenth, the consideration of Amendments to the Constitution of
the Society, if any such shall have been proposed in accordance
with Article VI of the Constitution.
Eleventh, the reading of the rough minutes of the meeting.
ix
X PHILOSOPHICAL SOCIETY OF WASHINGTON.
4. Elections of officers are to be held as follows
:
In each case nominations shall be made by means of an informal
ballot, the result of which shall be announced by the Secretary
;
after which the first formal ballot shall be taken.
In the ballot for Vice-Presidents, Secretaries, and Members of the
General Committee, each voter shall write on one ballot as many
names as there are officers to be elected, viz., four on the first ballot
for Vice-Presidents, two on the first for Secretaries, and nine on the
first for Members of the General Committee ; and on each subse-
quent ballot as many names as there are persons yet to be elected
and those persons who receive a majority of the votes cast shall be
declared elected.
If in any case the informal ballot result in giving a majority for
any one, it may be declared formal by a majority vote.
5. The Stated Meetings, with the exception of the annual meet-
ing, shall be devoted to the consideration and discussion of scientific
subjects.
The Stated Meeting next preceding the Annual Meeting shall be
set apart for the delivery of the President's Annual Address.
6. Sections representing special branches of science may be
formed by the General Committee upon the written recommenda-
tion of twenty members of the Society.
7. Persons interested in science, who are not residents of the Dis-
trict of Columbia, may be present at any meeting of the Society,
except the annual meeting, upon invitation of a member.
8. * On request of a member, the President or either of the Secre-
taries may, at his discretion, issue to any person a card of invitation
to attend a specified meeting. Five cards of invitation to attend a
meeting may be issued in blank to the reader of a paper at that
meeting.
9. Invitations to attend during three months the meetings of the
Society and participate in the discussion of papers, may, by a vote
of nine members of the General Committee, be issued to persons
nominated by two members.
10. Communications intended for publication under the auspices
of the Society shall be submitted in writing to the General Com-
mittee for approval.
* Amended January 17, 1885.
STANDING RULES. XI
11. Any paper read before a Section may be repeated, either
entire or by abstract, before a general meeting of the Society, if
such repetition is recommended by the General Committee of the
Society.
12. *It is not permitted to report the proceedings of the Society or
its Sections for publication, except by authority of the General Com-
mittee.
13. New members may be proposed in Avriting by three members
of the Society for election by the General Committee ; but no per-
son shall be admitted to the privileges of membership unless he
signifies his acceptance thereof in writing within two months after
notification of his election.
14. Each member shall pay annually to the Treasurer the sum
of five dollars, and no member whose dues are unpaid shall vote at
the annual meeting for the election of officers, or be entitled to a
copy of the Bulletin.
In the absence of the Treasurer, the Secretary is authorized to
receive the dues of members.
The names of those two years in arrears shall be dropped from
the list of members.
Notice of resignation of membership shall be given in writing to
the General Committee through the President or one of the Secre-
taries.
15. The fiscal year shall terminate with the Annual Meeting.
16. fAny member who is absent from the District of Columbia
for more than twelve consecutive months may be excused from pay-
ment of dues during the period of his absence, in which case he
will not be entitled to receive announcements of meetings or current
numbers of the Bulletin.
17. Any member not in arrears may, by the payment of one
hundred dollars at any one time, become a life member, and be
relieved from all further annual dues and other assessments.
All mo,neys received in payment of life membership shall be
invested as portions of a permanent fund, which shall be directed
solely to the furtherance of such special scientific work as may bo
ordered by the General Committee.
* Adopted January 17, 1885. f Amended December 19, 1885.
STANDING RULES
OP THE
GENERAL COMMITTEE OF THE PHILOSOPHICAL
SOCIETY OF WASHINGTON.
1. The President, Vice-Presidents, and Secretaries of the Society
shall hold like offices in the General Committee.
2. The President shall have power to call special meetings of the
Committee, and to appoint Sub-Committees.
3. The Sub-Committees shall prepare business for the General
Committee, and perform such other duties as may be entrusted to
them.
4. There shall be two Standing Sub-Committees ; one on Com-
munications for the Stated Meetings of the Society, and another on
Publications.
5. The General Committee shall meet at half-past seven o'clock
on the evening of each Stated Meeting, and by adjournment at
other times.
6. For all purposes except for the amendment of the Standing
Rules of the Committee or of the Society, and the election of mem-
bers, six members of the Committee shall constitute a quorum.
7. The names of proposed new members recommended in con-
formity with Section 13 of the Standing Rules of the Society, may
be presented at any meeting of the General Committee, but shall
lie over for at least four weeks before final action, and the concur-
rence of twelve members of the Committee shall be necessary to
election.
The Secretary of the General Committee shall keep a chronologi-
cal register of the elections and acceptances of members.
8. These Standing Rules, and those for the government of the
Society, shall be modified only with the consent of a majority of
the members of the General Committee.
xii
IR,TJ31.ES
PUBLICATION OF THE BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The President's annual address shall be published in full.
2. The annual reports of the Secretaries and of the Treasurer
shall be published in full.
3. When directed by the General Committee, any communication
may be published in full.
4. Abstracts of papers and remarks on the same will be pub-
lished, when presented to the Secretary by the author in writing
within two weeks of the evening of their delivery, and approved by
the Committee on Publications. Brief abstracts prepared by one
of the Secretaries and approved by the Committee on Publications
may also be published.
5. If the author of any paper read before a Section of the
Society desires its publication, either in full or by abstract, it shall
be referred to a committee to be appointed as the Section may
determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the Secretary of the Section, together with any
action of the Section taken thereon.
6. Communications which have been published elsewhere, so as
to be generally accessible, will appear in the Bulletin by title only,
but with a reference to the place of publication, if made known in
season to the Committee on Publications.
28 xii*
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 20, 1884.
President Asaph Hall.
Vice-Presidents J. S. Billings. Garrick Mallery.
William Harkness. J. E. Hilgard.
Treasurer Robert Fletcher.
Secretaries G. K. Gilbert. Henry Farquhar.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
Marcus Baker. H. H. Bates.
F. W. Clarke. W. H. Dall.
C. E. Dutton. J. R. Eastman.
E. B. Elliott. H. M. Paul.
C. V. Riley.
STANDING COMMITTEES.
On Communications :
J. S. Billings, Chairman. G. K. Gilbert. Henry Farquhar.
On Publications :
G. K. Gilbert, Chairman. Robert Fletcher. Henry Farquhar.
S. F. Baird.*
* As Secretary of the Smithsonian Institution.
XIV
OIFIFXaHIIR.S
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 19, 1885.
President J. S. Billings.
Vice-Presidents William Harkness. Garrick Mallery.
C. E. DUTTON. J. E. HlLGARD.
Treasurer Robert Fletcher.
Secretaries G. K. Gilbert. Marcus Baker.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates. F. W. Clarke.
W. H. Dall. C. E. Dutton.
J. R. Eastman. Henry Farquhar.
T. C. Mendenhall. H. M. Paul.
C. V. Riley.
Standing committees.
On Communications :
William Harkness, Chairman. G. K. Gilbert. Marcus Baker.
On Publications:
G. K. Gilbert, Chairman. Robert Fletcher. Marcus Baker.
S. F. Baird.*
* As Secretary of the Smithsonian Institution.
XV
LIST OF MEMBERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
Corrected to January i6, 1886.
The customary titles of members are hero for the first time given.
Names of gentlemen hero indicated as resigned will be omitted from future lists.
Name. Address and Eesidence.
Abbe, Prof. Cleveland •
ABEBT, Mr. S. T.(Sylvanus Thayer)
Adams, Mr. Charles Frederick
Adams, Mr. Henry
Alois, Hon. A. O. (Asa Owen)
Antisell, Dr. Thomas [Founder)
Avery, Mr. RoBEBT S. (Robert
Stanton)
Baird, Prof. SPENCEB P. (Spencer
Fullerton) (Founder)
BAKER, Dr. Frank
Baker, Mr. Marcus
Bancroft, George
Barnard, Dr. Wm. S. (William
Stebbins)
Barus, Dr. Carl
BATES, Mr. Henry H. (Henry
Bobart)
Beardslee, Capt. L. A. (Lester
Anthony) U. S. N. {Absent)
Bell, Mr. A. Graham (Alexander
< rraham)
Bell, Dr. C. A. (Chichester Alcx-
ander)
Benet, Gen. S. V. (Stephen Vin-
cent) U. S. A. (Founder)
Army Signal Office. 1871
2017 I st. N. W.
810 19th st. N. W. 1875
Civil Service Commission. 1885
2017 G st. N. W.
1G07 H st. N. W. 1881
1765 Muss. ave. N. W. ' 1873
Patent Office. 1871
1311 Q st. N. W.
320 A st. S. E. 1879
Smithsonian Institution.
1445 Mass. ave. N. W.
326 C st. N. W. 1881
Coast and Geodetic Survey Office. 1876
1205 Rhode Island ave.
1623 II st. N. W., or
Newport, R. I.
917 New York ave. N. W., or
Canton, 111.
Geological Survey. 1885
Patent Office. 1871
The Portland.
Navy Department. 1875
Scott Circle;
1500 Rhode Island ave.
1314 19th st. N. W.
Ordnance Office, War Dept.
1717 I st. N. W.
XVI
LIST OP MEMBERS. XVII
Name.
XVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name.
LIST OF MEMBERS. XIX
Name. Address and Eesidence.
Gallatjdet, President E. M. (Ed
ward Miner)
Gannett, Mr. Henry
Gihon, Dr. Albert L. (Albert
Leary) U. S. N. (Resigned)
Gilbert, Mr. G. K. (Grove Karl)
Godding, Dr. W. W. ("William
"Whitney)
Gooch, Dr. F. A. (Frank Austin)
Goode, Mr. G. Brown (George
Brown)
Goodfellow, Mr. Edward
Gore, Prof. J. H. (James How-
ard)
Graves, Mr. "Walter H. (Wal-
ter Hayden) (Absent)
Greely, Lieut. A. "W. (Adol-
phus Washington) U. S. A.
Green, Mr. Bernard 11. (Bern-
ard Eichardson)
Green, Commander F. M. (Fran-
cis Mathews) U. S. N. (Absent)
Greene, Prof. B. F. (Benjamin
Franklin) (Founder: absent)
Greene, Capt. Francis V. (Fran-
cis Vinton) U. S. A. (Absent)
Gregory, Dr. John M. (John
Milton)
Gunnell, Francis M., M. D., IT.
S. N.
Hains, Col. Peter C. (Peter
Conover)
Hains, Mr. Kobert P. (Kohert
Peter)
Hall, Prof. Asaph, U. S. N.
(Founder)
Hall, Mr. Asaph, Jr.
Hallock, Dr. William
Hampson, Mr. Thomas
Harkness, Prof. William, U. S.
N. (Founder)
Deaf Mute College, Kendall
Green.
Geological Survey.
1881 Harewood ave., Le Droit
Park.
Geological Survey.
1424 Corcoran st.
Government Hospital for the In-
sane.
Geological Survey.
825 Vermont ave.
National Museum.
1545 T st. N. W.
Coast and Geodetic Survey Office
Columbian University.
1305 Q st. N. W.
Denver, Colorado.
Armv Signal Office.
1914 G st N. W.
1738 N st. N. W.
Navy Department.
West Lebanon, N. H.
West Point, N. Y.
15 Grant Place.
GOO 20th st., N. W.
Engineer's Office, Potomac Kiv.
Improvement, 2136 Pa. ave.
1824 Jefferson Place.
Patent Office.
1714 13th st. N. W.
Naval Observatory.
2715 N st. N. W.
Yale College Observatory, New
Haven, Conn.
2715 N st. N. W.
Geological Survey.
Geological Survey.
504 Maple ave., Le Droit
Park.
Naval Observatory.
Cosmos Club, 23 Madison
Place.
1875
1874
1880
1873
1879
1885
1874
1875
1880
1878
1880
1879
1875
1871
1875
1884
1879
1879
1885
1871
1884
1885
1885
1871
XX PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name.
LIST OF MEMBERS. XXI
Name.
XXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name. Address and Residence.
Morgan, Dr. E. C. (Ethelbert
Carroll)
Moser, Lt. J. F. (Jefferson Frank-
lin) U. S. N.
Murdoch, Mr. John
Mussey, Gen. R. D. (Reuben Del-
avan)
Myers, Gen. William, U. S. A.
Netvcomb, Prof. Simon, U. S. N.
[Founder)
Nichols, Dr. Charles H. (Charles
Henry) [Absent)
Nicholson, Mr. W. L. (Walter
Lamb) (Founder)
Nordhoff, Mr. Charles
Norris, Dr. Basil IT. S. A. (Ab-
sent)
Nott, Judge C. C. (Charles Cooper)
Ogden, Mr. Herbert G. (Herbert
Gouverneur)
Osborne, Mr. J.W. (John Walter)
Parke, Gen. John G. (John
Grubb) U. S. A. (Founder)
Parker, Dr. Peter (Founder)
Parry, Dr. Charles C. (Charles
Christopher) (Absent)
Paul, Mr. H. M. (Henry Martyn)
Peale, Dr. A. C. (Albert Charles)
Pilling, Mr. James C. (James
Constantine) (Resigned)
Poe, Gen. O. M. (Orlando Met-
calfe) U. S. A. (Absent)
Poindexter, Mr.W. M. (William
Mundy)
Pope, Dr. B. F. (Benjamin Frank-
lin) U. S. A.
Powell, Major J. W. (John
Wesley)
Prentiss, Dr. D. W. (Daniel
Webster)
Pritchett, Prof. H. S. (Henry
Smith) (Absent)
918 E st. N. W.
Coast and Geodetic Survey Office
7 2d st. S. E.
Smithsonian Institution.
1441 Chapin st., College Hill.
P. O. Box 618.
508 5th st. N. W.
War Department.
Naw Department.
941 M st. N. W.
Bloomingdale Asylum, Boule-
vard and 117th st., New
York, N. Y.
Topographer, P. O. Dept.
1322 1st. N. W.
1731 K st. N. W.
Vancouver, Clarke Co., Wash.
Ter.
Court of Claims.
826 Connecticut ave. N. W.
Coast and Geodetic Survey Office
1324 19th st. N. W.
212 Delaware ave. N. E.
Engineer Bureau, War Dept.
16 Lafayette Square.
2 Lexington Place.
Davenport, Iowa.
Naval Observatory.
109 1st st. N. E.
Geological Survey.
1010 Mass. ave. N. W.
34 Congress st. West, Detroit,
Mich.
701 15th st. N. W.
806 17th st. N. W.
Surg. General's Office, U. S. A.
Geological Survey.
910 M st. N. W.
1224 9th st. N. W.
Director of Observatory, Wash.
University, St. Louis, Mo.
183
184
1«2
1374
880
1879
LIST OF MEMBEKS. XXIII
Name. Address and Residence.
Rathbun, Mr. Richard
(Gus-Ravene, Mr. Gustave L,
tave Louis)
Ray, Lieut. P. H. (Patrick Henry)
U. S. A.
Renshawe, Mr. Jno. H. (John
Henry)
Richey, Dr. S. O. {Resigned)
Ricksecker, Mr. Eugene
Riley, Dr. C. V. (Charles Valen-
tine)
Ritter, Mr. W. F. McK. (Will-
iam Francis McKnight)
Robinson, Mr. Thomas
Rogers, Mr. Joseph A. (Joseph
Addison) (Absent)
Russell, Mr. Israel C. (Israel
Cook)
Russell, Mr. Thomas
Salmon, Dr. D. E. (Daniel Elmer)
Sampson, Commander William
Thomas U. S. N. [Absent] %
Saville, Mr. J. H. (James Ham-
ilton)
Schott, Mr. Charles A. (Charles
Anthony) (Founder)
Shellabarger, Hon. Samuel
Sherman, Hon. John
Shufeldt, Dr. R. W. (Robert
Wilson) U. S. A. (Absent)
Shumway, Mr. W. A. (Willard
Adams) (Resigned)
Sicard, Capt. Montgomery, U.
S. N.
Sigsbee, Commander C. D.
(Charles Dwight) U. S. 1ST. (Ab-
sent)
Skinner, Dr. J. O. (John Oscar)
U. S. A.
Smiley, Mr. Chas. W. (Charles
Wesley)
Smith, Chf. Eng. David, TJ.
S.N.
Smithsonian Institution. 1882
1622 Mass. ave.
1417 6th st. N.' W. 1885
Fort Gaston, Cal. 1884
Geological Survey.
The Woodmont.
1882
Geological Survey. 1884
1323 Q st. N. W.
Agricultural Department, or 1878
National Museum.
1700 13th st. N. W.
Nautical Almanac Office. 1879
16 Grant Place.
Howard University. 1884
6th st. N. W., cor. Lincoln.
Naval Observatory. 1872
Geological Survey. 1882
1424 Corcoran st.
Army Signal Office. 1883
1447 Corcoran st. N. W.
Agricultural Department. 1883
1337 loth st. N. W.
Torpedo Station, Newport, R. I. 1883
1419 F st. N. W. 1871
1315 M st. N. W.
Coast and Geodetic Survey Office. 1871
212 1st st. S. E.
Room 23 Corcoran Building. 1875
812 17th st. N. W.
U. S. Senate. 1874
1319 K st. N. W.
Surg. Genl's Office, U. S. A., or 1881
Box 144, Smithsonian Inst.
1885
Ordnance Bureau, Navy Dept. 1877
Navy Department. 1879
Surg. General's Office, U. S. A. 1883
1529 O st. N. W.
U. S. Fish Commission. 1882
943 Mass. ave.
1330 Corcoran st. 1876
XXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name.
LIST OP MEMBERS. XXV
Name.
XXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name.
Alexander B. Dyer .
Amos Beebe Eaton
Charles Ewing
Elislia Foote
John Gray Foster
Leonard Dunnell Gale .
Isaiah Hanscom
Joseph Henry
Franklin Benjamin Hough .
Andrew Atkinson Humphreys
Ferdinand Kampf
"Washington Caruthers Kerr
Jonathan Homer Lane
Oscar A. Mack .
Archibald Robertson Marvine
Fielding Bradford Meek
James William Milner
Albert J. Myer .
George Alexander Otis
Carlile Pollock Patterson
Titian Bamsay Peale
Benjamin Peirce
John Campbell Kiley
John Bodgers
Benjamin Franklin Sands
George Christian Shaeffer
Henry Bobinson Searle
"William J. Twining
Joseph Janvier "Woodward
John Maynard "Woodworth
Mordecai Yarnall
Admitted,
Founder
Founder
1874
Founder
1873
1874
1873
Founder
1879
Founder
1875
1883
Founder
1872
1874
Founder
1874
Founder
Founder
1871
Founder
Founder
1877
1872
Founder
Founder
1877
1878
Founder
1874
1871
Active members
Absent members
SUMMARY.
179
46
Total
Deceased members
225
45
mf secretaries' report. xxvii
ANNUAL REPORT OF THE SECRETARIES.
Washington, City, December 19, 1885.
To the Philosophical Society of Washington :
We have the honor to present the following statistical data
for 1885.
At the beginning of the year the number of active members
was........... 173
This number has been increased by the addition of 22* new
members and by the return of 3 absent members. It has
been diminished by the departure of 6 members, by the
de^ith of 1, by the resignation of 5, and by the dropping
of 7 for non-payment of dues. The net increase of active
members has thus been 6
And the active membership is now .' . . . .179
The roll of new members is
:
C. F. Adams. H. L. Hodgkins. W. A. Shumway.
Carl Barus. J. P. Iddings. W. H. Weed.
T. M. Chatard. B. P. Mann. Bailey Willis.
P. A. Goocu. C. F. Marvin. H. M. Wilson.
E. P. Hains. . T. C. Mendenhall. J. L. Wortman.
William Hallock. J. F. Moser. G. M. Wright.
Thomas Hampson. C. C. Nott. Alex. Ziwet.
G. L. Bavene.
The names of deceased members (active and absent) are
:
Horace Capron. F. B. Hough. W. C. Kerr. T. R. Peale.
'
There have been 16 meetings for the presentation and discussion
of papers (not including the public meeting of Dec. 5) ; the average
attendance has been 48. There have been 6 meetings of the Mathe-
matical Section ; average attendance 15.
In the general meetings 32 communications have been presented
;
in the mathematical section 14. Altogether 46 communications
have been made by 32 members and one guest. The number of
members who have participated in the discussions is 41. The total
number who have contributed to the scientific proceedings is 54, or
31 per cent, of the present active membership.
The General Committee has held 17 meetings. Attendance below
10 on one evening only, and four times as high as 15. Average
12.2. Corresponding average last year 11.9, and in 1883 10.3,
when the attendance was below 10 at five meetings.
Very respectfully, G. K. Gilbert,
Henry Farquhar,
Secretaries.
*The figures in this report have been brought down to Jan. 16, 1886, so
as to correspond with the list of members. They differ somewhat from those
read to the Society at the annual meeting.
XXVIII PHILOSOPHICAL SOCIETY OP WASHINGTON.
REPORT OF THE TREASURER
Mr. President and Gentlemen :
The report which I have the honor to present to you to-night
covers the pecuniary transactions of the fiscal year which termi-
nates with this meeting.
You will see from the statement which I shall presently read
that the total receipts by the Treasurer have been $1,224.04, and
the total disbursements §740.02, leaving a cash balance of $484.02.
These sums do not, however, represent the net income and expendi-
ture for the year, since the receipts include a balance transferred
by the former Treasurer, and the amount collected of unpaid dues
of previous years. The payments, also, include the sum of $104.12,
for unpaid debts of 1884.
All the liabilities of the Society have been discharged to date,
and the actual income belonging to 1885 has been $1,041.00, which
includes $205.00 of dues yet outstanding. The disbursements for
the same period have been $635.90, leaving a net saving for the cur-
rent year of $405.10.
The unpaid dues of former years which have been collected,
amount to $160.00.
The Government bonds which belong to the Society were at the
beginning of the year exchanged for new issues of the same
amounts and denominations. This was done, under authority of
the General Committee, in order to obtain uniformity in the
designation of the Society, the former bonds having varied from
each other in that particular. The bonds consist of:—
1 $1,000 00 bond, bearing interest at 4 per cent.
1 500 00 " " " 4
1 1,000 00 " " " 4h "
Total, $2,500 00.
The assets of the Society are as follows:—
Cash, with Riggs & Co. . . . $482 02
Bonds 2,500 00
Unpaid dues 295 00
Total $3,279 02
The market value of the bonds is, of course, considerably in
excess of their face value; on the other hand, a part of the "un-
paid dues" will probably not be collected.
I have in my possession a still ample stock of the Bulletins.
A copy of Vol. VII was sent directly after its publication in
February last to every member entitled to receive it, as well as to
the various societies and scientific journals, at home and abroad,
with which it has been customary for the Society to exchange
publications.
TREASURER S REPORT. XXIX
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PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL ADDRESS OF THE PRESIDENT.
XXXI

ANNUAL ADDRESS OF THE PRESIDENT,
Asaph Hall.
Delivered December 5, 1885.
AMERICAN SCIENTIFIC SOCIETIES.
Mr. Chairman and Fellow-Members of the Philosophical Society
:
The termination of the office with which you have honored me
during the past year brings, in accordance with our custom, the
duty of addressing you, and I have chosen for my subject American
/Scientific Societies. The Philosophical Society of Washington is the
first scientific society of which I was a member, and, having still a
lively recollection of the curiosity and interest with which I watched
its formation and early progress, I propose to consider briefly the
history of such societies in our own country, and incidentally, some
of their benefits.
Nothing can be more natural than the union of men of similar
tastes and thought into associations for the investigation and dis-
cussion of matters that mutually interest them, and thus we see in
all civilized countries the formation of societies in every branch of
learning and of art. In the countries of Europe such bodies have
been a long time in existence, and many of them are still in vigor-
ous life. Most of these societies owe their establishment to the favor
of a powerful patron, generally an emperor or a king, who was wise
enough to understand that the well-being of his people would be en-
hanced by the progress of science and art. But Avhatever may have
been the motive of their foundation, these academies of scientific men
have exerted a great influence on the civilization of Europe. Such
an assertion may seem doubtful to the readers of what is called
history, but in fact the larger part of our civilization that is good
and permanent will be found closely connected with the works and
inventions of scientific men. It is these works that have changed
our ideas and conception of the world in which we live, and of the
universe around us. It is these works, also, that slowly but surely
compel the changes of political and theological theories. History,
as it is now written, deals mostly with battles and sieges, with the
3a xxxiii
XXXIV PHILOSOPHICAL SOCIETY OP WASHINGTON.
actions of emperors and kings, the amours of princes, and the in-
trigues of courtiers and priests. These are the bubbles and froth
of the social world that have attracted nearly all historical writers,
but there is a growing feeling that suqh recitals do not contain the
substantial parts of history. Who would not wish to know more
of the social forces that have been at work in Europe and in our
own country, and which have converted some of the most rugged
and barren parts of the world into the richest and most prosperous
—
of the ingenious and persevering industry that brings about the
greatest changes in the customs of men and in the political power
of nations? These changes come from an increase of command over
the forces of nature, and in our ability to make these forces work
for us. Now it is the discovery and study of these forces and their
modes of action that form a large part of scientific work; and if we
turn to the academies of Europe we shall find that they have a
splendid history. By their encouragement of the labors and writ-
ings of ingenious men, by just criticism, and by the publication of
memoirs these academies take a prominent place in the history of
science. It is in these enduring monuments of the human intellect,
rather than in brazen statues or marble shafts, that the real glory
of the race consists.
The men who settled our country were separated by a great ocean
and a month's journey from the civilization and learning of Europe.
They had ample work to do in building houses and roads, and in
establishing themselves securely in this new world. However, they
soon began to set up schools and colleges, so that the elements at
least of learning might be kept alive. But the inhabitants were
scattered over a great extent of country, and means of communica-
tion were poor. Under these circumstances concerted action and
union into societies were difficult, and a century and a half passed
away before the formation of a formal scientific society. The first
society of this kind that I find in our country is the American
Philosophical Society of Philadelphia, organized in 1769. At that
time Philadelphia was the largest and the leading city of this
country, and being in a good degree free of the bitter theological
quibbles and disputes that embroiled New England communities, it
was better adapted for the home of a scientific society. It was also
the residence of Benjamin Franklin, who appears to have taken an
active part in the formation of the new society, and who became its
first president. Franklin was a native of Boston, but when seven-
ANNUAL ADDRESS OF THE PRESIDENT. XXXV
teen years of age, having written and spoken disrespectfully of what
he called " religious knaves," and having thus provoked the enmity
of influential men in his native town, he sought and found a home
in a more genial climate. The new society began well. Its first
three presidents were Benjamin Franklin, David Rittenhouse, and
Thomas Jefferson. This society formulated and published an ex-
cellent plan of scientific work, including a study of the native inhab-
itants of the country, an examination of the ancient mounds of the
Western States, and researches in geology and natural history. In
1796 it offered several prizes, with premiums ranging from fifty to
one hundred dollars. The first premium offered was " for the best
system of liberal education and literary instruction adapted to the
genius of the government, and best calculated to promote the gen-
eral welfare of the United States, comprehending, also, a plan for
instituting and conducting public schools in this country on princi-
ples of the most extensive utility." Premiums were also offered for
improving the method of computing longitudes from lunar distances,
for the improvement of ship pumps, for the improvement of stoves
or fire-places, for the best method to prevent the premature decay
of peach trees, for a treatise on native American vegetable dyes,
and for the best improvement of lamps. This society published its
first volume of memoirs in 1771. Among the first contributors was
David Rittenhouse, the able and ingenious astronomer, and the first
volume contains a very full account of the Transit of Venus that
happened June 3, 1769. We find here, also, some account of im-
provements in the sextant, which appears to have been independ-
ently invented by Thomas Godfrey, of Philadelphia, in 1730.
Franklin was an early contributor to the memoirs, his writings
generally having a very practical bearing. His first paper is on
the causes and cure of smoky chimneys, and occupies thirty-six
quarto pages. It is an interesting paper on an important subject,
much discussed at that time. A correspondent of Franklin de-
clares its importance by quoting the lines
—
"A smoky house and a scolding wife
Are two of the greatest ills in life."
This was followed by other papers of Franklin on the formation
of the earth, the theory of light and heat and of magnetism, and
on the manufacture of paper. Franklin thought the interior of the
earth is a heavy fluid, and he imagined magnetism to be a general
XXXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
property of the universe, so that one might govern his course from
star to star by the compass. The succeeding volumes contain sev-
eral ingenious memoirs by Joseph Priestley, in some of which he
expounds the theory of phlogiston, which appears to have been
purely a hypothetical substance for explaining the theory of com-
bustion. The volume of these memoirs published in 1825 contains
a letter from Albert Gallatin, Secretary of the Treasury, under
date of March 25, 1807, and addressed to Mr. F. R. Hassler, of
Philadelphia, relating to the survey of our coast. There is a long
and interesting reply by Hassler, who gives a full account of the
methods of such a survey, with descriptions of instruments, forms
for keeping the observations, making maps, and carrying on the
work generally. Still later these volumes contain the memoirs of
Joseph Henry on his important researches in electricity and mag-
netism. These papers were read in January, 1835, and published
in 1837. The American Philosophical Society has published twenty-
one volumes of memoirs, which contain papers of enduring interest.
One feels regret that a society that began so well and which has
published so much of value should stop the publication of its
memoirs and seem to flag in its scientific work. Let us hope that
this may be only a temporary condition.
The next establishment of a scientific society in our country is
that of the American Academy of Arts and Sciences in Boston.
This society was chartered in 1780, James Bowdoin being the first
president. The Boston society does not appear to have started
under such favorable auspices as its sister society in Philadelphia,
but on the other hand it has kept up its scientific work better, and
is still active and efficient. Perhaps this may be owing to its prox-
imity to a large and flourishing college, which has now developed
into a university. The American Academy of Arts and Sciences
has published fifteen volumes of memoirs. Among its distinguished
members I cannot omit to mention Nathaniel Bowditch, the self-
taught mathematician, who was probably the first man in our coun-
try to really grasp the methods of the Mecanique Celeste. It is one
of the surprises of our prolific country that it produces so many
men who, it is said, read the Mecanique Celeste before they graduate
from college, and it is another surprise to meet these same men in
after life and be convinced from their own lips that they know but
little about that great work. But Nathaniel Bowditch mastered it.
These two societies, that of Philadelphia and that of Boston, are
ANNUAL ADDRESS OF THE PRESIDENT. XXXVII
the most widely known and they are among the best of our local
societies. Many others have been established or revived recently,
and some of them are doing good work. Among those which have
taken a high standing by the publication of valuable memoirs is
the Connecticut Academy of Arts and Sciences. Such societies
deserve a hearty support, and by their encouragement and direction
of local talent can render valuable service to science. But these
societies are too numerous to mention here.
I cannot, however, pass from the two elder societies without notic-
ing in the first place the gradual cessation of their memoirs and the
falling into what are styled " proceedings " for publication. It
seems to me a matter of regret that this should happen. Such pub-
lications are apt to degenerate into a dry account of meetings, and
elections, and deaths and resignations, and lists ofmembers. If this is
all a society is able to do it may be tolerated for awhile, but it is a
condition which should be outgrown. I think that keeping up a
good form for printing memoirs tends to elevate the character of a
society and to incite members to good works.
There is another matter in connection with these two elder socie-
ties which is curious and worthy of mention. Each of them had a
list of foreign honorary members. It is interesting now after the
lapse of a century to examine these lists, and to see what kind of
men were selected for such honors, and also to see how far the
judgment of the philosophers has been confirmed by time, which
makes such havoc with the estimates of men. At the time of the
organization of the American Philosophical Society, Euler was the
leading mathematician of Europe. He was then sixty-two years
old and at the height of his reputation. There is hardly a branch
of mathematics which Euler had not enriched by his ingenious and
wonderfully prolific labors. He had worked in the theory of numbers,
in all parts of the calculus, and had laid the foundations of the cal-
culus of variations, fie wrote a complete treatise on dioptrics, made
a laborious and valuable investigation of the lunar theory, and ap-
plied mathematical theories to a very great number of physical
questions. In 1766 he became blind by his incessant labors, but still
continued his work. I do not find the name of Leonard Euler in
the list of the fifty-five foreign associates of the American Philosoph-
ical Society. The successor of Euler as the leading mathematician
of the world was Lagrange. The Mecanique Analytique was not
published until 1788, but Lagrange had shown his power in a great
XXXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
number of memoirs on mathematical and astronomical questions.
The Mecanique Analytique put him at the head of all living inves-
tigators in the theory of rational mechanics; and this book
remains to-day a model worthy the study of every student. In fact
at the present time, when so many doctors and professors seize the
great analytical machine and turn out pages of elegant and trifling
formulae, there can be no better experience than to go back to the
luminous pages of Lagrange. Here is a master whose symbols are
always in subjection, and who has no need to startle us by mysterious
phrases. His inventions and improvements are among the most
valuable in the history of pure and applied mathematics. But the
name of Lagrange is not on the list of honorary members of the
American Philosophical Society. Laplace was a younger man than
Lagrange, but he was fortunate in securing a good position in Paris
in early life, and he immediately began that wonderful career of
scientific labors that culminated in the Mecanique Celeste. The first
volume of this work was published in the year seven, or in 1799.
It is the methodical arrrangement and condensation of the labors
of his great predecessors and colleagues of that century, together
with his own remarkable investigations—a work that placed him at
the head of the philosophers of his day. But his fame was not of
the kind to put him on the honorary list of the American Philo-
sophical Society. It may be worth while to look for one name more,
that of Legendre, the ingenious and persevering mathematician who
lived such a quiet and unpretentious life that we are not surprised
to find his name omitted. I think this example is worthy of notice,
since it shows that the scales of philosophers do not weigh men much
more accurately than those of other people. But it would be a
mistake to suppose that this society differed in this respect very
much from others of its own time. The matter may be instructive
in warning us against careless estimates of our cotemporaries, and
by giving us caution in judging scientific men from their social
position and rank. It may also throw light on the election to posi-
tions in our scientific societies of men whose chief recommendation is
a noisy and uncertain reputation. However these things may be
one thing is certain : the lords, counts, and gentlemen of the hono-
rary lists are dead, buried, and forgotten ; but the names of the four
men who could not command this distinction live in. the memories
of all men of science.
Omitting for the present any reference to the many scientific socie-
ANNUAL ADDRESS OF THE PRESIDENT. XXXIX
ties that have been organized recently I come to our national socie-
ties. The earliest of these is the American Association for the
Advancement of Science. The first meeting of this association
was held in Philadelphia in 1848, and was called to order by Pro-
fessor William B. Rogers, of Virginia, who had taken a prominent
part in its formation. Only one volume of memoirs has been pub-
lished by the American Association, but its annual volume of pro-
ceedings has been issued with regularity. This association has em-
braced among its members nearly all the prominent scientific men of
the country, and it is our most complete national scientific organiza-
tion. Theplan of its formation seems to have been a good one, and I
think it has exerted an excellent influence by bringing into acquain-
tance and sympathy men from different parts of the country. In
recent years its character has become more popular, and under the lead
of its energetic secretary its membership has reached nearly two thou-
sand. During its early days this society took an active part in dis-
cussing the scientific operations carried on by the General Govern-
ment, and its influence in this direction seems to have been wise.
With the increase in the number of members such discussions have
been judiciously avoided, and even the j:>assing of resolutions, so
common in all American bodies, might perhaps better be omitted.
In such large bodies there is apt to be so much confusion and dis-
pute that the resolutions are made extremely vague and meaning-
less or are manipulated to suit the purpose of a few. There is
another danger to this society arising from its easy conditions to
membership and its rapid increase of members. Our country pro-
duces a large number of men and women who are born with a mis-
sion. Educated in the schools and colleges, but never attaining
much distinction as scholars, these people begin in their own phrase
to think for themselves. The result of this thinking is often some
discovery in science, and one that contravenes doctrines estab-
lished by long observation and study. The questions considered
are generally vast and mysterious, such as the origin of gravitation,
the nebular hypothesis, and the nature of force. Having made his
discovery the author wishes of course to present it to the world, and
what method is more convenient than through a scientific society,
admission to which is so easy. And if we admit a person to mem-
bership and take his money how can we refuse to listen to his
theories. Who that has had the honor of presiding over one of
the sections of the American Association, in casting his eye over
XL PHILOSOPHICAL SOCIETY OF WASHINGTON.
the audience, has not had brought to mind the description of Dean
Swift
:
" The first man I saw was of meagre aspect, with sooty hands and
face; his hair and beard long, ragged, and singed in several places.
He had been eight years upon a project for extracting sunbeams
out of cucumbers, which were to be put into phials hermetically
sealed, and let out to warm the air in raw and inclement summers.
He told me he did not doubt in eight years more he should be able
to supply the governor's gardens with sunshine at a reasonable rate
;
but he complained that his stock was low, and he entreated me to
give him something as an encouragement to ingenuity, especially as
this had been a dear season for cucumbers."
Now although this matter has a comical phase, it has also its
serious and difficult side. No man of science wishes to suppress the
opinions of others, and ingenious speculations are worthy of atten-
tion, but he has a right to his own time, and should be freed from
the trouble of listening to absurd projects. How this can be done
with such an easy course of admission to membership I do not see.
There is another hindrance to the successful operation of the Ameri-
can Association which comes from the great extent of our country
and the cost and difficulty of attending its meetings. To those who
have ample time and means at their disposal this hindrance is not,
perhaps, very great. This vigorous and generous society may need
a little pruning, but on the whole its influence has been good, and
every one must wish it a long and honorable life.
We have another scientific organization of national character in
the National Academy of Sciences, established in 1863. This is a
body on a basis quite different from that of the American Associa-
tion for the Advancement of Science. The National Academy was
brought into existence during a great civil war, and its members
were of necessity chosen from one section of the country. It was
incorporated by act of Congress, and this act limited the number of
its members to fifty. From the language of the act we may fairly
infer that the academy was intended to be the adviser of the Gen-
eral Government in matters of science. During a time of great
civil commotion, when the powers of the Government were greatly
extended, such a society would very naturally come into existence;
but when the strife had subsided it became an object of criticism.
In filling vacancies in its membership it was difficult always to
ANNUAL ADDRESS OF THE PRESIDENT. XLI
select the best man, and sometimes abler men were left out of the
academy than those who had the right kind of influence to be
appointed. Scientific men are like other people, and they elect
their friends and those whom they think will help them. Within
a few years after the close -of the civil war the limitation of the num-
ber of members was removed by act of Congress. The National
Academy has now the power to determine the number of its members,
and for the present this has been practically fixed at one hundred.
Whether this number should be increased, and whether its member-
ship should be more evenly distributed throughout the country are
questions over which the academy has entire control. Its destiny,
therefore, is in its own hands, and it is to be hoped, and it is to be ex-
pected, that its career will be useful and honorable. To act such a
part as this the academy must maintain a high and independent char-
acter. It should choose for its members the best and ablest scientific
men of the country, and it must never become the tool of the shrewd
men who deal out the rich patronage of the Government. That there
is need for such an independent body to criticise and assist in the
direction of the scientific work done by public authority seems be-
yond question. It is assumed, of course, that the General Govern-
ment is to carry on scientific works of various kinds, a position
which may be disputed by some, but which appears to be already
practically conceded. How far the Government should enter on
such works, and how much should be left to private enterprise, is a
question of public policy. But there are certain works which belong
almost of necessity to the General Government. Thus the survey of
our coast and harbors, a general geological survey, and a good map
of the country seem to belong to the work of the Government.
These may be justified on the ground of their utility to the pub-
lic. But there are other scientific works, not so directly con.
nected with commercial and moneyed interests, that an enlightened
government may properly undertake. Why should not there be in
this country a first-class national astronomical observatory, where
observations may be continued from one age to another with the
best instruments of the times? Again, do not the elevated plains of
the West offer an excellent opportunity for the determination of an
arc of the meridian which may be extended from British America
to the City of Mexico, and why cannot our General Government
undertake such a determination? Must everything that is not
strictly utilitarian be prohibited in the public works of our Repub-
XLII PHILOSOPHICAL SOCIETY OF WASHINGTON.
lie? I do not think so. On the other hand the things that are
purely commercial may generally be left to themselves.
But if the Government is to do scientific work it should have the
aid of men of science. We all know the tendency of public offi-
cials to fall into habits of routine, and to spin out their work to an
almost interminable length. There should be, therefore, a body of
men who can criticise kindly, but boldly and justly, the labors of
officials, and make them perform their duties as they ought. This,
I think, should be one of the functions of the National Academy
of Sciences. But to make this advice influential the Government
must recognize the scientific men of the country, and give them
some regular channel of communication through which their opin-
ions can be made known to the public and to the executive author-
ities. Thus far in the history of our Government the scientific man
has generally been regarded as an expert who is to be carefully
watched, lest he get the better of the officials who are set over him,
and who sometimes undertake to manage affairs of which they have
but little knowledge. The jealousy thus engendered is unfortunate.
The man of science should be treated just as other men are treated,
and there should be no grumbling at paying him a fair recompense
for his labor. Our national military and naval academies are costly
institutions, and fortunate is the young man who has a Congressman
for an uncle or a cousin; but I have never heard a word from any
scientific man against the cost of these establishments. So far as I
know, their universal sentiment is, let us have the best of instruc-
tion in military and naval science, for this is the cheapest. Our
public buildings cost vast sums of money, but there is no objec-
tion to such expenditures if the buildings are well and solidly
constructed, since here, also, the best is the cheapest. On the
other hand, is there not something very absurd in the manner
the politician looks on the small expenditures for science, and
the lavish ones that are voted for other purposes ? Let us take a
single case. A public vessel is " repaired," to use an adopted
euphemism, at one of our navy yards, and the cost of the repairs
amounts to a million of dollars, or more than double the original
cost of the ship. There is some astonishment at this, but we are
told in a confident manner that the ship is greatly improved in
strength and speed. The trial comes off, and while the ship is going
along at her utmost speed, with the velocity of nine miles an hour,
the engine breaks down. Here is a serious collapse, since before
ANNUAL ADDRESS OF THE PRESIDENT. XLIII
she was repaired the vessel could make eleven miles an hour. The
head of the Department very properly orders an examination.
Now, it might occur to superficial persons that those who repaired
that ship had made mistakes. But the examining board weighs the
evidence carefully, and it deliberately comes to the conclusion that
the fault lies wholly with some unknown person who is more than
three thousand miles away. The matter is mysterious, but the
result is certain. The Government has been cheated, the money is
gone, and the local politicians are happy. And the curious thing
is that the public accepts the report of the examining board as en-
tirely satisfactory. There is not a whisper of dissent from any news-
paper in the land. And, after all, it is only half a million dollars,
and do we not throw away ten times as much every year on rivers
and harbors? Have we not seen a Senator boasting in his
speeches that during the last twenty years more of the public money
has been expended on the mountain streams of his own State than
that State has paid taxes into the public treasury.
Now change the case and let us suppose that some scientific man
by bad management of his own or by failure of an assistant, has
wasted ten thousand dollars of the public money. Ah, this is quite
a different matter, and must be looked at from a different stand-
point. How soon do we hear some smug official complacently re-
mark that he always knew that scientific men cannot do business.
And how eagerly the newspapers seize upon the case ; how indig-
nant the editors become, and how the head lines flare. Is there
one law for the public functionary and another for the man of
science ?
But it is not right to leave this matter without further considera-
tion. When we look at the advantageous position occupied by the
officer of the army or navy we see immediately that this doe's not
come from any personal merit he may have, but from the fact that
he is recognized by law as an essential part of the Government.
This position renders him in theory impersonal, and it is assumed
that he has no private business of his own, but all his interests are
one with those of the public. He has his member of the Cabinet
to represent his views. His appropriations never fail, and he has
no need to summon men from distant parts of the country to push
his bills through Congress. Now, so long as the scientific man is
looked upon merely as an expert and an adventurer, and has no
regular channel of communication with the Government he will
XLIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
stand at a great disadvantage Pie may gain a victory now and
then, just as militia may sometimes beat regular troops, but the
final result is pretty sure to be defeat. The position of the man of
science must, therefore, be recognized by law if he is to be con-
nected with public works in such a way that he may act freely and
usefully. Such considerations will bring up the question of how far
the Government is to proceed in the cultivation of science.
If Ave examine the history of a country like England, where we
have good records for a thousand years, we shall see that there has
been a steady tendency toward three results. The first of these is
personal liberty. The slave that was bought and sold has been
changed to the serf, and the serf to the laborer. These changes
have gone on with conflicts, and sometimes with retrograde move-
ments, but on the whole they have proceeded until now, in nearly
all civilized countries, personal liberty is secured by law. The sec-
ond result is the freedom of opinion. To control such au intangible
thing as the opinions of men is a difficult matter, but it is a business
which many men delight in, and the contest, though old, is yet a
living one. When Sir Richard Saltonstall reproached his friends
in Boston for persecuting Baptists and Quakers, on the ground that
such persecutions made men hypocrites, the Puritan ministers at
once replied that hypocrites are much better than profane persons
like Baptists and Quakers. But such people have been forced back
from one position to another, explaining, apologizing, and retreat-
ing, until now in several countries opinion is nearly free. There
remain a few able men who pray for more superstition and bigotry,
but they are the relics of a past time. The third result is the right of
free exchange, and toward this end we have gained but little, since
nearly all governments exercise their power in prohibiting among
men the free exchange of their products. The general course of
events is thus to restrict the sphere of government, and to leave to
the individual more and more freedom of action. The chief duty
of government is to see that justice is done between man and man,
and to this end that the courts are fair and intelligent, and that our
iudges are not owned by rich men and corporations; that the public
service is honest and efficient, and is not used for personal or polit-
ical aggrandizement. But, granting all this, it seems to me that
the Government may properly undertake such great scientific works
as I have mentioned, with the condition that they be placed under
proper control and inspection. To the successful accomplishment
ANNUAL ADDRESS OP THE PRESIDENT. XLV
of these works the man of science must be brought into the public
service. He must be held responsible, just as other officials are, in
his account of public money. Such a condition would subject him
to some limitations that might be irksome at first, since it is pleas-
ant for many to have at their disposal large sums of money which
they may use at their pleasure, and almost every one fancies that
he could do a great deal of good in this way. But such a method
of handling public money is dangerous, and is apt to lead into
trouble.
Supposing that our public scientific works are to be carried on
by men of science, what part the National Academy of Sciences
shall act I cannot say, and it is not my province to urge on the
Government the services of this academy, but here is a body of
scientific men who have pledged themselves to the public service
and they should be made to do their duty. And is there not ample
room for intelligent criticism and suggestion in all the methods
through which the public money is expended ? Take the case of
public schools, which is a kind of communism justified on the
ground of utility to the State. What shall be the course of educa-
tion in these schools ? There is an unfortunate class of our fellow
creatures that must be cared for at the public expense, but shall
benevolent institutions encourage the production of such beings ?
Have we not read of the English poorhouse where were found the
grandfather, the father, and the son, all hearty men,
—
paupers breed-
ing paupers? Do not some of our charitable institutions give
plausibility to the saying that the mistakes of the good do more
harm than the vices of the wicked ? In fact, turn to any of the
modes of public expenditure and examples will be found where
sober, scientific judgment is necessary for the wise conduct of busi-
ness.
I come now to consider our own home society, the Philosophical
Society of Washington. And, speaking cautiously and soberly, is
it not to-day the best local scientific society in the country ? This
is owing partly and perhaps chiefly to our position at the Capital of
a great people. Men from all sections come back to us as winter
approaches, and many of them have interesting information to give.
No other city of our country offers such advantages for fresh and
early information of the investigations that are going on in the
various departments of science. Our libraries in astronomy, math-
ematics, and medical science are among the best. As a general
30
XLVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
library that of Congress must surpass all others in the country.
These are advantages which make Washington an agreeable resi-
dence for men of science and literature.
I think also our society has a good plan of organization, thanks
to the men who formed it. The general business can be safely con-
fided to a committee, and in this way the meetings are made more
interesting. This committee is so large that by a generous rotation
in office most of the members may see and share, if they wish; the
governing of the society. We have simple rules and they should
always be enforced, since no society can afford to be overawed by
any man, especially a society where we all meet as equals and where
no favors are to be asked or granted. Our society has been estab-
lished on a broad basis, to include all brances of learning, and as
we have members from all the professions our meetings ought not
to lack in variety of subjects. In such meetings the purpose of a
paper should be to present the principal points clearly, and the
author may generally trust to the intelligence of his audience to fill
in the details. It is the failure to recognize this rule and the lack
of arrangement that make some papers so long and tedious.
Our society has its home in a beautiful city, and who that has
seen its wonderful growth during recent years can doubt its future
splendor and greatness ? It is a city cosmopolitan in its character.
Being the seat of political power, here will come the enterprising
and adventurous from all parts of the country, with additions from
other lands. Some of the brightest names in our scientific annals
are those of foreigners who have made their homes with us. Let us
welcome all earnest men, remembering that the principles of science
are universal, and are not confined to any language or country.
In respect of personal conduct we can have no better example
than the noble man who was our first President, whose simple and
devoted life was a model for every scientific man. If we need other
inducements to devote ourselves to labors that may not give a great
return of money, or lead to easy and luxurious lives, let us remem-
ber that we live in a magnificent country, and one that has been
dedicated as we hope to the liberty and welfare of the human race.
Each one of us may do a little in adding to her scientific renown,
which is now only beginning. Let us recall the words of the great
Athenian : " I would have you day by day fix your eyes upon the
greatness of Athens, until you become filled with the love of her
;
and when you are impressed by the spectacle of her glory, reflect
ANNUAL ADDRESS OF THE PRESIDENT. XLVII
that this empire has been acquired by men who knew their duty
and had the courage to do it, who in the hour of conflict had the
fear of dishonor always present to them, and who, if ever they failed
in an enterprise, would not allow their virtues to be lost to their
country, but freely gave their lives to her as the fairest offering
which they could present at her feast. The sacrifice which they
collectively made was individually repaid to them ; for they received
again each one for himself a praise which grows not old, and the
noblest of all sepulchres—I speak not of that in which their remains
are laid, but of that in which their glory survives, and is proclaimed
always and on every fitting occasion both in word and deed. For
the whole earth is the sepulchre of famous men ; not only are they
commemorated by columns and inscriptions in their own country,
but in foreign lands there dwells also an unwritten memorial of
them, graven not on stone but in the hearts of men."

BULLETIN
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
GENERAL MEETING.

BULLETIN
GENERAL MEETING
261st Meeting. January 3, 1885.
President Hall in the Chair.
The Chair announced the election to membership of Messrs.
William Mundy Poindexter and Asaph Hall, Jr.
The Auditing Committee, appointed at the annual meeting, sub-
mitted the following report
:
Washington, D. C, December 27, 1884.
Mr. President and Gentlemen of the
Philosophical Society of Washington :
We, your committee, appointed at the annual meeting, December
20, 1884, to audit the report of the Treasurer for the year 1884,
have the honor to submit the following report
:
We have examined the statement of receipts of dues from mem-
bers, and of interest on bonds, and find the former to be $745, and
the latter $95, as appears in the Treasurer's statements of accounts
for the year 1884.
In addition to the foregoing, $15 were repaid to the Treasurer by
a member for extra printing, thus making the total receipts $855.
We have examined the vouchers for disbursements for the same
period, and find them correct.
We have compared the return checks with the vouchers and with
the entries in the bank book, and find them correct.
We have examined the bank book, and found the balance as set
forth to be correct, said balance, deducting the amount of two checks
not yet returned, being $183.04, with Messrs. Riggs & Co.
4 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The bonds referred to in the statement of assets were exhibited
to us by the Treasurer, and consist of one $1,000 U. S. bond @ 4£
per cent., one $1,000 U. S. bond @ 4 per cent., and one &500 U. S.
bond also @ 4 per cent.
All of which is respectfully submitted.
H. C. Yarrow,
Marcus Baker,
William C. Winlock,
Committee.
On motion, the report was accepted and the committee discharged.
Mr. J. S. Billings made a communication on
THE VITAL STATISTICS OF THE TENTH U. S. CENSUS,
presenting a brief outline of results soon to be published in Vol.
XI of the Census Reports.
Remarks were made by Messrs. Elliott, Mallery, and Asaph
Hall.
262d Meeting. January 17, 1885.
The President in the Chair.
The Chair communicated an invitation to the members of the
Society to attend the annual meeting of the Biological Society and
listen to an address by Dr. C. A. White.
By request, Professor G. Stanley Hall, of the Johns Hopkins
University, made a communication on
RECENT EXPERIMENTS ON REACTION TIME, AND THE TIME SENSE,
reviewing the methods of investigation and the results attained.
An animated discussion followed by Messrs. Robinson, Hilgard,
Newcomb, Billings, Eastman, Paul, Winlock, Asaph Hall,
and Professor George Davidson, of San Francisco.
Mr. C. E. Dutton then began a communication on
practical geology versus speculative physics,
which was unfinished when the hour of adjournment arrived.
general meeting. 5
263d Meeting. January 31, 1885.
The President in the Chair.
Fifty-eight members and guests present.
The Chair communicated an invitation to the members of the
Society to attend the ninetieth regular meeting of the Anthropo-
logical Society, and listen to an address by Major J. W. Powell.
Mr. C. E. Dutton finished the communication begun by him at
the last meeting on
PRACTICAL GEOLOGY Versus SPECULATIVE PHYSICS,
and the subject was further discussed by Messrs. Doolittle,
Mason, Clarke, Ward, Walcott, Paul, Taylor, M. Baker,
and Robinson.
264th Meeting. February, 14, 1885.
The President in the Chair.
Thirty-one members present.
The Chair announced the election to membership of Messrs. Carl
Barus, Frank Austin Gooch, and William Hallock.
Messrs. F. W. Clarke and J. S. Diller made a joint communi-
cation on
TOPAZ FROM STONEHAM, MAINE,
describing the alteration of topaz into damourite. [The paper is
published in the American Journal of Science, 3d series, Vol.
xxix, pp. 378-384.]
Mr. William H. Dall made a communication on
TWO REMARKABLE FORMS OF MOLLUSKS.
Mr. Dall described the anatomical features of the remarkable
Chlamydoconcha Orcutti, of San Diego, California,* which is in fact
a degraded lamellibranch, in which the shell has become internal
and functionless, and is no longer adjusted by adductor muscles.
He also described a remarkable feature which he had just dis-
covered in Milneria minima, a small California bivalve, belonging
*The main features of this notice appear in Science, No. 76, Vol. IV, p.
50, 1884.
G PHILOSOPHICAL SOCIETY OF WASHINGTON.
to the Carditidce, and living on the backs of Haliotis shells. The
female has the base of the shell pushed up into a dome in the median
line, the opening to which is closed by an extension of the mantle.
In the pocket so formed the young of the species are protected by
the mother. The only other case among the laraellibranchs of such
a protective modification is that of Thecalia concamerata, in which
the same end is reached in a different manner. Both belong to the
same family. The males of Milneria are without the pocket. Both
sexes adhere by a byssus.
Mr. W. B. Taylor read a communication on
GEOLOGICAL AND PHYSICAL THEORIES,
in which, controverting the claims of practical or field geology—to
the exclusion of physical theory—in the solution of physiographic
problems, he contended that the family ties of planetary relationship
cannot be disowned by geology. He thought the value of "exter-
nal" inductions fully shown by the probable effects of varying
eccentricity in the earth's orbit on secular changes of climate, as
well as by a reference to the general inter-relation between the
meeting boundaries of astronomical, geological, physical, and chem-
ical science. On the physical side, he maintained that the sup-
posed demonstrations of the earth's comparatively recent consol-
idation, (as well as of the limit assigned to the sun's active life,)
were entirely inconclusive: first, from the admitted uncertainty of
the data, and secondly, from our ignorance that unknown factors
might not enter into the problem. He therefore heartily agreed
with Captain Dutton in recognizing the strong demands of geological
induction for an incomparably longer chronology than terrestrial
physics could as yet cipher out.* At the same time, the speaker
contended that the certainty remained entirely unimpaired of an
origin and a limit to solar—as well as to planetary—energy ; unless
we were prepared to accept the absurdity of an infinite potential.
He also pointed out that the doctrine of " uniformitarianism " does
not require (as sometimes too readily supposed) an unvarying
degree of energy in geological dynamics throughout the distant past;
but that the contrary was the more probable—if only from the broad
generalization that all action whatever has its period or periods of
maximum and minimum.
*Mr. Taylor's paper was a reply to one by Mr. Dutton, of which tho
Society obtained no abstract. See pp. 4 and 5.
GENERAL MEETING. 7
On the question whether geology itself gave us " traces of a begin-
ning, or prospects of an end," Mr. T. argued that stratigraphical
geology unmistakably indicated its own genesis in the plutonic char-
acter of its primseval "Archaean," or Laurentian
—
pointing to a
time when the primitive surface was a molten ocean; and that
when read in the light of palaeontology such indication of a begin-
ning was strengthened into convincing proof by the receding grada-
tions of animal and vegetable life, starting in the lower Silurian
and its underlying Cambrian, with the humblest invertebrate forms
of molluscan and crustacean life, and the simplest cryptogamous
thallogens—the marine algse and fucacese. And in this connection
he referred to the memorable generalization of Louis Agassiz—that
the geological successions of animal types correspond remarkably
with the phases of embryonic development—as one of the most sug-
gestive contributions ever made to the theory of evolution.
The speaker then turned to the question of the earth's interior
fluidity ; and after stating that the celebrated mathematical argu-
ments of Hopkins from the " precession " value, and of Thomson
from the hydrographic tides, had both been practically abandoned
by the latter—though he still persisted in his pre-possessions for a
solid globe (mainly on the specific-gravity skepticism), Mr. T. said
he felt no difficulty whatever in accepting the.geological evidences of
a fluid earth enveloped by a flexile, friable egg-shell. With regard
to the large amount of contraction and corrugation every where
exhibited by this shell, he admitted that Mr. O. Fisher had conclu-
sively disproved the sufficiency of Elie de Beaumont's plausible
hypothesis that the contraction is due to the secular cooling of the
planet. Mr. Fisher had however no better speculation to offer;
and the answer to the riddle must come ultimately—not from petrol-
ogy; nor from structural, or stratigraphical, or physiographical
geology—but from cosmological physics. In conclusion, the speaker
urged that the same inductions which so clearly establish the birth,
the childhood, and the manhood of our planet, as inevitably impli-
cate its decline, decadence, and decease; and he quoted passages
from Byron's familiar lines on "Darkness," as in the main a scien-
tific prophecy.
Mr. Paul spoke of the importance of a recent contribution to the
subject of the earth's rigidity by Mr. George H. Darwin. Mr. Gil-
bert thought that Darwin's deduction of high rigidity was vitiated
by his postulate of homogeneity.
8 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The President remarked on the great interest of the discussion
opened by Captain Dutton's communication to a preceding meet-
ing, and expressed his especial approval of the method in which Mr.
Ward had approached the subject.
265th Meeting. February 28, 1885.
The President in the Chair.
Fifty members and guests present.
The Chair announced the election to membership of Messrs.
Thomas Corwin Mendenhall, Alexander Ziwet, Howard
Lincoln Hodgkins, Bailey Willis, Joseph Paxson Iddings,
and C. F. Marvin.
Announcement was also made of the death of the Hon. Horace
Capron.
Mr. C. Abbe made a communication on
METHODS OF VERIFYING WEATHER PREDICTIONS,
giving a general account of the rules under which the U. S. Signal
Office deduces from "indications " and subsequent observations the
published percentages of verifications. For purposes of prediction
and verification the area of the United States is divided into a small
number of districts. The " indication " for each district refers to the
subsequent 24 hours, and is compared with the three next following
weather-maps constructed from the observations, and the degree of
correspondence for each station in the district is marked on a scale of
five terms—0, 25, 50, 75, and 100. The published percentages are
means of these marks. For certain special classes of phenomena
—
such as high-winds, frosts, and cold-waves—in which the indication
only discriminates the occurrence and non-occurrence of a specific
event, the formula for percentage of verification is
n -\- o
in which n is the whole number of times the event is predicted, v is
the number of verifications, or of events coincident with predictions,
and o is the number of unpredicted events.
It has been found for a large area in Europe, an area comparable
GENERAL MEETING. 9
in size with one of the districts above mentioned, that, on the aver-
age, a given type of weather
—
e. g., rain, threatening, fair, hot,
cloudy, clear—can prevail simultaneously over only 85 per cent, of
the area. If this law holds for the United States, we can hope for
no better predictions while the existing system of districts is adhered
to, for our percentage of verification is now approximately 85.
Mr. Curtis described the method of verification adopted by the
Deutsche Seewarte. It differs from that of the U. S. Signal
Service in that the predictions are compared for verification with
the observations at a single representative station in each district.
Thus, for northwest Germany, the observations at Hamburg are
employed. The limits for the prediction of stationary temperature
are taken as dz 1° C, on the basis of an investigation by Hann who
found that the " change in 24 hours at Hamburg, in two-thirds of
all cases, averages less than two degrees C." Mr. Curtis showed
that, for verifications to be directly comparable with respect to skill
in prediction, the limits for " stationary " must vary in different dis-
tricts and at different seasons of they ear. Unless such variations
are adopted, the verifications should exhibit a uniform geographical
difference, and an annual period, if the method employed possesses
any scientific accuracy. As any such change of definition would be
impracticable, it would seem desirable to base the range allowed for
"stationary" temperature entirely on physiological considerations,
leaving the question of comparability for subsequent discussion.
In reply to a question by Mr. Paul, Mr. Abbe said that the rules
required that a prediction covering 24 hours should be verified by
the maps compiled at the 8th and 16th hours, as well as by that
compiled at the 24th. The desirablity of subdividing the geo-
graphic sections to which the weather predictions apply was dis-
cussed by Messrs. Gilbert, Paul, and Abbe ; and Mr. Abbe said
that if any change was made, it would consist in the abandonment
of specially defined districts and the substitution of individual States.
Mr. H. A. Hazen remarked that if the prevailing weather in a
district treated as a unit actually pertained, on an average, to but
85 per cent, of the district, then only omniscience could attain to a
success in weather prediction measured by 85 per cent, of verifica-
tion.
10 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. A. Hall made a communication on
VARIATIONS OF LATITUDE,
discussing the observations tabulated by Mr. Fergola, and reaching
the conclusion that the evidence fails to show that latitudes are
variable.
[The paper is published in the American Journal of Science, 3d
series, Vol. XXIX, pp. 223-27.]
Mr. R. S. Woodward said that he had recently undertaken the
discussion of the subject with somewhat fuller data than those used
by Mr. Hall. Postulating that the pole was changing its position
by motion at a uniform rate on the arc of a great circle, he. com-
puted the direction to be along the meridian 50° west of Green-
wich, and the rate of motion about 2" per century. His inves-
tigation was not yet completed, but he inclined to the opinion that
actual change was indicated by the data used.
Other remarks were made by Messrs. Farquhar, Baker, and
Paul.
266th Meeting. March 14, 1885.
The President in the Chair.
Fifty-four members and guests present.
The Chair announced the election to membership of Messrs.
Robert Porter Hains and George Mitchell Wright.
The Chair read a letter from Mr. A. C. Peale, announcing the
death, on the 13th of March, of Mr. Titian Ramsay Peale, one
of the founders of the Society. Mr. Peale accompanied Colonel
Long in his explorations of the Rocky Mountains as naturalist, and
was afterwards a member of the Wilkes' exploring expedition.
Mr. H. Allen Hazen made a communication on
THUNDERSTORMS OF 1884.
This paper was a resume of some of the investigations made by
the Signal Office, looking to a detailed study of the origin, progress,
and development of thunderstorms. Over 13,000 special reports
were received and studied. An attempt to connect thunderstorm
frequency with the phases of the moon showed a rather marked
GENERAL MEETING. 11
increase during the time of new moon, thus corroborating the result
previously obtained by Dr. Koppen.
A comparison of storm frequency with the period of solar rotation
gave a marked maximum during the rotation. It was shown that
taking the mean temperature over the whole storm region there was
a close relation between the occurrence of high temperature and
storm action, the former preceding the latter by about 24 hours.
Taking the mean of the meteorological elements on 20 days of
many storms at many of the stations, it was found that a marked
low-pressure area was present to the northwest of the storm region,
there was also a high temperature, while the humidity and weather
were normal. On 20 days of few storms the reverse was found true,
namely, a relatively high pressure and low temperature, the humid-
ity and weather being normal as before. These results were highly
interesting as bearing upon the conditions favorable to thunderstorm
action. The detailed study gives promise of large additions to our
knowledge of these meteors.
In the ensuing discussing, Messrs. Mussey, Ray, Antisell, E.
Farquhar, Paul, Gilbert, Robinson, and Hazen spoke of the
topographic, geographic, and seasonal distribution of thunderstorms
and of the relation of the precipitation to the electric phenomena.
Mr. Antisell said that moisture is essential to their generation
;
they are a secondary effect of the influence of the sun, not a pri-
mary. Mr. E. Farquhar spoke of the concentration of electricity
by diminution of aqueous surface, when cloud-particles coalesce and
form raindrops.
Mr. S. M. Burnett exhibited and explained
THE JAVAL AND SCHIOTZ OPHTHALMOMETER.
Mr. A. B. Johnson began a communication on
THE DIFFICULTY IN DETERMINING THE DIRECTION OF SOUND.
267th Meeting. March 28, 1885.
The President in the Chair.
Forty-two members and guests present.
The Chair announced the election to membership of Messrs.
Gustave Louis Ravene, Thomas Marean Chatard, Herbert
12 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Michael Wilson, Willard Adams Shumway, and Jefferson
Franklin Moser.
Mr. A. B. Johnson then completed his communication on
THE DIFFICULTY IN DETERMINING THE DIRECTION OF SOUND,
illustrating his remarks by a model of the topophone. The follow-
ing is an abstract of the entire paper.
Mr. Johnson said the hunter could not locate his game by the
sound it made, unless the sound was frequently repeated ; that the
plainsmen could not locate each others' site by shouts, until they
were frequently repeated ; that a child calling its mother in a house
could not tell which room she was in, or even the floor she was on,
until her voice was heard several times ; that it was hard to tell,
from its noise alone, whether a street-car was going to the right or
left, in approaching it at right angles ; in fact that it was not easy
to fix by the ear alone, the location of the source of any sound.
A dog aroused from sleep by the call of his unseen master fre-
quently dashes in different directions before hitting the right one.
Game startled by hearing a hunter's tread will as readily run into,
as out of danger. Blind people, despite the highly developed con-
dition of their remaining senses, do not appear to be more able to
determine the source of sound, other things being equal, than seeing
people. It seems to be a question whether people generally do not
use sight, touch or smell, involuntarily in locating sound. Hence,
when they are so placed that they must depend on hearing alone,
and err unusually in doing so, they consider such instances as ab-
normal.
After referring to subjective errors in audition, which frequently
arise, Mr. Johnson spoke of the peculiar class of errors in audition
into which mariners are apt to fall, often resulting in disaster. The
collision between the ocean steamers Edam and Lepanto, was-
referred to, in which the former was sunk, as the latter had erred
an eighth of the compass circle in fixing her position by the sound of
her fog signal, and thus ran into her. A lawsuit ensued, in which
Judge Addison Brown, of the U. S. District Court of New York,
decided against the plaintiff, holding " that an error of five points,
in locating a vessel by the sound of her whistle in a fog, is not nec-
essarily a fault, under the proved aberrations in the course of
sound."
GENERAL MEETING. 13
Mi*. Johnson then read from Judge Brown's opinion, extracts
from papers read before the Washington Philosophical Society by
three of its former Presidents, Henry, Taylor, and Welling, and by
himself, all as to the difficulty of determining the direction of sound,
and he congratulated the Society that its conclusions had been
adopted by the courts.
As it was evident that the unaided ear could not be relied upon
to fix the direction from which sound came, Mr. Johnson said atten-
tion should be directed to giving the ear all possible assistance.
That something of this kind could be done was proved, he thought,
by Professor Morton's experimentation with the topophone. This
instrument had been devised by Professor Mayer of the Stevens
Institute of Technology. It consisted of an arrangement by which
two Helmholtz resonators were connected on the deck of a steamer
with rubber tubes running into the cabin and with bars and rods
which could be moved from the cabin. The actuating principle of
the device was the neutralization of the dynamic force of the full
sound wave by the half sound wave, thus approximating silence,
and thus indicating automatically, within ten degrees, or less than
one point of the compass, the direction of the sound.
Mr. Paul remarked that the bar connecting the resonators should
be shorter than the wave length of the sound under observation,
since otherwise deceptive results would be obtained with the two
resonators in similar phases of different waves. Mr. Taylor ques-
tioned the utility of the instrument, though heartily applauding its
ingenuity. The real difficulty in determining sound direction arises
from the heterogeneity of the air in point of density and moisture,
and especially from its indeterminate differences of movement,
whereby diffractions and refractions are occasioned many times
greater than those affecting light. The topophone, like the ear, is
cognizant only of the final direction of the incident beam of sound,
so to speak, and can tell us nothing of the direction of the source of
sound. Mr. E. Farquhar remarked that the verdict of the ear in
regard to direction is usually just ; the conditions under which it
errs are exceptional. He thought there was a rapid adjustment by
motion of the head, from which the general direction is almost in-
voluntarily ascertained. Mr. F. Baker said that animals, such as,
for example, the carnivora, make fewer mistakes than man, and this
is probably due to their muscular control of the external ear. When
the ears are pricked up in listening, special tensions may be given
o 1
14 PHILOSOPHICAL SOCIETY OF WASHINGTON.
to the concha. When man listens intently he adjusts the tensions of
the membrana tympani.
The possible influence of wind velocity on the pitch of sound was
discussed by Messrs. Paul, Taylor, and Gilbert, and other
remarks were made by Messrs. King, Hall, Elliott, and H.
Farquiiar.
Mr. Washington Matthews began a communication on
mythological dry paintings of the navajos,
which occupied the remainder of the evening. Its completion was
deferred.
268th Meeting. April 11, 1885.
Vice-President Billings in the Chair.
Forty-six members and guests present.
Mr. Washington Matthews concluded his paper on
MYTHOLOGICAL DRY PAINTING OF THE NAVAJOS.
This paper described an art in use among the medicine men of
the Navajo Nation, by which they represent various mythological
conceptions on the sanded floor of the medicine lodge with dry pig-
ments of five different colors. These dry paintings are from ten to
twelve feet in diameter, and are quite intricate, containing from five
to thirteen mythological figures of large size. About a dozen men
labor from eight to ten hours in making them. When completed,
they are after some ceremonies completely obliterated, and even the
sand on which they are drawn is carried out of the lodge and thrown
away. The existence of such an art is not generally known and
the figures are not copied from any visible standard but are retained
in the memories of the medicine men.
The paper was illustrated with seven water-color paintings
—
reproductions of the Navajo drawings. Four were pictures of the
esoteric portion of a Navajo ceremony called dsilyidje-qacal or "song
in the mountains," and represented visions or revelations of the
Indian prophet who instituted these ceremonies. The remaining
three pictures were from a ceremony known as kledje-qacal or "song
of the night," and represented the revelations of another Navajo
GENERAL MEETING. 15
prophet, lie who, according to their mythology, instituted the latter
ceremonies. The symbolism of the pictures was explained, and such
portions of the myths as directly referred to the pictures were
related.
The first picture showed the house of the great snakes. The
second represented the gods of the domestic plants, with the prin-
cipal domestic plants of the Indians, corn, bean, pumpkin, and to-
bacco, indicated by highly conventionalized figures. The third pic-
ture was of certain goddesses of great height, called the Bitsihi-nez
or Long-bodies, which the prophet is said to have seen in a house
made of dewdrops. The fourth drawing depicted the sacred arrows
used in the dance, which the medicine men pretend to swallow.
The lecturer explained the trick by which this imposture Avas car-
ried out. The fifth picture represented the peculiar myth of the
tsis-naole or whirling sticks. It represents two logs placed in the
center of a lake so as to form a cross. Eight divine beings sat on these
logs, which were kept constantly whirling by other gods who poked
the logs with plumed staves. There Avere tAvelve apotheosized human
figures in the picture. The sixth picture shoAved the kledjc qacal as
it took place in the abodes of the gods Avhen the Navajo'prophet
first saAV it, and is a fair representation of the dance as it is per-
formed among the Na\rajos to-day. The seventh painting repre-
sented a portion of the dance among the gods, at a time Avhen a spell
had been cast upon them by the angry Coyote-god.
The figures in the east of the pictures are painted in Avhite, those
in the south blue, those in the Avest yelloAV, those in the north black.
This is the usual order of Navajo color symbolism ; but sometimes
the Avhite is assigned to the north and the black to the east ; instances
Avere given where this interchange took place.
The gods in many cases are shoAvn standing on rafts made of sun-
beams, such rafts being favorite vessels of the gods Avhen they make
their aerial journeys. The gods are depicted Avith round heads, the
goddesses Avith quadrangular heads. In the dances, the actors Avear
masks of corresponding shapes to indicate males and females.
Seven of the pictures Avere surrounded Avith symbols of the rain-
boAv deity, Avhich Avith the Navajos, as Avith the Greeks, is a goddess.
The sanded floor on Avhich the pictures are drawn is slightly
sprinkled with charcoal; this is to convey the idea of a surface of
clouds, for it is said that in the houses of the gods these pictures
were draAvn on sheets of clouds.
16 PHILOSOPHICAL SOCIETY OP WASHINGTON.
The speaker closed by referring to the transitory nature of the
pictures, and showing how it might easily have nappened that no
knowledge of them would ever transpire.
Mr. Gilbert Thompson described pictures on the walls of a
shallow cave near San Antonio Spring, New Mexico, and exhibited
copies of the same. The outlines of the pictures are etched on the
rock, and several different colors are employed, both in the etched
grooves and on the plane surface of the rock. Mr. Matthews
explained the relations of these drawings to Navajo myths and cere-
monies.
In response to questions by Messrs. Billings, M. Baker, Paul,
and Mallery, Mr. Matthews said that individual drawings are
not repeated on the same occasion. The ceremonial dances, most
of which take place only during the season when the snakes hiber-
nate, are executed for the benefit of invalids, or foi the gratification
of individuals who by conventional fiction are regarded as ill. They
are paid for, and they are very expensive luxuries, the gross bill of
expenses sometimes amounting to the value of $300. The patient
or his friends select the particular dance to be performed. After
the completion of the picture, the patient enters the lodge, and is
seated upon the east figure, while a litany is chanted. Sand from
one of the painted figures is then applied to his body, sand from the
arm being applied to his arm, &c.
Mr. Paul described a similar art of dry-painting, practiced by the
Japanese, but for amusement only. Bold designs of great variety
are executed skillfully and rapidly in public places, for which the
artist receives compensation from the by-standers. Wealthy Japan-
ese also employ persons to dance for them, and, for that matter, to
fish for them ; but the motive appears to be pleasure, and not religion,
or health.
Other remarks were made by Mr. Jenkins.
Mr. W. C. Winlock made a communication on
COMETS II AND III, 1884,
illustrating his subject by models exhibiting each cometary orbit in
its proper relation to the earth's orbit, and also by plane diagrams
and sketches of the comets.
GENERAL MEETING. 17
Mr. Ravene spoke of the perturbations of Barnard's comet
occasioned by the attraction of Jupiter, and thought it might have
been brought into the solar system by that attraction.
Other remarks were made by Mr. Paul.
Mr. H. M. Paul commenced a communication on
PROBLEMS CONNECTED WITH THE PHYSICS OF THE EARTH'S CRUST.
Its completion and discussion were deferred to a future meeting.
269th Meeting. April 25, 1885.
The President in the Chair.
Fifty-three members and guests present.
Announcement was made of the election to membership of Mr.
Charles Frederic Adams.
Mr. Frank Baker made a communication on
MODERN IDEAS OF BRAIN MECHANISM.
Remarks were made by Messrs. E. Farquhar, H. Farquhar,
M. Baker, and Doolittle.
Mr. L. F. Ward began a communication on
THE FLORA OF THE LARAMIE GROUP,
the completion of which was deferred for lack of time.
270th Meeting. May 9, 1885.
The President in the Chair.
Forty-four members and guests present.
Announcement was made of the election to membership of Mr.
Walter Harvey Weed.
Mr. Lester F. Ward completed the reading of his communica-
tion on
THE FLORA OF THE LARAMIE GROUP.
[It will appear in the Sixth Annual Report of the U. S. Geological
2
18 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Survey, as a portion of the author's " Synopsis of the Flora of the
Laramie Group."]
Remarks followed by Messrs. Gilbert, Elliott, and White.
Mr. T. C. Mendenhall made a communication on
THE MEASUREMENT OF TEMPERATURE AT DISTANT POINTS.
Remarks were made by Mr. Elliott.
Mr. Gustave Ravene gave an abstract of a communication pre-
pared on
THE ASTEROIDS.
Remarks were made by Messrs. Taylor, H. Farquhar, and
Elliott.
271st Meeting. May 23, 1885
The President in the Chair.
Forty-one members and guests present.
The Chair announced that only one more meeting would be held
before the summer vacation.
Mr. A. Graham Bell made a communication on
THE MECHANISM OF " CLICKS" AND " CLUCKS."
Remarks were made by Messrs. M. Baker, Gilbert, and Rob-
inson.
Mr. H. M. Paul completed his communication on
THE CONDITION OF THE EARTH'S INTERIOR.
Mr. W. B. Taylor made a communication on
THE CRUMPLING OF THE EARTH'S CRUST,
in which, referring to the plausible hypothesis of contraction by cool-
ing—which had been so largely accepted, he contended that the
amount of cooling and contraction since the formation of a consis-
tent crust had been much less than even the opponents of that
hypothesis had conceded; while the maximum amounts estimated
by its adherents would still be wholly inadequate to represent the
GENERAL MEETING. 19
actual measure of compression indicated by the average degrees of
plication of the stratified rocks. Supposing these to represent a
a reduction from the original circumference of the crust of one-elev-
enth, this would involve a former excess of volume of about one-
third.
The speaker then gave an historical sketch of the growing con-
viction among physicists that from the tidal retardation of the
earth's rotation, the length of the day must have been much shorter
in remote geological eras than at present—and consequently the ob-
lateness of the terrestrial ellipsoid considerably greater. Estimating
that a day of six hours would give an equatorial enlargement of about
one-tenth (without taking any account of volumetric change by reduc-
tion of temperature), he thought this morphologic change an adequate
explanation of the
.
observed crumpling of the earth's crust ; and
claimed that the cause assigned is both a true and a sufficient one.
This larger oblateness would imply an equatorial bulge 396 miles
greater in radius than the present ; and a corresponding depression
of the poles 658 miles below their present levels. As in a general
way confirmatory of this hypothesis, Guyot's statement was quoted
that " On the whole, the reliefs begin with the vast, low plains
around the polar circle, and go on increasing from the shores of the
Arctic ocean toward the tropical regions ; " and that " the ocean
basins become less deep toward the North pole
—
just as the lands
become lower toward the same region."
[This paper is printed in full in the American Journal of Science,
3d Series, Vol. XXX, pp. 249-266.]
272nd Meeting. June 6, 1885.
The President in the Chair.
Twenty-eight members present.
Mr. J. P. Iddings made a communication on
THE COLUMNAR STRUCTURE IN THE DIABASE OF ORANGE
MOUNTAIN, N. J.
[Abstract.]
The paper describes the occurrence and structure of the " trap "
rock in the neighborhood of Orange, with special reference to the
arrangement of the columns in John O'Rourke's quarry and in the
20 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Undercliff quarry in Llewellyn Park. The chief interest centers in
the groups of radiating columns which form the, upper portion of
the exposures, the lower portion being divided into vertical columns
or blocks of larger size. That these two portions of the lava sheet
belong to one and the same mass is shown, not only by the contin-
uity of the rock of the upper and lower parts, but also by the mutual
accommodation of the different sets of columns, which taper off and
curve in one direction along lines of oblique junction ; and by the
fact that the positions of the columns are not what they should be
along the supposed lines of contact.
The columnar structure in volcanic lavas is unquestionably a
cracking produced by shrinkage upon further cooling, after the
mass has consolidated into rock.
Considering the origin and progress of a crack produced by the
shrinkage of a homogeneous mass, we see that, starting with a plane
surface over which forces producing contraction are acting uni-
formly, the contraction produced on the surface of the mass in a
given time will be greater than that produced at some depth within
the mass, and that it will decrease gradually from the surface in-
ward. As the contraction progresses, the limit of tension in the
direction of the surface will be reached before that in the direction
of depth, causing a rapture across the direction of the surface, and
as the limit of tension for the layer next to the surface is reached
it will rupture in the same direction as the surface layer did,
and so on. The direction of the crack is at right angles to that
of greatest contraction, or normal to the line of maximum strain.
Moreover the condition of the mass at the moment the limit of
tension along the surface is reached may be graphically repre-
sented as in figure 1, the contraction being a maximum in the
! \
\
FCg.l.
top layer and diminishing successively in each layer beneath to that
with the initial expansion. The distance of this layer from the
surface being taken as unity, the maximum contraction at the
GENERAL MEETING. 21
moment of rupture will be equal to twice the tangent of a. In
other words 2 tan a represents the limit of tension, and will be con-
stant for any given substance.
As the conductivity of a cooling body is not directly proportional
to the degree of radiation from its surface, Uie difference between
the contraction of successive layers of a rapidly cooling mass will be
greater than between those of one cooling less rapidly, and what
may be styled the angle of contraction will be greater in the former
case than in the latter. And if we assume a certain rate of cooling
to have caused a single rupture in a given extent of mass (repre-
sented in fig. 1), then a greater rate of cooling, which would pro-
duce in the same extent of mass a contraction represented by a
i a mi t tan /3
greater angle, p, will cause as many ruptures as the ratio, j •
If the forces producing contraction are unequally distributed over
the surface a b, figure 2, being a maximum at c, the maximum
Fig. 2.
strain at the beginning will be in the direction of the surface, and
the cracks will start normal to it ; but their progress inward will
no longer be uniform. At the end of a given time the limit of ten-
sion reached by a greater force, at /, will be farther from the sur-
face than that reached by a less force, at g, and the line of maxi-
mum strain in this portion of the mass will be g'f, to which the
crack of parting will be normal. At the end of another given time
the direction of the crack will be again changed, and the same
action taking place in the other parts of the mass will result in a
system of diverging cracks.
So far we have considered the shrinkage in one direction in one
plane only, that is, parallel to the cooling surface in a plane at right
angles to it. But a homogeneous mass contracts equally in all
22 PHILOSOPHICAL SOCIETY OF WASHINGTON.
directions, and the contractile force which produces cracks at
certain distances in a given mass will exert itself equally in all
directions over a surface uniformly subjected to the cooling forces,
and will, at the instant of fracture, act towards centres, whose dis-
tance apart is dependent on the rate of cooling. If the mass is per-
fectly homogeneous the centres of contraction will be disposed over
the surface with the greatest uniformity possible, that is, they will
be equidistant throughout, and the resultant fractures Avill be in a
system of hexagons. If from any irregularity in the composition
or petrographic structure of the rock the contractile force acts un-
equally in different directions, the form of the polygons will be less
regular.
The mutual influence of the forces producing different columns as
they approach each other is readily understood from the foregoing.
Take the case of two columns, S, S', approaching one another (Fig.
3,) and suppose the progress of the maximum strain to have reached
a b, a' b', the forces producing contraction acting through a and a'
will meet and react on each other before those acting through b
and b', so that the points of maximum strain at any given time will
have advanced farther along the lines through a and a' than through
b and V. The lines of greatest strain will then be c d and c' d', and
the cracks normal to them will take the directions e e and c' e\
This will continue till they become parallel.
If there were but two columns forming at equal rates they would
curve symmetrically and continue in parallel directions and of con.
stant width, but if one column progresses more rapidly than the
GENERAL MEETING. 23
other they will no longer curve to the same extent, and the slower
one will curve more than the faster one.
Now, instead of two single columns, there,are always two groups
approaching one another, and these prevent the continuation of the
columns beyond the bend, pinching them out and causing them to
taper off as already observed in the quarry described.
The difference in the systems of cracks of the lower and upper
portion of this lava sheet may then be accounted for by a difference
in the rate of cooling from the lower and upper surfaces, the more
frequent fractures arising from the more rapid cooling, and the two
systems proceeding from their initial planes until they blend in one
another within the mass.
If for any reason the cooling from one surface should take place
irregularly and from any point proceed more rapidly than from
others, it is evident that there would result a set of columns diverg-
ing from this point as a focus.
Besides the columnar fracturing, a division of the mass by trans-
verse cracks, especially near the top of the lava sheet, is more or less
noticeable.
There remains to be considered the contraction exerted in all
other directions through the mass. Since the uniform contraction
of a homogeneous body acts equally in every direction through it,
its effect corresponds to the equal shortening of the radii of a sphere
of such a body. If through any resistance cracking or parting
occurs it will take the form of concentric spherical shells.
If for any reason the resistance to the contracting force in a par-
ticular direction be counteracted by some other force acting in the
esame direction the parting will no longer be spherical, but ellipsoidal,
as will be seen from Figure 4, where a b c represents a section
3L b
through the sphere along the radii of which contraction takes place.
A uniform resistance in the direction of the radii represented by
24 PHILOSOPHICAL SOCIETY OF WASHINGTON.
c c', d d', etc., will produce a parting parallel to the arc of the circle
c' d' e', etc. If, however, the resistance in a direction parallel to ae
be neutralized by some force, the resistance along the different radii
will be diminished by the amount of the vertical component in each
case, and the resulting fracture will be parallel to the ellipse c b'.
The relative tendency to fracture also is represented by the area
be V.
Such a parting is actually present in the large columns in John
O'Rourke's quarry, the major axis of the ellipsoid being vertical, as
it should be if the weight of the superincumbent mass counteracted
any resistance to contraction in a vertical direction.
The wavy form of the columns, large and small, suggests irregu-
larities in the mass which disturbed the uniform advance of the lines
of maximum strain and caused them to deviate from parallelism.
The superficial banding of the large vertical columns by nearly
horizontal notches or grooves, resembling layers of bricks or rude
chiseling, appears to be simply a modification of the plane of the
crack.
The paper closes with a description of the microscopical charac-
ter of the Orange rock, which from its identity with many recvnt
basalt flows leads the writer to the conclusion that it should be
classed as a coarse-grained basalt or dolerite, as Prof. E. S. Dr.na
has called the similar rocks in the Connecticut valley.
The occurrence of the rock in question as a surface flow is ren-
dered highly probable by its glassy nature, and the disposition of
the columns, which resembles that of many lava sheets in western
America, as well as of those in central France. G. Poulett Scrope,
in his work on "Volcanos" (2d edition, London, 1872), discusses
the question of the origin and nature of columnar structure in
lavas and other substances, and by a somewhat different course of
reasoning arrives at essentially the same conclusions as those reached
in the present paper.
Mr. W. J. McGee then made a communication on
THE TERRACES OF THE POTOMAC VALLEY.
Remarks were made by Messrs. Ward, Toner, Robinson and
Bates.
GENERAL MEETING. 25
273d Meeting October 10, 1885.
The President in the Chair.
Thirty-nine members and guests present.
Announcement was made of the death since the last meeting of
two members of the Society, Franklin Benjamin Hough and
Washington Caruthers Kerr.
Messrs. J. S. Billings and Washington Matthews made a
joint communication on
anthropometric and reaction-time apparatus.
They exhibited a set of the anthropometric apparatus, devised
chiefly by Mr. Francis Galton, and recently employed in the anthro-
pometric laboratory of the London Health Exhibition. The appara-
tus test acuteness of hearing, strength of vision, color discrimination,
the estimation of the aliquot parts of a line, the estimation of a right
angle, the rapidity of arm movement in striking a blow, the strength
of certain muscles, the weight, the height (sitting and standing),
span of arms, and chest capacity. Their peculiar characteristic is
their simplicity, which permits of their use by the person measured,
with a minimum of instruction and supervision. There was also
exhibited a device by Mr. James McKeen Cattell, for the determina-
tion of the time occupied by various sensations, mental processes
and muscular actions.
There followed an informal discussion by Messrs. H. A. Hazen,
E. Farquhar, Hall, H. Farquhar, Harkness, Mussey, AVood-
ward and Mason.
274th Meeting. October 24, 1885.
The President in the Chair.
Fifty-three members and guests present.
Mr. H. Allen Hazen made a communication on
THE CONDENSING HYGROMETER AND SLING PSYCHROMETER.
[Abstract.]
By way of introduction the results of a few experiments were
given, tending to show the best interval that can be obtained in the
26 PHILOSOPHICAL SOCIETY OF WASHINGTON.
graduation of degrees upon a thermometer scale. These were made
with a common vernier of a mercurial barometer. A mark on the
vernier was placed at each tenth (by estimation) of intervals of .05",
.10", .15", .20", .30", and .40", marked on the limb, and the vernier
read for each estimation. Over 1300 readings were made, and these
showed little difference in the splitting to tenths for the last 5 inter-
vals above, but .05" seemed too small for accurate work.
Results and methods of observing the Alluard form of Regnault's
condensing hygrometer were given. It was shown that if the ther-
mometer immersed in the liquid is placed quite near the plate where
dew is to appear, there is little or no danger of the air as it passess
into the liquid harmfully affecting the thermometer. The com-
plaint of some that the dew is deposited in the air, having a tem-
perature frequently 40 or 50 degrees above the liquid, and hence
that the thermometer can hardly give a correct dew-point tempera-
ture Avas shown to have little weight, since the results, with a slight
difference between the air and dew-point, at which time the effect
would be small, are neai'ly identical with those where the difference
is large, and the effect would be large. It was shown that the great
difficulty in nearly all psychrometric work up to the present time
has been the disregard of a sufficient ventilation of the wet-bulb
thermometer. The sling psychrometer, with a few precautions in
its use, furnishes results entirely satisfactory.
The comparisons so far made between the two instruments have
shown a remarkable uniformity under all conditions of moisture and
temperature, and have left little to be determined in order to make
either apparatus one of precision. A probable effect of compression
of ice on the wet bulb at temperatures of 0° F., and below, was
shown to exist, though this may be due to the lack of conduction
on the part of the ice for the residuum of heat in the bulb. The
question of the effect of height above sea on the indications of the
above instruments was touched upon, and it was shown that the
effect was small and only to be detected by the most refined obser-
vations. Also, that until we have some law for reducing humidity
results to sea level, the propriety of introducing such effect into tables
is questionable.
Mr. T. C. Mendenhall exhibited a new volt-meter devised by
Sir William Thompson. The principal difficulty encountered by
earlier instruments of this class has arisen from the inconstancy of
the magnetic force of the terrestrial field. By this instrument ter-
GENERAL MEETING. 27
restrial magnetism is eliminated. The force produced by the current
is opposed by a weight and is thus measured in terms of gravity.
Mr. Mendenhall also renewed the discussion of the preceding
evening on reaction time, reciting the methods and results of his
own experiments in 1871.
Remarks on the volt-meter were made by Mr. Elliott, on re-
action time by Messrs. Paul, Mason, and Matthews.
Mr. William Harkness made a communication on
FLEXURES OF TRANSIT INSTRUMENTS,
pointing out that the flexures induced by the weight of a transit, in
positions other than vertical, are not eliminated by reversing the
instrument, and developing equations for the discussion of the errors
so far as they can be determined by the aid of collimators.
275th Meeting. November 7, 1885.
The President in the Chair.
Sixty-nine members present.
Mr. F. W. Clarke made a communication on
AN ATTEMPT AT A THEORY OF ODOR,
in which he accounted for the lack of knowledge as to the con-
ditions of action of this sense by the difficulty of dissociating it from
taste; and, while disclaiming any thought of attempting a physio-
logical explanation of the sense, proposed the following as the essen-
tial objective conditions
:
1. To be odorous, a substance must be volatile, so that it may
come into contact with the mucous tissue of the nose, and
2. It must be chemically unstable, so that it may undergo chemi-
cal changes in contact with that tissue.
Mr. Clarke gave some confirmatory instances, from the compounds
of hydrogen with sulphur, selenium, and tellurium, and from the
Cn H2Q 2 group of acids (formic, acetic, etc.)
Mr. Antisell called attention to the connection between a low
boiling-point and simplicity of chemical constitution, and to the
associated fact that organic substances containing a large number
28 PHILOSOPHICAL SOCIETY OF WASHINGTON.
of equivalents of carbon are inodorous. He ascribed the smell of
prussic acid to arriere-gout rather than true odor. *
Mr. Billings showed that from the peculiarly exposed condition
of the olfactory nerve-terminal, it was subject to irritations that
must be distinguished from odors properly speaking.
Mr. Clarke then made a communication on
THE FLOOD ROCK EXPLOSION,
in which he described the arrangements for observing earth tremor
at stations near New York city, and particularly that at Ward's
Island, occupied by Mr. Mendenhall and himself. The tremor was
felt at that station a full second before any disturbance was seen
in the surface of the water above Flood Rock.
Mr. C. F. Marvin, in a communication on the same subject, de-
scribed the form of seismoscope used, in which a small agitation
closed an electric circuit, and sounded an alarm.
Mr. Paul followed with a communication on the same subject.
Mr. Clarke quoted some results of observations made at Gen.
Abbot's stations, giving a mean velocity for the tremor from Flood
Rock to Pearsall's of 2.6, and to Patchogue of 2\ miles per second,
and thus indicating a retarded rate of transmission.
Mr. Robinson suggested that the blasts at the new water-works
reservoir would afford a good opportunity for measuring the velocity
of earth tremors.
Mr. H. Farquhar spoke of the sounds coincident with the flight
of meteors reported by some observers, as indicating the need of
caution in accepting observations of sound in this connection.
Mr. Robinson had distinctly heard two sounds after blasts at the
water-works; one immediately following the tremor, through the
earth, and a later one through the air.
Mr. Chatard had made a similar observation in connection with
mining blasts.
Mr. Dutton said that his impression, from eruptions of Hawaiian
volcanoes, had been otherwise, and that the general testimony with
regard to earthquakes is that the sound precedes the shock.
general meeting. 29
276th Meeting. November 21, 1885.
The President in the Chair.
Fifty-seven members present.
Announcement was made of the election to membership of Mr.
Thomas Hampson.
The Chair communicated to the members an invitation from the
Chemical Society to attend its meetiug on December 10th and listen
to the address of its retiring president, Prof. F. W. Clarke.
Mr. G. Brown Goode and Mr. C. V. Riley made communica-
tions on
THE SYSTEMATIC CARE OF PAMPHLETS,
exhibiting the appliances employed by them and illustrating their
methods.
Mr. Goode furnishes each pamphlet with a firm, durable cover,
by which it is protected from injury, and at the same time kept
separate for convenient use and classification. Photographs, draw-
ings, newspaper clippings, etc., are preserved in the same manner.
[A full description of his appliances may be found in Science, vol.
VI, p. 337.]
Mr. RiLEy employs inexpensive, flexible covers, occupying less
space, and stores them in the " institute pamphlet case."
Mr. B. Pickmann Mann, being invited to participate in the dis-
cussion, exhibited his method of binding pamphlets together, a method
in which four holes are punched at standard intervals in each pam-
phlet and corresponding holes, in flexible hinges to stiff covers, so
that a convenient volume can be made up by merely inserting and
tying two cords, and any desired rearrangement or insertions can
be made, the holes for binding always corresponding. [See Science,
vol. VI, p. 407, and Library Journal, vol. VIII, p. 6.]
Mr. Billings described the tin boxes used in the storage of the
immense file of pamphlets in the library of the Army Medical
Museum. Mr. Ward and Mr. Toner spoke in approval of the
substantial covers adopted by Mr. Goode. Messrs. Gilbert, Toner
and Harkness opposed the binding of several pamphlets together,
believing that such combination interferes with their use and ready
classification and reclassification.
Other remarks were made by Messrs. Dall, Mussey, and Doo-
LITTLE.
32
30 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. J. S. Billings made a communication on
GERM CULTURES,
exhibiting specimens of cultures of chromogenetic and pathogenetic
micro-organisms, to illustrate the improvements in methods of
investigating these organisms which have been made of late years.
Attention was called to the value of culture upon semi-solid media
such as peptonized gelatin, agar agar, coagulated blood serum, etc.,
as a means of differentiating micro-organisms, and of obtaining pure
cultures to be used for experimental purposes; and the applications
of the method to testing the efficacy of disinfectants, to water
examinations, &c, were pointed out.
277th Meeting. December 5, 1885.
By courtesy of the officers of the Columbian University, the
meeting was held in the law lecture room of the University build-
ing. Members of the Anthropological, Biological, and Chemical
Societies and their friends were present by invitation.
Vice-President Billings occupied the Chair.
Present, one hundred and sixty members and guests.
The President, Mr. Asaph Hall, read his annual address, taking
for his subject
:
AMERICAN SCIENTIFIC SOCIETIES.
[Printed in full on pp. xxxiii-xlvil]
A resolution of thanks was moved and unanimously passed.
278th Meeting. December 19, 1885.
the fifteenth annual meeting.
The President in the chair.
Thirty-eight members present.
The minutes of the 260th, 276th, and 277th meetings were read
and approved.
GENERAL MEETING. 31
The Chair announced the election to membership of Mr. Jacob
Lawson Wortman.
The report of the Secretaries was read and accepted.
The report of the Treasurer was read, received, and referred to
an auditing committee, consisting of Messrs. J. M. Toner, O. T.
Mason, and T. C. Mendenhall.
On motion of Mr. Harkness, the thanks of the Society were
tendered to the Treasurer and Secretaries for the efficient perform-
ance of the duties of their offices.
Officers were then elected for the year 1886. (The list is printed
on page xv.)
The rough minutes of the meeting were read, and the Society
adjourned.

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
MATHEMATICAL SECTION.
33

STANDING RULES
MATHEMATICAL SECTION,
1. The object of this Section is the consideration and discussion
of papers relating to pure or applied mathematics.
2. The special officers of the section shall be a Chairman and a
Secretary, who shall be elected at the first meeting of the Section
in each year, and discharge the duties usually attaching to those
offices.
3. To bring a paper regularly before the Section it must be sub-
mitted to the Standing Committee on Communications for the
stated meetings of the Society, with the statement that it is for the
Mathematical Section.
4. Meetings shall be called by the Standing Committee on Com-
munications whenever the extent or importance of the papers sub-
mitted and approved appear to justify it.
5. All members of the Philosophical Society who wish to do so
may take part in the meetings of this Section.
6. To every member who shall have notified the Secretary of the
General Committee of his desire to receive them announcements of
the meetings of the Section shall be sent by mail.
7. The Section shall have power to adopt such rules of procedure
as it may find expedient.
35
OFFICERS
MATHEMATICAL SECTION FOR 1885.
Chairman, G. W. Hill. Secretary, Marcus Baker.
LIST OF MEMBERS WHO RECEIVE ANNOUNCEMENT OF THE
MEETINGS.
Abbe, C.
Avery, K. S.
Baker, M.
Bates, H. H.
Billings, J. S.
Burgess, E. S.
Christie, A. S.
Coffin, J. H. C.
Curtis, G. E.
DeLand, T. L.
DOOLITTLE, M. H.
Eastman, J. E.
Eimbeck, W.
Elliott, E. B.
Farquhar, H.
Flint, A. S.
Gilbert, G. K.
Gore, J. H.
Green, B. E.
Hall, A.
Woodward, E. S.
Hall, A. Jr.
Harkness, ~W.
Hazen, H. A.
HlLGARD, J. E.
Hill, G. W.
HODGKINS, H. L.
King, A. F. A.
Kummell, C. H.
Lefavour, E. B.
McGee, W. J.
Newcomb, S.
Paul, H. M.
Kavene, G. L.
Eitter, W. F. M'K.
EOBINSON, T.
Smiley, C. W.
Stone, O.
Taylor, W. B.
Upton, W. W.
WlNLOCK, W. C.
36
BULLETIN
OF THE
MATHEMATICAL SECTION,
16th Meeting. January 7, 1885.
The Chairman, Prof. Asaph Hall, presided.
Nineteen members and guests present.
Election of officers of the Section for the year 1885 was then
held and resulted in the selection of Mr. G. "W. Hill as Chairman
and Mr. Marcus Baker as Secretary.
Mr. E. B. Elliott then presented a communication entitled
example illustrating the use of a certain symbol in the
calculus of affected quantity.
The example selected was a demonstration of the Pythagorean
Theorem by the aid of a new symbol.
Mr. Marcus Baker presented a communication entitled
A COLLECTION OF FORMULAE FOR THE AREA OF A PLANE
TRIANGLE,
which elicited some criticism of details and of notation.
[This paper is published in full in the Annals of Mathematics,
vol. 1, No. 6, and vol. 2, No. 1.]
Mr. W. C. Winlock (by permission of Rear Admiral S. R.
Franklin, Superintendent U. S. Naval Observatory) presented a
communication on
PHYSICAL OBSERVATIONS OF WOLF'S COMET (1884 III).
[Abstract.]
The first observation of Wolf's comet that I obtained was with
the transit circle of the U. S. Naval Observatory on September 24,
37
38 PHILOSOPHICAL SOCIETY OF WASHINGTON.
1884. The aperture of the instrument is 8 inches and the magni-
fying power employed 186.
On October 13, using the 9-inch equatorial and a power of 132,
" the comet seemed to be a circular nebulous mass with quite a
well marked central condensation. The nucleus was not sharply
defined, but blended gradually into the fainter light surrounding it."
Nov. 8. Transit circle. Nucleus quite well defined. Faint but
not difficult to observe.
Nov. 12. Transit circle. Nucleus elongated in the preceding fol-
lowing direction and apparently composed of a number of bright
points. Faint and difficult to observe. The nebulous envelope
seems to extend farther on the upper or south side than on the lower
side. Seeing, very poor.
Nov. 13 with the 9-inch equatorial and the same power as before
a sketch (omitted here) was made. The remarks I give sub-
stantially as in my note-book : Watched the comet carefully for
about an hour (seeing not very good,—a little fog hanging over the
river). It is a very slightly oval nebulous object. The central
part is a little condensed ; the nucleus proper more so. Filar
micrometer measures give for the extent of the outer nebula, meas-
ured in the direction of a circle of declination, V 52", and for the
inner disc 18". The nucleus is perhaps extended a little in the
preceding following direction, but I looked in vain for any indica-
tion of the beaded appearance which I thought I saw last night
with the transit circle. I might add that using the distance of the
comet given in Kriiger's ephemeris these measures would represent
distances of 47,000 and 7,500 miles, respectively. No tail.
Nov. 20. Transit circle. Nucleus stellar, 10th magnitude.
On November 22 another observation was obtained with the
9-inch equatorial, magnifying power 132 as before. Micrometer
measures of the outer nebula and the inner disc gave V 30" and
16", respectively, differing but little from the measures of the 13th.
Seeing, fair. The following note was made : I divide the comet
into three parts, the outer nebula, the inner envelope (or coma I
presume it might be called), and the nucleus proper. It is almost
impossible to assign a definite limit to this outer envelope, Avavering
and flickering like a mass of smoke, but the micrometer measures
will fix it roughly. The inner envelope blends into the outer with-
out any sharp division, though there is sufficient difference in bright-
ness to attempt a measurement. The inner envelope condenses in
turn into the brighter nucleus.
MATHEMATICAL SECTION. 39
Nov. 24. Transit circle. Nucleus sharp and stellar and about
10th magnitude.
Dec. 2. Transit circle. Seeing poor. Extremely faint. Like a
12.5 magnitude star, surrounded by a large but faint nebula.
Dec. 8. 9-inch equatorial and power 132. The diameter (in de-
clination) of the outer envelope, from a micrometer measurement,
w,as 2' 21", the seeing being noted a little better than on Nov. 22.
Occasionally I think I see the inner condensed disc, but am not
sure of it ; also think that at times there is an indication of a more
or less rounded outline to the head on the south preceding side, but
it is unstable. Cannot be sure of anything like a tail, and indeed
any definite form other than an irregular circle is, after all, largely
a matter of imagination.
The communication gave rise to some comment and discussion
on the difficulties encountered in making satisfactory observations
of faint comets and also on the resisting medium in space.
Mr. Taylor called the attention of the Section to
A SLIGHT MODIFICATION OF THE NEWTONIAN FORMULA OF
GRAVITATION
with which he had been struck in reading Mr. Bates' paper on " The
Physical Basis of Phenomena" recently read before the General
Meeting. (See vol. vii, p. 51.)
[Abstract.]
There is a widespread fallacy
—
particularly displayed by those
kinematists who fancy they have an exceptional insight into the
" mechanism of gravitation," that this influence is simply a
radiant emanation, necessarily observing the geometry of radial
space relations, having as such emanation the same total energy
on all concentric spheres whatever their radii, as in the case of
luminous radiation for example. Of course every well instructed
astronomer and physicist knows that this is not so. In truth " the
inverse square " is not geometrical—not a square at all, having no
relation whatever to surface,—but simply an algebraical second
power, very much like the familiar " velocity squared " (m v X v,
or momentum multiplied by velocity), which forms the measure of
all kinetic energy and which no one supposes to represent a square.
40 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Our late colleague, General Alvord, in confutation of this not un-
usual misconception, made a communication to the Society some
two or three years ago (as those present doubtless remember) in
which he showed that as gravitation was known to act equally on
every particle of matter (i. e. proportionally to the mass) and as
solid homogeneous spheres subtending any given conical angle from
a center of reference possess volumes (or masses,
—
d being constant)
directly proportional to the cubes of the conical altitudes or radii
of distance, it follows— if gravity were a radial emanation—its
effect must obey the law of inverse cubes of distance, contrary to the
facts of observation.
The fallacy here criticised springs evidently from the too common
tendency to regard gravitation simply as a central force or as a
single influence radial in direction, whereas it is always a duplex
and reciprocal action ; and however insignificant one of the terminal
elements its presence and measure of distance cannot be neglected
without completely nullifying all action. Thus m and mf being
two masses at any given distance apart, the action in the direction
and through the distance m' m, is as real and positive as that in the
direction and through the distance m m'. In other words, it would
seem that the mutuality of the re-action necessarily involved with it
the idea of reciprocity of the distance relation. Thus, adopting the
suggestion of Mr. Bates, if we write the formula of the effect as
(m -p- d) X (wi' -r- d), we have this reciprocity distinctly brought
out, and obtain at once the Newtonian formula. The speaker wished
to learn from those more conversant than himself with mathemati-
cal literature whether the suggested modification is new, and also
whether any mathematical objection appears to its form.
Mr. Hill remarked that one fault of the notation proposed ap-
peared to be its want of generality, as it is evidently inapplicable to
any other force having a higher or different exponent of the space
function.
Mr. Doolittle observed that, admitting the " reciprocity of the
distance relation," he yet failed to perceive how this function could
appear in the formula as a product. Why should we write the dis-
tance twice taken—as d multiplied by d rather than as d plus dt
Further remarks were made by Messrs. Elliott, Bates, and
Robinson.
mathematical section. 41
17th Meeting. February 10, 1885.
The Chairman, Mr. G. W. Hill, presided.
Present, eleven members and one guest.
In the absence of the Secretary the reading of the minutes of the
last meeting Avas deferred, and Mr. R. S. Woodward designated as
Secretary pro tern.
Mr. Kummell made a communication on
AN ARTIFICE SOMETIMES USEFUL FOR THE ADJUSTMENT OF
CONDITIONED OBSERVATIONS.
[Abstract.]
The general process consists in multiplying equations of condition
by such factors as will extinguish side-coefficients in the normal
equations for correlates. This was shown to be possible in an infinite
number of ways. One such way leading to linear equations for the
multipliers was shown to require for the extinguishment of all the
side-coefficients the solution of the normals, i. e., the very work
which was to be evaded. The method would, however, be advan-
tageous for the partial extinguishment of large side-coefficients, and
the normal equations could thus be solved with advantage by Gauss'
indirect method. A useful symmetrical rule was given for extin-
guishing the side-coefficients for a pair of conditions. Illustrations
of this rule in the adjustment of simple geometrical figures were
given, beginning with a simple figure of two triangles and extend-
ing to a complete pentagon.
Mr. Hill remarked that Jacobi had proposed a similar method
for removing side-coefficients. Further remarks were made by Mr.
"Woodward.
The next communication was by Mr. Gustave L. Ravene on
THE THEORY OF MERCURY.
[Abstract.]
The method here used of computing the secular variation of the
elements of an orbit is due»to Gauss.
42 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The notation employed for the disturbed body is
t: = longitude of perihelion
;
= longitude of the ascending node
;
i = inclination to the ecliptic
;
a = mean distance from the sun
;
n = mean annual motion ;
e = eccentricity
;
tp = eccentric angle = arc sin e
;
r = radius vector
;
/ = true anomaly ;
c = eccentric anomaly
;
w = mass; and the same symbols with accents, r', 0', i', etc, rep-
resent corresponding quantities for the disturbing body.
From the definition of the secular perturbations, according to
Gauss, the perturbing function may be expressed by
2*2*
v m' C f1 — ecose
o o
in which p is expressed by
p
2 = d2
-J- r
2
— 2a' r cos (a', r).
We also have
r
2 = a2 (1 — e cos e)2
aV cos (a',r) = a' cos e' {cos * (a cos e — ae) — a cos <p sin e sin * ]•
-f- a ' sin e' la cos y> sin e cos s -f* sin r (a cos e — ae)}.
Putting for brevity
a2 (1 — e cos e) 2 —- p
2 {cos * (a cos e — ae) — a cos f sin e sin *} = 9£
2 {sin *(a cos e — ae)
-f- a cos <p sin e cos *} = se
we get
P
1
= (a'2 + p£) — a' (o£ cos e' + s£ sin e')-
The differential equation for the secular variation of the peri-
helion is
an |/1 — e2 dV
a* = —p.—; r— • —y at
(1
-f- m)e de
MATHEMATICAL SECTION. 43
and also
dV mf C , C J cos s 1 — e cos £ cl(P2 ) "I „
,
rfT = -4^J deJ \~T~~ +
—W— ' ~dT r£ -
If we now put
A = — a cos n — ae cos £ cos r
-f- sin tt sin e
e ' COS <p
a (2 - e2 ) .
sin r sin £ cos s + la cos - cos" e :
cos 9? '
'
£ = — a sin - — ae cos £ sin r — cos n sin £
a (2 e2)+ cos - sin £ cos £ 4- 2a sin - cos2 £
;
cos <p
' '
we obtain
dV m' a' r j feose' fsin/, 1
V 2 f C&
This expression contains the following integrals
2-
R
~JWl + ^)-«'
<fe'
j (a'
2
i> ) —
«' $ cos e' — a' 8 sin e' I
2*
5
-/{(«"
sin e' c?£
j(a'2 + jp ) — a' 5 cos e' — a' s sin efl 2 '
o
2rr
COS e' de'T
~/{(«"2 + A)-*j (a' ^£) — a' q cos e' — af 8 sin e' i 2 *
o
which must be computed for every value of £ obtained by dividing
the circumference into,?' parts.
If we put
a'
2
+P
e
= x ! <£ % = 9 cos Q ; a' S£ = q sin Q,
we get
j (a'
2 + p ) — a' g cos e' — a! s sin e'l~*
= {A-5cos(£'- Q)}~1
(3) (3) n)
= a + 2at cos <Y - Q) + 2a2 cos 2 (V - Q) + - .-
44 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The quantities a . av a2 , etc., may be computed by Hansen's for-
mulae given in his work, Auseinandersetzung, etc., 1 Abth., § 61,
and when found R, S, aud T are found from the formulae
R = 2a - ; S = 2av sin Q ; T — 2a,, cos Q.
It would be interesting to know what influence the supposed
intra-Mercurial planet would have on the other bodies of the
system, especially on Venus.
The differential equation of the motion of the ascending node is
dd
_
365.25 k dV
dt \/ a (1 -|-m)sin i di
The quantity k is the well known Gaussian constant, expressed in
seconds of arc, and its logarithm is log k = 3.5500065746.
The value of />2 is expressed by
p
2 = a2 -}- a
n
— 2aa' cos (a7
,
a)
from which we have
dip2) n , d [cos (a, a')]
-
dT =-2aa m
But cos (a, a') = cos e cos e' -j- sin e sin e' cos I,
cos I= cos i cos $
-f- sin i sin i' cos (0 — 0'),
cot $ sin {6 — 0') — cot i' sin i = — cos (0 — 0') cos i.
Differentiating we get
d<p sin2$
di - rin(g-0 (c0i * C0S • + C°S (* " ^ Sln ° = h '
We also have
d (COS J) ..... • • •/ fa af\ *
—
^-p = — cos i sin i + cos % sin % cos {d — ff) = t2 .
From these expressions we obtain
oleosa, a')
= ^_ cog £
,
gin g + g
.
n £
,
cQg g cQg j^ + gin £, gin ( ^
and therefore d(p*) becomes
—^V = p cos e + Q sm £
in which
» = 2aa' sin e t,
c
and
g = — 2aa' (cos e cos I tx -f- sin e £8).
MATHEMATICAL SECTION. 45
The expression -p wu"l m tfte actual computation be written in
the form
in which
do
_
365.25 k m'
di |/a (1 + m) sin i 2*
jC= Tp
c
+ %
Using the values 0'= 14° 36', a' = 0.200,/ = 7°,andro'= k2000000
derived by me some time since for the intra-Mercurial planet, the
perturbation of the node of Venus' orbit is found to be
do = - 3."92120
in a century.
Mr. Hill, commenting on this paper, discussed briefly the prob-
able mass aud density of Mercury on grounds of probability and
analogy, pointing out that its density would on such grounds appear
to be far less than the ordinarily accepted value.
18th Meeting. April 15, 1885.
In the absence of the Chairman, Mr. Doolittle was made Chair-
man pro tern.
Present, ten members and one guest.
Minutes of the sixteenth and seventeenth meetings were read and
approved.
Mr. Marcus Baker then read the following paper on
A GROUP OF CIRCLES RELATED TO FEUERBACH's CIRCLE.
In any plane triangle the middle points of the sides and the feet
of the perpendiculars drawn from the vertices to the opposite sides
are six points in the circumference of a circle. This circle also
bisects the segments of the perpendiculars between orthocenter and
vertices, thus making nine noteworthy points. These properties
33
46 PHILOSOPHICAL SOCIETY OF WASHINGTON.
were first published in January, 1821, in Gergonnes' Annales, vol.
II, in a memoir by Brianchon and Poncelet on tb.e determination
of an equilateral hyperbola from four given conditions.
In 1822 Prof. K. W. Feuerbach, of Nurenburg, showed that this
circle is tangent to the inscribed and three escribed circles. This
property is known as Feuerbach's theorem, and the circle is known
to the Germans as Feuerbach's circle, In 1828 Steiner showed that
this circle passed through twelve noteworthy points and was tangent
to the in and escribed circles. This was done without a knowledge
of the earlier work by Feuerbach.
In 1842 Terquem, the editor of the Nouvelles Annales de Mathe-
matiques, called it the nine-points circle. In some books it has been
called the six-points circle. In an article, by myself, in the Mathe-
matical Magazine for January, 1882, I have called it the twelve-
points circle.
Of the twelve points considered noteworthy six are in the sides
of the triangle and six are not. If all the noteworthy points now
known are to determine its designation, then twelve-points circle ap-
pears to be a proper designation. If only those points in the sides
of the triangle should determine the designation then six-points circle
would appropriately name it. In either case nine-points circle would
be an imperfect designation, and as the name Feuerbach's circle was
the first name it received it seems on the whole best to adhere to it.
A somewhat analogous case is the seven-points circle known as Bro-
card's circle, not named for the number of noteworthy points it
contains but for its discoverer. The name twelve-points circle may
therefore be rejected and the name Feurbach's circle adopted.
The following proof of the fundamental properties of Feuerbach's
circle is offered as being simpler than that usually given
:
Preliminary.
1. Definition. When we determine upon a right line AB a point
Csuch that AC= BC — h AB the line is said to be bisected.
This restricts us to one point C.
Fig. 1. C A C B C"
!
t r t t
It will be found convenient in what follows to extend this
definition so as to include the points C and C", Fig. 1, where
AC = BC = AC — BC" = h AB ; i. e., by considering a defi-
MATHEMATICAL SECTION. 47
nite line AB to be bisected when a segment equal to one-half the line is
laid offfrom either extremity in either direction.
2. Theorem. The perpendiculars of a plane
triangle meet in H, and, being prolonged to
intersect the circumference in A', B', C , the
segments HA', HB' and HC are bisected by
the sides of the triangle. {See Fig. 2.)
Proof: AB'D = AHD = angle C.
Note.—Here bisection is used in its ordi-
nary sense.
H is the orthocenter, and the theorem may be otherwise stated as
follows : The segments of the perpendiculars included between the
orthocenter and circum-circle are bisected by the sides of the triangle.
The point of intersection of the medians is the eidocenter,* which
we call G, and the well-known theorem that the medians are con-
current and mutually divided into segments of which the greater is
twice the less may be otherwise stated thus : The segments of the
medians included between the eidocenter and vertices are bisected by
the sides of the triangle.
Note.—Here bisection is used in its extended sense.
Using bisection in this extended sense it is therefore possible to
unite these propositions into a single general statement, as follows
:
The segment, of the {P^f^ *««» *» {SSSST
f f
and circumcircle measured
-I f
wa
^
rom
the vertices are bisected
( towards
by the sides of the triangle.
Thus in Fig. 3.
aH= aL=\ HL; and EP= h EA;
m=m= i HM; EQ = hEB;
rH= rN = i HN; ER=l EC.
3. Conceive the triangle ABC (Fig. 4) and
its circumcircle to be the base of an oblique
cone withinscribed tetrahedron. Let the ver-
tex of this cone be so taken that when the whole is projected
* This term from e
r
ido$, form, and xivTpov, center, has been suggested by
Mr. Henry Farquhar as being a more accurate derivation than the term
centroid often used. It is, moreover, analogous to orthocenter, circum-
center, etc.
48 PHILOSOPHICAL SOCIETY OF WASHINGTON.
upon the plane of the base the projection of the vertex shall fall at
the orthocenter H. Now let the whole be orthogonally projected
upon the plane of the base.
Fig. d.
From this conception it is seen that HA, HB, HC and HA',
HB', HC are projections of elements of the cone and HO the
projection of the axis. Let the axis of the cone be bisected by
planes parallel to the base. There are three such bisecting planes
:
one midway between apex and base, another below the base, and a
third above the base. Finally let all these sections be orthogonally
projected upon the plane of the base.
From these conceptions it follows immediately that
—
(a.) These projections are circles whose diameters are, respect-
ively, i, f, i, the diameter of the circumcircle.
(6.) The centers of these circles F, F/, F", all lie in the line HO,
MATHEMATICAL SECTION. 49
joining the circum center to the orthocenter, and are points of
bisection, in the ordinary and extended sense, in such manner that
FH= FO=F' = F"H= I HO.
(c.) The segments of the perpendiculars HA, FEB, HC, and HA',
HBf
,
HC are all bisected by each of these circles. In the case of
the first circle F, the segments are bisected in the ordinary sense,
and since the segments HA', HB', and HC are also bisected by
the sides of the triangle this circle p>asses through the feet of the per-
pendiculars.
The points of bisection on the perpendiculars determined by the
circle F are points of bisection in the ordinary sense.
The points of bisection on the perpendiculars determined by the
f F'
circle
-j pf, are points of bisection in the extended sense, and in
such wise that the segments cut off from A and A', B and B', C and
f towards
( away from
(d.) Every line drawn' from H to the circumcircle is bisected by
the three circles F, F', and F". H is therefore a direct center of
similitude common to the circles 0, F, and F' and an inverse
center of similitude common to all four circles.
4. The eidocenter is collinear with the circumcenter, orthocenter,
and Feuerbach center*; for from a known theorem we have
HB = 2 OM, and therefore HO must divide BM into segments of
which the greater is twice the less, i. e., it must pass through the
eidocenter.
5. Again conceive the triangle AB C (Fig 5) as the base of an
oblique cone, etc, as in section 3, except that its vertex is to be con-
ceived as perpendicularly over the eidocenter instead of over the
orthocenter, and the whole projected as before. In this case FA,
EB, EC, and EA', EB',EC are projections of the elements of the
cone and EO, coincident with HO from section 4, the projection
of the axis.
Let the axis be bisected as before by three planes parallel to the
base : one midway between apex and base, another below the base,
and a third above the apex, and the sections so formed projected
upon the plane of the base.
*The center of Feuerbach 's circle may be so called for brevity.
50 PHILOSOPHICAL SOCIETY OF WASHINGTON.
We then have
—
(a.) These projections are circles whose diameters are, respect-
ively, \, f, and \, the diameter of the circumcircle.
Fig. 5.
(b.) The centers of the circles F", F'" , F all lie in EO and there-
fore in HO joining circumcenter to orthocenter and are points of
bisection of EO in both the ordinary and extended sense in such
wise that F" E = F" = F'" = FE = i EO.
(c.) The segments of the medians EA, EB, EG and EA! , EB',
EC are all bisected by each of the circles. In the case of the
third circle F, the segments are bisected in the extended sense, and
since the segments of the medians, EA, EB, EC, are also bisected
in the extended sense by the sides of the triangle the circle F bisects
the sides of the triangle.
The points of bisection on the medians determined by the circle
F" are bisections in the ordinary sense.
MATHEMATICAL SECTION. 51
The points of bisection on the medians determined by the circles
f F'"
j p are points of bisection in the extended sense, and in such
manner that the segments cut off from A and A', B and B', C and
C are measured from the eidocenter \ ? the vertices.
( away from
(d.) Every line drawn from E to the circumcircle is bisected by
the three circles F", F'", F ; E is therefore a direct center of simili-
tude common to three circles 0, F" , F'" and an inverse center of
similitude common to all four circles.
6. If we now compare figures 4 and 6 and consider the three
circles in each which resulted from projection, we find that circle F,
and only circle F, is identical in the two figures.
This identity appears from the fact that their diameters are equal,
each equaling half the diameter of the circumcircle, and their cen-
ters coincident. The coincidence of their centers appears from
drawing the projections of the axes of the cones side by side, thus
:
F H
I
1 1 From Ficr. 4.
I-
From Fig. 6.
E F
From Fig. 4 we find that this circle, Feuerbach's, passes through
6 noteworthy points, being 2 points on each perpendicular ; and
from Fig. 6 we find that the same circle passes through 6 other
noteworthy points, being 2 on each median, or in all Feuerbach's
circle passes through 12 noteworthy points.
7. It is apparent from the foregoing that if we should not bisect
the axis of the cone but should cut it in any ratio (Fig. 4) by a
plane parallel to the base then the projection of the section would
be a circle cutting the perpendiculars in that ratio and its center Fn
would divide HO in that ratio. The medians would not be divided
in that ratio, but a point in HO exists (call it En ) through which,
if lines be drawn from the vertices to the opposite sides, these lines
would be divided in the given ratio.
The four points 0, En , Fn , H would in this case, as before, be
four harmonic points.
8. Since Feuerbach's circle bisects the sides of the triangle it is
the circumcircle of a triangle similar to the original and of half its
52 PHILOSOPHICAL SOCIETY OF WASHINGTON.
size. The results here deduced may therefore be considered to be
results of a comparison of the circumcircles of these two triangles.
A corresponding study of the relations of the tangent circles (in-
and escribed) would therefore be expected to yield many more
properties as there are four times as many circles to be considered.
Concerning the phrase " bisection in the extended sense," Mr.
Doolittle suggested that the term " sesquisection " might be advan-
tageously employed. As to the name "nine-points circle," Mr.
Kummell said that it was plainly defective, either " six-points "
or " twelve-points " circle being satisfactory, according to the point
of view taken, but that nine-points circle was not a correct desig-
nation from any point of view. Further remarks were made by
Mr. Elliott.
Mr. C. H. Kummell presented a communication entitled
DISTANCES ON ANY SPHEROID.
[Abstract.]
The present form of solution of the problem to determine the
shortest distance between two points on a spheroid which are given
by their latitudes and longitudes is characteristic in making use of
the Gaussian algorithm of the arithmetico-geometric mean. This
and a corresponding transformation of the amplitudes give the
necessary elements for computing in three terms the distance precise
to the eighth order at least. The form is also remarkable for its
symmetry and easy extensibility to still higher precision.
Also the preliminary part of the problem in which the excess of
the spherical longitude over the spheroidal is determined by succes-
sive approximations is much facilitated by the introduction of an
angle *7, which is closely related to e, the angle of eccentricity, and
which varies between and £. It was thus possible to express the
excess of spherical over spheroidal longitude in one term, precise to
the 6th order at least
[This paper has been published in, full in the Astronomische
Nachrichten, No. 2671.]
In reply to a question, Mr. Kummell said that the ordinary for-
mulae for computing distances between intervisible points on the
terrestrial spheroid are all that can be desired. The formulae here
MATHEMATICAL SECTION. 53
presented, however, are designed for much greater distances and
for any spheroid, and would serve, if need ever arose, for comput-
ing the shortest distance between any two points on the terrestrial
spheroid no matter how remote.
19th Meeting. April 29, 1885.
The Chairman, Mr,, G. W. Hill, presided.
Present, nineteen members and one guest.
Minutes of the eighteenth meeting read and approved.
Mr. A. Ziwet read a paper entitled
on grassmann's system of geometry.
This paper will appear in full in the Annals of Mathematics, vol.
2, Nos. 1 and 2.
In reply to a question by Mr. Curtis as to whether Grassmann's
system could be advantageously substituted for the Cartesian sys-
tem, Mr. Ziwet expressed the opinion that it could not be so sub-
stituted in general, but that it might in certain special cases.
Grassmann has not, said Mr. Ziwet, made applications of his
method to astronomy, nor indeed does its value consist in its
adaptability to the solution of special problems. But for present-
ing general geometrical truths it appears superior to Hamilton's
methods, to which it is closely related and with which it might be
advantageously joined.
Mr. Hall remarked that he had seen planetary orbits worked
out after Hamilton's method by J. Willard Gibbs, but the process
appeared rather more laborious than the usual Gaussian one.
The labor of computation of results, Mr. Hill remarked, was
practically the same by all methods. By introducing the needful
symbols the general expressions may be made exceedingly simple,
but when the numerical work begins it will be found that after par-
ing off more or less extraneous matter there still remains a central
kernel or core of computation from which there is no escape by
any method whatsoever.
With this view Mr. R. S. Woodward heartily concurred, and
added that the supreme test of the usefulness of such systems as
54 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Grassruann's, Hamilton's, etc., consists in their ability to reveal new
truths ; a test which, according to Mr. Ziwet, Grassmann's system
successfully stands.
Mr. M. H. Doolittle presented a communication on
CAUSE AND CHANCE IN THE CONCURRENCE OF PHENOMENA.
The author's views set forth in this communication were stated
to be preliminary and incomplete, and he therefore reserves them
to be more fully elaborated before publication.
20th Meeting. May 13, 1885.
The Chairman, Mr. G. W. Hill, presided.
Present, eleven members and three guests.
Minutes of the nineteenth meeting, read, corrected, and adopted.
Mr. G. L. Ravene read a paper entitled
THE ASTEROIDS.
This communication elicited a general discussion, participated in
by Messrs. Kummell, Ritteb, Baker, Woodward, Elliott,
Paul, and Hill.
Mr. Ritter then read a paper on
SECULAR PERTURBATIONS OF POLYHYMNIA BY JUPITER.
[Abstract.]
In the computations of these perturbations Gauss's method has
been employed, using the formulas adapted to facilitate the appli-
cation of this method given by Mr. G. TV. Hill.
The eccentricity of Polyhymnia being very large the circum-
ference, with reference to the eccentric anomaly of Polyhymnia,
has been divided into twenty-four parts. This is a greater number
than necessary, but it seemed worth the additional labor required
to have the forces and the other quantities involved for as large a
number of points as practicable.
MATHEMATICAL SECTION. 55
The epoch for both systems of elements is 1873, July, 17.0,
Berlin mean time.
The ecliptic and mean equinox are for 1873.0.
The resulting secular variations in one Julian year are the fol-
lowing :
Secular variation of the eccentricity, or 5e= + 1".268
" inclination, or <S{ = — 1.649
" ascending node, or 8£i= — 61.031
"
" longitude ofthe perihelion, or 8it= + 59.116
"
" mean longitude, or dL= — 83.429
The paper was discussed by Messrs. Paul, Hill, and Wood-
waed.
21st Meeting. May 27, 1885.
The meeting was called to order at 8:15 by the Chairman, Mr.
G. W. Hill.
Seventeen members present.
At the request of the Chair Mr. Winlock acted as secretary pro
tern., Mr. Baker being absent.
Mr. R. S. Woodward read a paper on
SOME PRACTICAL FEATURES OF A FIELD TIME DETERMINATION
WITH A MERIDIAN TRANSIT.
[Abstract.]
An important desideratum in all kinds of field work is the
adoption of those methods which will secure the accuracy essential
in the results sought with the minimum amount of computation.
It is in general easier and more conducive to precision to eliminate
unnecessary factors involved with the quantity sought than to
determine their values and allow for them by computation. Very
frequently also a systematic arrangement of observations will secure
the maximum precision with the minimum of computation.
In a field time determination for telegraphic longitude' the essen-
tial quantity is the error of the time-piece used at some determinate
epoch, and the unessential factors are the azimuth and collimation
of the transit and the rate of the time-piece. It is evident that a
56 PHILOSOPHICAL SOCIETY OF WASHINGTON.
minimum of computation will be required if the observations can
be so arranged as to eliminate the effect of these factors in the final
value of the correction to the time-piece. Although it is usually im-
possible to eliminate the effect of the azimuth, collimation, and rate
completely, it is generally possible to make a close approximation
thereto. To show this fact analytically let
At = the correction to the time-piece at the epoch t ;
t bb the observed time of a star's transit
;
a = the star's right ascension
;
a = the azimuth of the transit
;
c = the collimation of the transit;
r = the rate of the time-piece
;
A = the azimuth factor
;
C = the collimation factor;
p = the weight of (t — a) ;
v = the residual error.
Then the type observation-equation will be
At + Aa + Cc + (t — O r + t — a = v. (1)
The normal equation in At, using brackets to indicate summation
of like quantities, is
[p] At + [pA-] a + [>C] c + O (t - U] r + O (t - a)] = 0. (2)
This shows that in order to secure the complete elimination of
the effect of a, c, and r, we must have
[PA] = 0, [pC] = 0, [> (t - Q] = 0. (3)
The last of these conditions can always be fulfilled by making
t -
M- (4-)w (4)
It may be shown that the value of At corresponding to t as
defined by (4) has a maximum weight. A close approximation to
the first two conditions of (3) can be secured by selecting for obser-
vation stars of suitable declinations and by reversals of the tele-
scope.
If we put
equation (2) gives Af = — At — /? a — yc. (5)
This shows that in case /? and y are small, as supposed above, an
MATHEMATICAL SECTION. 57
approximate value of At is — A/ . After some preliminary obser-
vations at a station it is easy to render a and c small, and their ap-
proximate values may always be found from the observation equa-
tions by a brief inspection ; so that with such values of a, c, /?, and
y as are nearly always readily attainable At may be derived from
(5) to the nearest O'.Ol.
We may thus dispense entirely with the other three normal equa-
tions and reach the same result which would follow from their use.
The solution may also be checked ; for by one or two approxima-
tions the values of At, a and c which make [_pv] = can be readily
found.
The practical steps in deriving At from (5) may be summarized
as follows
:
1. The mean of the observation-equations for clamp west minus
the mean of those for clamp east will give an approximate value of
the collimation c.
2. The application of this value of c to each observation equation
will give a corrected value of (t — a) for each star.
3. An approximation to the value or values of the azimuth will
then result by eliminating At from one or more pairs of the corrected
observation equations. The azimuth may then be applied to correct
the values of (t — a), reached in step 2.
4. The approximate values of a and c will now give an approxi-
mate value of At from (5), and the application of this value of At
to the values of (t — a), derived in step 3, will give approximate
values of v.
5. Form \_pv~\. If this sum is not zero within 0".01 or 3.02, a
brief inspection will show what changes in a and c (and possibly
Af) will make it zero within those limits.
By this process of determining the residuals or their approximate
values as soon as possible in the computation any large errors in
the values of (t — a) or the azimuth and collimation factors will be
easily detected.
In precise longitude determinations it is customary to have for
each night's observations two complete time determinations, one
immediately preceding and one immediately following the tele-
graphic comparison of time-pieces. In this case there will be two
values of At Calling these At' and At" and denoting the corres-
58 PHILOSOPHICAL SOCIETY OF WASHINGTON.
ponding epochs by tj and t" the rate of the time-piece will be
given with sufficient accuracy for interpolation by the equation
Af - Af
r = t" — i'
'
l O '0
Mr. Paul thought it an objection to this method that in arrang-
ing the groups valuable stars might be lost, so that in a limited
time the accuracy of the results would be impaired by the smaller
number of observations ; moreover, the method did not furnish the
computer with a clear idea of the performance of the instrument.
Mr. Hall said that he liked the method, and that he thought it
especially good for time work. He had discovered the method once
himself, and he knew that it had also been used by Prof. Ormond
Stone.
Mr. Kummell said that in connection with this subject he had
investigated the question of the advisability of using stars towards
the pole for time determinations ; that is, he had examined the
weight co-efficient formulse to see at what distance north of the
zenith a maximum value would be obtained. He found that in
general the limit of declination was about 60°.
Mr. Paul thought that every weight-formula should take account
of the increase of atmospheric disturbance with increase of zenith
distance.
Mr. Kummell then read the following paper entitled
CAN THE ATTRACTION OF A FINITE MASS BE INFINITE ?
In Price's Calculus, vol. Ill, art. 201, discussing the result for
the attraction of a thin rectangular plate on a particle external to
it and in its own plane it is found that if the attracted particle is at
an angle of the rectangle the attraction is infinite. Price's method
of determining the attraction of plates consists in integrating be-
tween the proper limits the following differentials
:
w_ „ xdxdy ,d?X = mOr *—g ; f\\
(V + ff
dzY= mOr V X y 3 ; (1 )
O2 + ff
where X= x — axial component of attraction
;
Y'= y — axial component of attraction
m = mass of attracted particle
;
= density of attracting mass, supposed homogeneous
;
t = thickness of the plate.
MATHEMATICAL SECTION. 59
Referring to the attracted particle as origin let (a , b ) be the
corner nearest and (ap b } ) that farthest from the particle; then
//"* xdx
b aQ
= m0rJ*dy ((a » + 2/2)"
}
~ « + !/2) *)
= muTi < t r- y fo\U + CV + VT hl +W+ hrf ) W
and a similar expression for Y by exchanging the a's for the b's.
If in this we place a = b = then X= mO- 00.
This is taken by Price to be infinite
;
yet, since the thickness r
must be taken infinitesimal, this is an entirely unfounded conclu-
sion.
At first, however, I did not suspect this result, and when Mr.
Woodward found an infinite attraction of a circular disk on a point
at its circumference, which result I checked, it seemed to be possible
that the attraction of a finite mass could be infinite. Yet neither
Mr. Woodward nor myself was entirely convinced. To settle this
question I then resolved to determine the attraction of a right
prism and also of a right circular cylinder on a particle at mid-
height, which, being then moved to the surface and taking the
height infinitesimal, would give the attraction of a plate on a par-
ticle in a position at which an infinite attraction had been found.
For a right rectangular prism we have, 2h being its height,
b
x
a
x
h
X = mO fdyf xdxJ(g, +^ + g2)f
bi <h
„ C 1 C Ihxdx
= m6 j dyj (x> + tf){x> + f + h^ w
Comparing this with (2), putting 2h = t, we readily see that
these values are by no means identical, for (2) is of the form
T/2 (av a<» bv b ) while (3) is t/s (av a , bv b , r). Here/2 is independ-
ent of r while
/
3 is not.
60 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Placing a — b = o or supposing the attracted particle at the
edge of the prism Ave have
b
x
a,//* xdx
b
x l/< + f + h*
= 2m0h jdyj
^ _ ^
o Vf + V
b
x V< + y2 + V
= 2m0h fdy^ I jj^j]
o Vf + A1
6, VV + 2/2 + V
= m0 /^['Hpfl <4>
o Vf + h2
This form shows clearly that Xvanishes with h; therefore the
attraction of a rectangular plate on a particle at one of its corners
is not infinite, but, on the contrary, it is infinitesimal.
Similarly the attraction of a circular plate on a particle at its
circumference may be found by considering the plate a vanishing
cylinder. Using cylindrical co-ordinates to a vertical line through
the attracted particle as axis we have, if p = horizontal radius
vector, v = vectorial angle, for the attraction of a cylinder, radius
r, density 0, on a particle at midheight h and distance d from axis
of cylinder where
p^d3 — r>
cosv = 2pd
1
and sin v =^ i/[(d + r)* - f\ |>» - (d - r)
2
]
d-\- r v h
A = mOJ p* dpj cos vdvj , , , g.2 f
d — r — v — h
d-\-r
C . 2/*,
= mO I p2 dp ' 2 sin v
P \/p*+h%
d— r
MATHEMATICAL SECTION. 61
d + r
h Cdp J[(d + r)'-^]l>'-Cd-r)']
- 2m0 SJ T V TTh2
d-r
yV— A2
-"iftf-'-JM**-*
Vh1 - A2
where a= l/(d + rf -f A2 ; and b = V id — r) 2 + A2 (5)
Assume tan <p = -y *JP2 _ 2 _ , 2 then ^ has the limits _J and
a? V b2
0. We have then p2 + h2 = . .— , 2 • »
„
= 7—2' where Apr a 1* COS V ~T sin r ^ Y
I
¥~
is an elliptic a function to the modulus
-y 1 — -j. Transform-
ing we have, expressing in A functions
J J J ]
"<J A^+J ^ a2 b2 J a_V^*9\
. 62 J
2m0 hd
J J
a&2 ! rd<p h2 r .
= 2m^i J A-^-^J ^ A^
j 1
{d + Q 2 /* d<p
I
a* J m j_ 4r^ • . w T
n a6
2
f _ h
2
_ (d + r\ 2 T,( 4rdh2 \1
where J7
, 2£, and /7 denote quadrantal elliptic integrals of the 1st,
2d, and 3d species, according to Legendre's notation. If our object
was to obtain here a formula for convenient computation of the
attraction the third term could still be expressed in integrals of the
1st and 2d species, which have been tabulated by Legendre.
34
G2 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Let us now move the particle to the surface of the cylinder, then
we have d = r; a = j/4r* + hl ; b — h, and (6) becomes
A'=2viO°^-(F-E). (6')
Mr. Woodward, as already stated, had found an infinite attrac-
tion of a circular disc on a particle on its circumference by using
Price's method. Now, since A' is mrely a finite quantity, we have
here the manifest absurdity that the attraction of a cylinder on a
particle on its surface would be less than that of a circular disk
which is only an infinitesimal part of it.
If we wish to ascertain the attraction of a circular disk of finite
small thickness we may, of course, use (6'), and since then F tends
to infinity, E may be neglected ; therefore
A' =
h =
2m6 dtp
J
J ~~/7
sin '<p
h = o
= 4m0
J
r
MATHEMATICAL SECTION. 63
The notion of an infinite attraction exerted by a finite mass has
thus been dispelled in two special cases in which it seemed to have
been proved, and I add some remarks on its general impossibility.
The attraction of a mass element on a particle at distance p is
dx cly dz
mO f
—
P
This is then an infinitesimal of the third order, and the summa-
tion of its components with respect to a fixed direction requires
three integrations, which give surely a finite result if p is always
finite.
If p is infinitesimal there will be one element of attraction, which,
instead of being of the third order, is only of the^rs^ order of in-
finitesimals, and this one element being added to the finite sum of
the other elements has no effect. Hence I conclude that a finite
mass exerts only a, finite attraction on a particle.
The paper was discussed by Messrs. Hall, Hill, and Wood-
ward. Mr. Woodward said that he had arrived at a result simi-
lar to Mr. Kummell's by a somewhat different route. The fallacy
in Price's Calculus arose from neglecting the thickness of the plate.
Note.
The communications and abstracts printed in the proceedings of
the Mathematical Section have each been examined by a special
committee consisting of the Chairman, the Secretary, and a third
member appointed by the Chairman. These third members were
as follows
:
Title. Author. Third Member.
Physical observations of Wolf's comet.W. C. Winlock. — — —
The Theory of Mercury G. L. Kavene. E. B. Elliott.
A group of circles related to Feuer-
bach's circle Marcus Baker. C. H. Kummell.
Some practical features of a time de-
termination K. S. Woodward. H. Farquhar.
Can the attraction of a finite mass be
infinite ? C. H. Kummell. K. S. Woodward.

INDEX.
Page.
Abbe, 0.: communication on methods of
verifying weather predictions 8, 9
Adams, C. F., Election to membership of 17
Adjustment of conditioned observations 41
American Academy of Arts and Sciences..xxxvi
American Association for the Advancement
of Science xxxix
American Philosophical Society. ..xxxiv, xxxvii
American scientific societies xxxiii
Annual address of the President xxxi
Annual meeting it)
Anthropological Society, Invitation from 5
Anthropometric and reaction-time apparatus 25
Antisell, T. : remarks on the nature of odors 27
thunderstorms 11
Artifice sometimes useful for the adjustment
of conditioned observations 41
Attempt at a theory of odor 27
Attraction, Infinite, of a finite mass 58
Auditing committee, Appointment of. 31
Report of. 3
Baker, Marcus: communication on a group
of circles related to Feuerbach's circle.. 45
a collection of formulee for the area
of a plane triangle 37
— elected Secretary of Mathematical Section 37
— report of auditing committee 3
Baker, Frank: communication on modern
ideas of brain mechanism 17
— remarks on the recognition of the direc-
tion of sound 13
Barus, Carl, Election to membership of. 5
Bell, A. G. : communication on the mSfehan-
ism of "clicks" and "clucks" 18
Billings, J. S. : communication on anthropo-
metric and reaction time apparatus 25
germ cultures 30
vital statistics of the tenth U. S.
census 4
— remarks on the olfactory sense organs 28
care of pamphlets 29
Biological Society, Invitation from 4
Brown, Addison, cited on aberration of
sound 12
Bulletin, Rules for pulication of xiii
Burnett, S. M. : communication on the Javal
and Sehiotz ophthalmometer 11
Page.
Calendar xxx
Can the attraction of a finite mass be infi-
nite? 58
Capron, Horace, Death of 8
Cause and chance in the concurrence of phe-
nomena 54
Chatard, T. M., Election to membership
°f-
v 11
— remarks on transmission of sounds and
earth tremors 28
Chemical Society, Invitation from 29
Chlamydoconcha Orcutti 5
Circles related to Feuerbach's circle 45
Clarke, F. W.
: communication on an at-
tempt at a theory of odor 27
the Flood Rock explosion 28
topaz from Stoneham, Maine 5
Collection of formulae for the area of a plane
triangle (Title only) 37
Columnar structure in the diabase of Orange
Mountain, N. J 19
Comets II and 111,1884 (Title only) 16
Committee, auditing, Appointment of. 31
Report of. 3
— General xii, xiv, xv
— on communications xiv, xv
mathematical communications 63
publications xiv, xv
Condensing hygrometer and sling psyehro-
meter 25
Condition of the earth's interior (Title only)
17,18
Conditioned observations 41
Connecticut Academy of Arts and Sciences
xxxvii
Constitution vii
Crumpling of the earth's crust 18
Curtis, G. E. : remarks on methods of veri-
fying weather predictions 9
Pall, W. H. : communication on two remark-
able forms of mollusks 5
Deceased members xxv, xxvii, 8, 10, 25
Diabase, Columnar structure of. 19
Diller, J. S. : communication on topaz from
Stoneham, Maine 5
Distances ou any spheroid 52
65
66 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Doolittle, M. H. : communication on cause
and chance in the concurrence of phe-
nomena 54
— remarks on bisection and sesquisection... 52
notation for gravitation formula 40
Dutton, C. E. : communication on practical
geology versus speculative physics 4, 5
— remarks on transmission of sounds and
earth tremors 28
Earth, Interior of. 7
Earth's crust, Crumpling of. 18
Elliott, E. B. : communication entitled Ex-
ample illustrating the use of a certain
symbol in the calculus of affected quan-
tity. 37
Endowment of research xli
Example illustrating the use of a certain
symbol in the calculus of affected quan-
tity (Title only) 37
Farquhar, E. : remarks on the recognition
of the direction of sound 13
thunderstorms 11
Farquhar, H. : remarks on sounds connected
with meteors and earthquakes 28
Feuerbach's circle 45
Flexures of transit instruments 27
Flood Rock explosion 28
Flora of the Laramie group (Title only) 17
General Committee, Members of. xiv, xv
Rules of xii
— government in its relations to research... xli
Geometry, Grassmahn's system of. 53
Germ cultures 30
Gooch, F. A., Election to membership of 5
Goode, G. B.: communication on the syste-
matic care of pamphlets 29
Grassmann's system of geometry 53
Gravitation, Modification of Newtonian
formula of. 39
Group of circles related to Feuerbach's circle 45
Hann, J., cited on temperature changes at
Hamburg 9
Hains, R. P., Election to membership of 10
Hall, Asaph: communication on variations
of latitude 10
— Presidential address xxxiii
— remarks on a communication by Mr. Dut-
ton 8
field-time determinations 58
Hamilton's geometric system 53
Hall, Asaph, Jr., Election to membership of. 3
Hall, Prof. G. Stanley: communication on
recent experiments on reaction time
and the time sense ... 4
Page.
Hallock.William, Eleetjpn to membership of. 5
Hampson, Thomas, Election to member-
ship of. 29
Harkness, William: communication on flex-
ures of transit instruments 27
— remarks on care of pamphlets 29
Hazen, H. A. : communication on the con-
densing hygrometer and sling psychro-
meter 25
thunderstorms of 1884 10
— remarks on the verification of weather
predictions 9
Hill, G. W. : elected President of Mathemat-
ical Section 37
— remarks on adjustment of conditioned
observations 41
geometric systems 53
Mercury 45
notation for gravitation formula 40
Hodgkins, H. L., Election to membership of 8
Honorary members of American Societies
xxxvii
Hough, F. B., Death of 25
Hygrometers 25
Iddings, J. P. : communication on the col-
umnar structure in the diabase of Or-
ange Mountain, N. J 19
— Election to membership of. 8
Infinite attraction of a finite mass 58
Javal and Schiotz ophthalmometer, Exhibi-
tion of. 11
Johnson, A. B. : communication on the diffi-
culty in determining the direction of
sound 11, 12
Kerr, W. C, Death of 25
Kummell, C. II.: communication entitled,
Can the attraction of a finite mass be
infinite? 58
an artifice sometimes useful for the
adju^ment of conditioned observations. 41
— remarks on distances on any spheroid 52
Feuerbach's circle 52
field-time determinations 58
Latitude, Variations of 10
List of members xvi
Mann, B. P. : remarks on the care of pamph-
lets 29
Marvin, C. F., Election to membership <>f..... 8
Mathematical communications, Committees
on 63
— Section, Bulletin of. 37
Members of 3G
INDEX. 67
Page.
Mathematical Section, Officers of 36, 37
Rules of 35
Matthews, Washington: communication on
mythological dry painting of the Nava-
jos „ 14
anthropometric and reaction time
apparatus 25
McGee, W. J. : communication on the ter-
races of the Potomac valley 24
Measurement of temperature at distant
points (Title only) 18
Mechanism of clicks and clucks (Title only) 18
Members, Deceased xxv, xxvii, 8, 10, 25
— List of. xvi
— New xxvii
Mendenhall, T. C. : communication on mea-
surement of temperature at distant
points 18
— Election to membership of. 8
— exhibition of a volt meter 26
— remarks on reaction time 27
Mercury, Mathematical theory of. 41
Methods of verifying weather predictions... 8
Milneria minima 5
Modern ideas of brain mechanism (Title
only) 17
Mollusks, Two remarkable forms of. 5
Moser, J. F., Election to membership of 12
Mountain structure 18
Mythological dry painting of the Navajos.... 14
National Academy of Sciences xl, xlv
Navajos, Painting by 14
Newtonian formula of gravitation 39
Nine-points circle 46
Odor, Theory of. 27
Officers, Election of. 31,37
— of the Mathematical Section 36
Society xiv, xv
Orange Mountain, N. J 19
Painting by the Navajos .";. 14
Pamphlets, Care of 29
Paul, H. M. : communication on the earth's
interior- 17,18
the Flood Rock explosion 28
— remarks on the earth's rigidity 7
dry painting by the Japanese 16
field time determinations 58
the topophone 13
Peale, T. R., Death of 10
Perturbations of Polyhymnia 54
Physical observations on Wolfs comet (1884,
HI)
- 37
Poindexter, W. M., Election to membership
of 3
Page.
Polyhymnia, Perturbations of. 54
Practical geology versus speculative physics
(Title only) 4, 5, 6
President's address xxxiii
Psychrometers 25
Publications, Committee on xiv, xv
Ravene, G. L. : communication on the aste-
roids 18,54
the theory of Mercury 41
— Election to membership of. 11
— remarks on comets 17
Reaction time apparatus 25, 27
Recent experiments on reaction time and
the time sense (Title only) 4
Report of Secretaries xxvii, 31
Treasurer xxviii, 31
Research, Endowment of. xli
Riley, C. V.: communication on the system-
atic care of pamphlets 29
Ritter, F. W. McK. : communications on sec-
ular perturbations by Jupiter 54
Robinson, T. : remarks on the observation
of earth tremors 28
Rules for the publication of the Bulletin xiii
— of the General Committee xii
Mathematical Section 35
Society }x
Secretaries, Report of. xxvii, 31
Secular perturbations ofPolyhymnia by Jup-
iter 54
Seismometric observation 28
Shumway, W. A., Election to membership of 12
Signal service investigations of thunder-
storms 10
rules for verification of predictions 8
Six-points circle 46
Slight modification of the Newtonian form-
ula of gravitation 39
Sling psychrometer 25
Smell, Sense of 27
Societies, American scientific xxxiii
Some practical features of a field time de-
termination with a meridian transit 55
Sound, Aberration of. n, 12
Spheroid, Distances on 52
Standing rules of the General Committee... xii
Mathematical Section 35
Society jx
Swift, Dean, cited x l
Systematic care of pamphlets 29
Taylor.W. B. : communication on the crump-
ling of the earth's crust 18
geological and physical theories 6
a slight modification of the Newton-
ian formula of gravitation 39
68 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Taylor, W. B. : remarks on the topophone.... 13
Terraces of the Potomac valley (Title only). 24
Theory of Mercury 41
Thompson, Gilbert, on rock paintings in
New Mexico 16
Thunderstorms of 1884 10
Time determination with meridian transit.. 55
Toner, J. M. : remarks on the care of pamph-
lets 29
Topaz from Stoneham, Maine 5
Topophone 13
Transit instruments, Flexures of. 27
Trap, Columnar 19
Treasurer, Report of. xxviii, 31
Twelve-points circle 46
Two remarkable forms of mollusks 5
Variations of latitude 10
Velocity of transmission of earth tremors... 28
Verifying weather predictions 8
Vital statistics of the tenth U. S. censua
(Title only) 4
Volt-meter, Exhibition of. 26
Ward, L. F.: communication on the flora of
the Laramie group 17
Weather predictions, Verification of.„... 8
Page.
Weed, W. H., Election /o membership of..... 17
Willis, Bailey, Election to membership of... 8
Wilson, H. M., Election to membership of... 11
Winlock, W. C. : communication on comets
II and III, 1884 16
— — — physical observations on Wolfs
comet (1884, III) 37
— report of auditing committee 3
Woodward, R. S. : cited on infinite attrac-
tion 59, 62
— communication on some practical fea-
tures of a field time determination with
a meridian transit 55
— remarks on geometric systems 53
infinite attraction of a finite mass.... 63
variations of latitude 10
Wolfs comet 37
Wortman, J. S., Election to membership of.. 31
Wright, G. M., Election to membership of... 10
Yarrow, H. C: Report of auditing com-
mittee 3
Ziwet, Alexander: communication onGrass-
mann's system of geometry 53
— Election to membership of _ 8
BULLETIN
PHILOSOPHICAL SOCIETY
WASHINGTON.
VOL. IX.
Containing the Minutes of the Society and of the Mathematical
Section for the year 1886.
PUBLISHED BY THE CO-OPERATION OF THE SMITHSONIAN INSTITUTION.
WASHINGTON:
1887.

CONTENTS.
Page.
Constitution vii
Standing Kules of the Society ix
Standing Kules of the General Committee xn
Kules for the Puhlication of the Bulletin xiii
Officers elected December, 1885 xiv
Officers elected December, 1886
. xv
List of Members xvi
List of Deceased Members xxvi
Calendar xxvm
Annual Report of the Secretaries z xxix
Annual Report of the Treasurer xxx
Annual Address of the President, J. S. Billings xxxv
Bulletin of the General Meeting 1
Report of the Auditing Committee 3
Notes on the geology of northern California, J. S. Diller 4
Notes on the faults of the Great Basin and of the eastern base
of the Sierra Nevada, I. C. Russell 5
Recent changes of level in the basin of Lake Ontario, G. K.
Gilbert, (Title only) 8
Lieutenant Lockwood's expedition to farthest north, George E.
Curtis 8
Two examples of similar inventions in areas widely apart, O. T.
Mason 12
Historical sketch of deep-sea temperature observations, J. H.
Kidder, (Title only) 14
Annual profit to banks of national bank note circulation, E. B.
Elliott, ( Title only) 14
Quantity of United States subsidiary silver coin existing and
in circulation, E. B. Elliott, (Title only) 14
The new star in the nebula of Andromeda, Asaph Hall, (Title
only) 14
The images of stars, Asaph Hall, (Title only) 15
On the changes of terrestrial level surfaces due to variations in
distribution of superficial matter, R. S. "Woodward, (Title
only) 15
On the observed changes of level surfaces in the Bonneville
area and their explanation, G. K. Gilbert, (Title only) 15
On the varying altitudes of former level surfaces in the Great
Lake region and the applicability of proposed explanations,
T. C. Chamberlin, (Title only) 15, 16
The enlargement of mineral fragments as a factor in rock alter-
ation, R. D. Irving, (Title only) 16
IV CONTENTS.
The subaerial decay of rocks and the origin of the red clay of
certain formations, I. 0. Kussell, {Title only) r 16
Kecent improvements in microscopic objectives, with demon-
stration of the resolving power of a new l-16th inch, Romyn
Hitchcock, {Title only) 16
A phonetic alphabet, Henry Farquhar 17
Customs of every-day life, Garrick Mallery 19
"When I first saw the cholera bacillus, R. D. Mussey, {Title only) 22
The distribution of fishes in the oceanic abysses and middle
strata, G. Brown Goode and T. H. Bean, {Title only) 22
The physical geographical divisions of the southeastern portion
of the United States and their corresponding topographical
types, Gilbert Thompson 22
Temperatures at which differences between mercurial and air
thermometers are greatest, Thomas Russell, {with figure)— 25
The gilding of thermometer bulbs, J. H. Kidder, {Title only)- 33
Effects of solar radiation upon thermometer bulbs having dif-
ferent metallic coverings, H. A. Hazen 33
Organic cells of unknown origin and form found in human
faeces (two cases), Newton L. Bates 35
On museum- specimens illustrating biology, J. S. Billings, G.
Brown Goode, and Frederick A. Lucas 35
On geological museums, George P. Merrill, {Title only) 36
The Charleston earthquake, by
—
T. C. Mendenhall 37
W J McGee 37
Charles G. Rockwood 37
Everett Hayden, {with one plate) 38
H. M. Paul 41
Bowyers and fletchers, O. T. Mason 44
Certain new and small mountain ranges, G. K. Gilbert, {Title
only) 45
Normal barometers, T. Russell 46
On the occurrence of copper ores in the Trias of the eastern
United States, N. H. Darton, {Title only) 46
The latest volcanic eruption in northern California and its
peculiar lavaj J. S. Diller, {Title only) 46
Presentation of the annual address 47
Annual Meeting 47
Bulletin of the Mathematical Section 49
Standing Rules of the Section 51
Officers of the Section 52
List of members who receive announcements of the meetings. 52
Comparison of the Boss and Auwers' declination standards,
Henry Farquhar 53
On the position and shape of the geoid as dependent on local
masses, R. S. Woodward, {Title only) 53, 54
On the use of Somoff's theorem for the evaluation of the ellip-
tic integral of the 3d species, C. H. Kummell, {Title only) 54
Index 55
BULLETIN
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON,
CONSTITUTION, RULES,
OFFICERS AND MEMBERS,
AND REPORTS OF
SECRETARIES AND TREASURER.

CONSTITUTION
OF
THE PHILOSOPHICAL SOCIETY OF WASHINGTON.
Article I. The name of this Society shall be The Philosophi-
cal Society of Washington.
Article II. The officers of the Society shall be a President,
four Vice-Presidents, a Treasurer, and two Secretaries.
Article III. There shall be a General Committee, consisting of
the officers of the Society and nine other members.
Article IV. The officers of the Society and the other members
of the General Committee shall be elected annually by ballot ; they
shall hold office until their successors are elected, and shall have
power to fill vacancies.
Article V. It shall be the duty of the General Committee to
make rules for the government of the Society, and to transact all
its business.
Article VI. This constitution shall not be amended except by
a three-fourths vote of those present at an annual meeting for the
election of officers, and after notice of the proposed change shall
have been given in writing at a stated meeting of the Society at
least four weeks previously.

STANDING RULES
FOR THE GOVERNMENT OP THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The Stated Meetings of the Society shall be held at 8 o'clock
p. m. on every alternate Saturday; the place of meeting to be
designated by the General Committee.
2. Notice of the time and place of meeting shall be sent to each
member by one of the Secretaries. *
When necessary, Special Meetings may be called by the President.
3. The Annual Meeting for the election of officers shall be the
last stated meeting in the month of December.
The order of proceedings (which shall be announced by the
Chair) shall be as follows
:
First, the reading of the minutes of the last Annual Meeting.
Second, the presentation of the annual reports of the Secretaries,
including the announcement of the names of members elected since
the last Annual Meeting.
Third, the presentation of the annual report of the Treasurer.
Fourth, the announcement of the names of members who, having
complied with section 14 of the Standing Rules, are entitled to vote
on the election of officers.
Fifth, the election of President.
Sixth, the election of four Vice-Presidents.
Seventh, the election of Treasurer.
Eighth, the election of two Secretaries.
Ninth, the election of nine members of the General Committee.
Tenth, the consideration of Amendments to the Constitution of
the Society, if any such shall have been proposed in accordance
with Article VI of the Constitution.
Eleventh, the reading of the rough minutes of the meeting.
35 ix
X PHILOSOPHICAL SOCIETY OF WASHINGTON.
4. Elections of officers are to be held as follows
:
In each case nominations shall be made by means of an informal
ballot, the result of which shall be announced by the Secretary
;
after which the first formal ballot shall be taken.
In the ballot for Vice-Presidents, Secretaries, and members of the
General Committee, each voter shall write on one ballot as many
names as there are officers to be elected, viz., four on the first ballot
for Vice-Presidents, two on the first for Secretaries, and nine on the
first for members of the General Committee ; and on each subse-
quent ballot as many names as there are persons yet to be elected
and those persons who receive a majority of the votes cast shall be
declared elected.
If in any case the informal ballot result in giving a majority for
•any one, it may be declared formal by a majority vote.
5. The Stated Meetings, with the exception of the Annual Meet-
ing, shall be devoted to the consideration and discussion of scientific
subjects.
The Stated Meeting next preceding the Annual Meeting shall be
set apart for the delivery of the President's Annual Address.
6. Sections representing special branches of science may be
formed by the General Committee upon the written recommenda-
tion of twenty members of the Society.
7. Persons interested in science, who are not residents of the Dis-
trict of Columbia, may be present at any meeting of the Society,
except the Annual Meeting, upon invitation of a member.
8. On request of a member, the President or either of the Secre-
taries may, at his discretion, issue to any person a card of invitation
to attend a specified meeting. Five cards of invitation to attend a
meeting may be issued in blank to the reader of a paper at that
meeting.
9. Invitations to attend during three months the meetings of the
Society and participate in the discussion of papers, may, by a vote
of nine members of the General Committee, be issued to persons
nominated by two members.
10. Communications intended for publication under the auspices
of the Society shall be submitted in writing to the General Com-
mittee for approval.
STANDING RULES. XI
11. Any paper read before a Section may be repeated, either
entire or by abstract, before a general meeting of the Society, if
such repetition is recommended by the General Committee of the
So<fiety.
12. It is not permitted to report the proceedings of the Society or
its Sections for publication, except by authority of the General
Committee.
13. *New members may be proposed in writing by three mem-
bers of the Society for election by the General Committee ; but no
person shall be admitted to the privileges of membership unless he
signifies his acceptance thereof in writing, and pays his dues to the
Treasurer, within two months after notification of his election.
14. Each member shall pay annually to the Treasurer the sum
of five dollars, and no member whose dues are unpaid shall vote at
the Annual Meeting for the election of officers, or be entitled to a
copy of the Bulletin.
In the absence of the Treasurer, the Secretary is authorized to
receive the dues of members.
The names of those two years in arrears shall be dropped from
the list of members.
Notice of resignation of membership shall be given in writing to
the General Committee through the President or one of the Secre-
taries.
15. The fiscal year shall terminate with the Annual Meeting.
16. Any member who is absent from the District of Columbia
for more than twelve consecutive months may be excused from pay-
ment of dues during the period of his absence, in which case he
will not be entitled to receive announcements of meetings or current
numbers of the Bulletin.
17. Any member not in arrears may, by the payment of one
hundred dollars at any one time, become a life member, and be
relieved from all further annual dues and other assessments.
All moneys received in payment of life membership shall be
invested as portions of a permanent fund, which shall be directed
solely to the furtherance of such special scientific work as may be
ordered by the General Committee.
^Amended Oct. 9, 1886.
STANDING RULE3
OF THE
GENERAL COMMITTEE OF THE PHILOSOPHICAL
SOCIETY OF WASHINGTON.
1. The President, Vice-Presidents, and Secretaries of the Society
shall hold like offices in the General Committee.
2. The President shall have power to call special meetings of the
Committee, and to appoint Sub-Committees.
3. The Sub-Committees shall prepare business for the General
Committee, and perform such other duties as may be entrusted to
them.
4. There shall be two Standing Sutf-Committees ; one on Com-
munications for the Stated Meetings of the Society, and another on
Publications.
5. The General Committee shall meet at half-past seven o'clock
on the evening of each Stated Meeting, and by adjournment at
other times.
6. For all purposes, except for the amendment of the Standing
Rules of the Committee or of the Society, and the election of mem-
bers, six members of the Committee shall constitute a quorum.
7. The names of proposed new members recommended in con-
formity with section 13 of the Standing Rules of the Society, may
be presented at any meeting of the General Committee, but shall
lie over for at least four weeks before final action, and the concur-
rence of twelve members of the Committee shall be necessary to
election.
The Secretary of the General Committee shall keep a chronologi-
cal register of the elections and acceptances of members.
8. These Standing Rules, and those for the government of the
Society, shall be modified only with the consent of a majority of
the members of the General Committee.
BULES
FOR THE
PUBLICATION OF THE BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The President's Annual Address shall be published in fulL
2. The annual reports of the Secretaries and of the Treasurer
shall be published in full.
3. When directed by the General Committee, any communication
may be published in full.
4. Abstracts of papers and remarks on the same will be pub-
lished, when presented to the Secretary by the author in writing
within two weeks of the evening of their delivery, and approved by
the Committee on Publications. Brief abstracts prepared by one
of the Secretaries and approved by the Committee on Publications
may also be published.
5. If the author of any paper read before a Section of the
Society desires its publication, either in full or by abstract, it shall
be referred to a committee to be appointed as the Section may
determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the Secretary of the Section, together with any
action of the Section taken thereon.
6. Communications which have been published elsewhere, so as
to be generally accessible, will appear in the Bulletin by title only,
but with a reference to the place of publication, if made known in
season to the Committee on Publications.
OFFICERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 19, 1885.
President J. S. Billings.
Vice-Presidents William Harkness. Garrick Mallert.
C. E. DUTTON. J. E. HlLGARD.*
Treasurer Robert Fletcher.
Secretaries G. K. Gilbert. Marcus Baker.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates. F. W. Clarke.
W. H. Dall. G. B. Goods.
J. R. Eastman. Henry Farquhar.
T. C. MENDENHALL.f H. M. PAUL.
C. V. Riley.
STANDING COMMITTEES.
On Communications:
William Harkness, Chairman. G. Js.. Gilbert. Marcus Baker.
On Publications:
G. K. Gilbert, Chairman. Robert Fletcher. Marcus Baker.
S. F. Baird.J
* Resigned membership Nov. 20, 188G.
t Resigned Oct. 9, 1886; vacancy filled by election of W. B. Taylor, Oct. 23, 1886.
X As Secretary of the Smithsonian Institution.
xiv
OFFICERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 18, 1886.
President William Harkness.
Vice-Presidents Garrick Mallery. C. E. Dutton.
J. R. Eastman. G. K. Gilbert.
Treasurer Robert Fletcher.
Secretaries Marcus Baker. J. H. Kidder.
MEMBERS AT LARGE OP THE GENERAL COMMITTEE.
H. H. Bates. F. W. Clarke.
W. H. Dall. E. B. Elliott.
G. B. Goode. C. V. Riley.
H. M. Paul. W. C. Winlock.
R. S. "Woodward.
STANDING COMMITTEES.
On Communications:
J. R. Eastman, Chairman, Marcus Baker. J. H. Kidder.
On Publications:
Marcus Baker, Chairman. Robert Fletcher. J. H. Kidder.
S. F. Baird.
LIST OF MEMBERS
OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
Corrected to December 18, 1886.
Names of gentlemen here indicated as resigned will be omitted from future lists.
Name.
Abbe, Prof. Cleveland
Abert, Mr. S.T.(Sylvanus Thayer
Adams, Mr. Charles Frederick
Adams, Mr. Henry
Aldis, Hon. A. O. (Asa Owen)
Anttsell, Dr. Thomas (Founder)
Avery, Mr. Kobert S. (Robert
Stanton)
Baird, Prof. Spencer F. (Spencer
Fullerton) (Foimder)
Baker, Prof. Frank
Baker, Mr. Marcus
Bancroft, George
Bards, Dr. Carl
Bates, Mr. Henry H. (Henry
Hobart)
Bates, Dr. N. L. (Newton Lem-
uel) U. S. N.
Bean, Dr. T. H. (Tarleton Hoff-
man)
Beardslee, Capt. L. A. (Lester
Anthony) U. S. N. (Absent)
Bell, Mr. A. Graham (Alexander
Graham)
Bell, Dr. C. A. (Chichester Alex-
ander) (Absent)
Benet, Gen. S. V. (Stephen Vin-
cent) U. S. A. (Founder)
Address and Residence.
Army Signal Office.
2017 I st. N. W.
810 19th st. N. W.
Civil Service Commission.
316 C st. N. W.
1603 H st. N. W.
1765 Mass. ave. N. W.
Patent Office.
1311 Q st. N. W.
320 A st. S. E.
Smithsonian Institution.
1445 Mass. ave. N. W.
1315 Corcoran st. N. W.
Geological Survey.
1125 17th st. N. W.
1623 H st. N. W., or, in summer,
Newport, R. I.
Geological Survey.
Patent Office.
The Portland.
Navv Department.
1233 17th st. N. W.
National Museum.
1616 19th st. N. W.
Little Falls, N. Y.
Scott Circle
;
1500 Rhode Island ave.
University College.
London, England.
Ordnance Office, War Dept.
1717 I st. N. W.
IH S
0.2
1871
1S75
1885
1881
1873
1871
1879
1871
1881
1876
1875
1885
1871
1866
1884
1875
1879
1881
1871
LIST OF MEMBERS. XVII
XVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name. Adivvess and Residence. a .3
^1
Craig, Dr. Thomas (Absent)
Cummings, Prof. G. J. (George
Jotham)
Curtice, Mr. Cooper
Curtis, Mr. Geo. E. (George Ed-
ward)
Dall, Mr. Wm. H. (William
Healey) (Founder)
Darton, Mr. Nelson H. (Nelson
Horatio)
Davis, Commander C. H. (Charles
Henry) U. S. N.
Dean, Dr. R. C. (Richard Crain)
U. S. N. (Absent)
De Caindry, Mr.WM. A. (William
Augustin)
De Land, Mr. Theodore L. (The-
odore Louis)
Dewey, Mr. Fred. P. (Frederic
Perkins)
Diller, Mr. J. S. (Joseph Silas)
Doolittle, Mr. M. H. (Myrick
Hascall)
Dunwoody, Lt. H. H. C. (Henry
Harrison Chase) U. S. A. (Absent)
Dutton, Capt. C. E. (Clarence
Edward) U. S. A.
Earll, Mr. R. Edward (Robert
Edward)
Eastman, Prof. J. R. (John Ro-
bie) U. S. N.
Eimbeck, Mr. William
Eldredge, Dr. Stewart (Absent)
Elliott, Mr. E. B. (Ezekiel
Brown) (Founder)
Emmons, Mr. S. F. (Samuel Frank-
lin)
Endlich, Dr. F. M. (Frederic
Miller) (Absent)
Ewing, Gen. Hugh (Absent)
Farquhar, Mr. Edward
Farquhar, Mr. Henry
Ferrel, Prof. William
Johns Hopkins Univ.,
Baltimore, Md.
Howard University.
Agricultural Department.
Army Signal Office.
1401 16th st. N. W.
Care Smithsonian Institution.
1119 12th st. N. W.
Geological Survey.
1101 K st. N. W.
Navy Department.
1705 Rhode Island ave.
Navy Department.
45 Lafayette Place, New York
city.
Commissary General's Office.
1713 HsL N.W.
Treasury Department.
115 7th st. N. E.
National Museum.
Lanier Heights.
Geological Survey.
1804 16th st. N. W.
Coast and Geodetic Survey Office.
1925 I st. N. W.
War Department.
Geological Survey.
2119 H st. N. W.
Smithsonian Institution.
1336 T st. N. W.
Naval Observatory.
1905 I st. N. W.
Coast and Geodetic Survey Office.
Yokohama, Japan.
Gov't Actuary, Treas. Dept.
1210 G st. N. W.
Geological Survey.
1708 H st. N. W.
Reading, Pa.
Lancaster, Ohio.
Patent Office Library.
1915 H st. N. W.
Coast and Geodetic Survey Office.
Brooks Station, D. C.
1641 Broadway,
Kansas City, Mo.
1879
1886
1886
1884
1871
1886
1880
1872
1881
1880
1884
1884
1876
1873
1872
1884
1871
1884
1871
1871
1883
1873
1874
1876
1881
1872
LIST OF MEMBERS. XIX
XX PHILOSOPHICAL SOCIETY OF WASHINGTON.
LIST OF MEMBERS. XXI
XXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
Name. Address and Kesidence.
<3 §
si
to g
Mann, Mr. B: Pickman (Benja-
min Pickman)
Marcou, Mr. J. B. (John Belknap)
Martin, Mr. Artemas
Marvin, Prof. C. F. (Charles
Frederick)
Marvin, Mr. Jos. B. (Joseph
Badger) (Absent)
Mason, Prof. Otis T. (Otis Tufton)
Matthews, Dr. W. (Washington)
U. S. A.
Meigs, Gen. M. C. (Montgomery
Cunningham) U. S. A. (Founder)
Mendenhall, Prof.T. C. (Thomas
Corwin) (Absent)
Merriam, Dr. C. Hart (Clinton
Hart)
Merrill, Mr. George P. (George
Perkins)
Mitchell, Prof. Henry
Morgan, Dr. E. Carroll (Ethel-
bert Carroll)
Moser, Lt. J. F. (Jefferson Frank-
lin) U. S. N. (Absent)
Murdoch, Mr. John
Newcomb, Prof. Simon, U. S. N.
(Founder)
Nichols, Dr. Charles H. (Charles
Henry) (Absent)
Nicholson, Mr. W. L. (Walter
Lamb) (Founder)
Nordhoff, Mr. Charles
Norris, Dr. Basil, U. S. A.
(Absent)
Nott, Judge C. C. (Charles Cooper)
Ogden, Mr. Herbert G. (Herbert
Gouverneur)
Osborne, Mr. J.W. (John Walter)
Parke, Gen. John G. (John
Grubb) U. S. A. (Founder)
Parker, Dr. Peter (Founder)
Parry, Dr. Charles C. (Charles
Christopher) (Absent)
Department of Agriculture.
1918 Sunderland Place, N.W.
Geological Survey.
Cosmos Club.
Coast and Geodetic Survey Office.
55 C st. S. E.
Army Signal Office.
1736 13th st. N. W.
Internal Kevenue Bureau.
National Museum.
1305 Q st. N. W.
Surg. General's Office, U. S. A.
1239 Vermont ave.
Terre Haute, Ind.
Department of Agriculture.
1912 Sunderland Place, N.W.
National Museum.
1602 19th st. N. W.
Coast and Geodetic Survey Office.
1331 L st. N. W.
918 E st. N. W.
Coast and Geodetic Survey Office.
National Museum.
1441 Chapin st., College Hill.
Navy Department.
941 M st. N. W.
Bloomingdale Asylum, Boule-
vard and 117th St., New York,
N. Y.
Topographer, P. O. Dept.
2109 G st. N. W.
1731 Kst. N.W.
Vancouver Barracks,Wash. Ter.
Court of Claims.
826 Connecticut ave. N. W.
Coast and Geodetic Survey Office.
1324 19th st. N. W.
212 Delaware ave. N. E.
Engineer Bureau,War Dept.
16 Lafayette Square.
2 Lafayette Square.
Davenport, Iowa.
1885
1884
1886
1885
1878
1875
1884
1871
1885
1886
1884
1886
1883
1885
1884
1871
1872
1871
1879
1884
1885
1884
1878
1871
1871
1871
LIST OF MEMBERS. XXIII
XXIV PHILOSOPHICAL SOCIETY OP WASHINGTON.
Name.
Sigsbee, Commander C. D.
(Charles Dwight) U. S. N. (Ab-
sent)
Skinner, Dr. J. O. (John Oscar)
U. S. A.
Smiley, Mr. Chas. W. (Charles
Wesley)
Smith, Chf. Eng. David, U.
S. N.
Smith, Mr. Edwin
Snell, Mr. Merwin M. (Merwin
Marie)
Spofford, Mr. A. E. (Ainsworth
Kand)
Stearns, Mr. Robert E. C. (Rob-
ert Edwards Carter)
Stone, Prof. Ormond (Absent)
Taylor, Mr. F. W. (Frederick
"William) (Absent)
Taylor, Mr. William B. (William
Bower) (Founder)
Thompson, Prof. A. H. (Almon
Harris)
Thompson, Mr. Gilbert
Todd, Prof. David P. (David
Peck) (Absent)
Toner, Dr. J. M., (Joseph Mere-
dith)
Trenholm, Hon. William L.
(William Lee.)
True, Mr. Frederick W. (Fred-
erick William)
Upton, Mr. Wm. W. (William
Wirt)
Upton, Prof. Winslow (Absent)
Walcott, Mr. C. D. (Charles
Doolittle)
Waldo, Prof. Frank (Absent)
Walker, Mr. Francis A. (Fran-
cis Amasa) (Absent)
Walling, Mr. Henry F. (Henry
Francis) (Absent)
Ward, Mr. Lester F. (Lester
Frank)
Address and Residence.
Navy Department.
Surg. General's Office, U. S. A.
1529 O st. N. W.
U. S. Fish Commission.
943 Mass. ave.
Navy Department.
Coast and Geodetic Survey Office.
2024 Hillyer Place.
National Museum.
715 Mt. Vernon Place.
Library of Congress.
1621 Mass. ave. N. W.
Smithsonian Institution.
1635 13th st. N. W.
Leander McCormick Observa-
tory, University of Virginia,
Va.
Care Smithsonian Institution.
Smithsonian Institution.
306 C st. N. W.
Geological Survey.
Geological Survey.
1448 Q st. N. W.
Amherst College Observatory,
Amherst, Mass.
615 Louisiana ave.
Controller of the Currency.
1812 N st. N. W.
National Museum.
1335 N st. N. W.
1416 F st. N. W.
1746 M st. N. W.
Brown University, Providence,
R. I.
Geological Survey ; National
Museum.
Armv Signal Office, Fort Myer,
Va.
Massachusetts Institute of Tech-
nology, Boston, Mass.
U. S. Geological Survey, Cam-
bridge, Mass.
Geological Survey.
1464 Rhode Island ave.
1879
1883
1882
1876
1880
1886
1872
1884
1874
1881
1871
1875
1884
1878
1873
1886
1882
1882
1880
1883.
1881
1872
1883
187fi
LIST OF MEMBERS. XXV
XXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
LIST OF DECEASED MEMBERS.
Name.
Benjamin Alvord
Orville Elias Babcock .
Theodorus Bailey-
Joseph K. Barnes
Henry Wayne Blair
Horace ('apron .
Salmon Portland Chase
Frederick Collins
Benjamin Faneuil Craig
Charles Henry Crane
Josiah Curtis
Richard Dominicus Cutts
Charles Henry Davis
Frederick William Dorr
Alexander B. Dyer .
Amos Beebe Eaton
Charles Ewing
Elisha Foote
John Gray Foster
Leonard Dunnell Gale .
Isaiah Hanscom
Joseph Henry
Franklin Benjamin Hough
Andrew Atkinson Humphreys
Ferdinand Kampf .
Washington Caruthers Kerr
Jonathan Homer Lane
Oscar A. Mack .
Archibald Eobertson Marvine
Fielding Bradford Meek
James William Milner
Albert J. Myer .
George Alexander Otis
Carlile Pollock Patterson
Titian Ramsay Peale
Benjamin Peirce
John Campbell Riley
John Rodgers
Benjamin Franklin Sands .
George Christian Shaeffer
Henry Robinson Searle
William J. Twining
Joseph Janvier Woodward
John Maynard Woodworth
Mordecai Yarnall
Admitted.
1872
1871
1873
Founder
1884
Founder
Founder
1879
Founder
Founder
1874
1871
1874
1874
Founder
Founder
1874
Founder
1873
1874
1873
Founder
1879
Founder
1875
1883
Founder
1872
1874
Founder
1874
Founder
Founder
1871
Founder
Founder
1877
1872
Founder
Founder
1877
1878
Founder
1874
1871
Active members
Absent members
Total
Deceased members
SUMMARY.
PHILOSOPHICAL SOCIETY OF WASHINGTON. XXVII
rQ
3
ft.
g 12 5
H
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SECRETARIES REPORT XXIX
ANNUAL REPORT OF THE SECRETARIES.
Washington, D. C, December 18, 1886.
To the Philosophical Society of Washingto7i :
We have the honor to present the following statistical data for
1886:
The last Annual Report brought the record of membership
down to January 16, 1886. The number of active mem-
bers was then 179
This number has been increased by the addition of 18 new
members, by the return of 1 absent member, and by the
reinstatement of 2 members previously dropped. It has
been diminished by the departure of 9 members, by the
resignation of 1, and by the dropping of 7 for non-pay-
ment of dues. There has been no death. The net in-
crease of active members has thus been .... 4
And the active membership is now 183
The roll of new members is
:
N. L. Bates. J. C. Gordon. Marshall McDonald.
H. G. Beyer. R. T. Hill. Artemas Martin.
J. H. Bryan. W. F. Hillebrand. C. H. Merkiam.
G. J. Ctjmmings. R. D. Irving. Henry Mitchell.
Cooper Curtice. C. A. Kenaston. M. M. Snell.
N. H. Darton. A. G. McAdie. W. L. Trenholm.
There have been 14 meetings for the presentation and discussion
of papers (not including the public meeting of December 4) ; the
average attendance has been 47. There have been 2 meetings of
the Mathematical Section ; average attendance 16.
In the general meetings 39 communications have been presented
;
in the mathematical 3. Altogether 42 communications have been
made by 29 members and candidates for membership and by 2
guests. The number of members who have participated in the dis-
cussions is 38. The total number who have contributed to the
scientific proceedings is 49, or 27 per cent, of the present active
membership.
The General Committee has held 15 meetings ; average attend-
ance 12, the smallest attendance at any meeting being 7 and the
largest 15.
G. K. Gilbert,
Marcus Baker,
Secretaries.
XXX PHILOSOPHICAL SOCIETY OF WASHINGTON.
THE REPORT OF THE TREASURER.
Mr. President and Gentlemen
:
The report which I shall presently have the honor to submit to
you shows the total receipts and disbursements for the fiscal year
ending with this meeting.
The actual income belonging to the year 1886 was $878.00, and
the expenditures for the same period were $451.50, leaving a net
surplus of $426.50.
The unpaid dues of former years which have been collected this
year, amount to $175.00.
By a resolution of the General Committee, passed May 22, 1886,
the Treasurer was authorized to invest six hundred dollars of the
surplus funds of the Society in six second-mortgage bonds of the
Cosmos Club of this city. The present high premium on Govern-
ment bonds reduces the annual interest upon them to about 2| per
cent. The bonds purchased were obtained at par, and pay an
interest of five per cent, per annum, the security being an extremely
valuable piece of city property.
The assets of the Society consist of:
2 Government bonds, $1,000 and $500, at 4 per cent., $1,500 00
1 " bond, 1,000, " 4i " 1,000 00
6 Cosmos Club bonds, " 5 " 600 00
Cash with Riggs & Co 485 52
Unpaid dues 265 00
Total $3,850 52
Of the " unpaid dues " it is probable that a part cannot be col-
lected ; on the other hand, the market value of the bonds is in
excess of their face value.
Volume VIII of the Bulletin was duly sent in February to all
members entitled to receive it, and to the societies and scientific
journals with which it is the custom of the Philosophical Society to
exchange its publications.
TREASURER S REPORT. XXXI
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I
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BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL ADDRESS OF THE PRESIDENT.

ANNUAL ADDRESS OF THE PRESIDENT,
John S. Billings.
Delivered December 4, 1886.
SCIENTIFIC MEN AND THEIR DUTIES.
Mr. Chairman and Fellow-Members of the Philosophical Society:
The honor of the presidency of such a society as this—carrying
with it, as it does, the duty of giving at the close of the term of
office an address on some subject of general interest, has been aptly
compared to the little book mentioned in the Revelations of St.
John—the little book which was " sweet in the mouth but bitter in
the belly." I can only thank you for the honor, and ask your in-
dulgence as to the somewhat discursive remarks which I am about
to inflict upon you.
There is a Spanish proverb to the effect that no man can at the
same time ring the bell and walk in the procession. For a few mo-
ments to-night I am to ring the bell, and being thus out of the pro-
cession I can glance for a moment at that part of it which is nearest.
At first sight it does not appear to be a very homogeneous or well-
ordered parade, for the individual members seem to be scattering in
every direction, and even sometimes to be pulling in opposite ways;
yet there is, after all, a definite movement of the whole mass in the
direction of what we call progress. It is not this general movement
that I shall speak of, but rather of the tendencies of individuals or
of certain classes ; some of the molecular movements, so to speak,
which are not only curious and interesting of themselves, but which
have an important bearing upon the mass, and some comprehension
of which is necessary to a right understanding of the present con-
dition and future prospects of science in this country.
The part of the procession of which I speak is made up of that body
or class of men who are known to the public generally as " scientists,"
" scientific men," or " men of science." As commonly used, all these
terms have much the same significance ; but there are, nevertheless,
shades of distinction between them, and in fact we need several other
XXXV
XXXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
terms for purposes of classification of the rather heterogeneous mass
to which they are applied. The word "scientist" is a coinage of the
newspaper reporter, and, as ordinarily used, is very comprehensive.
Webster defines a scientist as being " one learned in science, a
savant "—that is, a wise man—and the word is often used in this
sense. But the suggestion which the word conveys to my mind is
rather that of one whom the public suppose to be a wise man,
whether he is so or not, of one who claims to be scientific. I shall,
therefore, use the term "scientist" in the broadest sense, as including
scientific men, whether they claim to be such or not, and those who
claim to be scientific men whether they are so or not.
By a scientific man I mean a man who uses scientific method
in the work to which he specially devotes himself; who possesses
scientific knowledge,—not in all departments, but in certain
special fields. By scientific knowledge we mean knowledge which
is definite and which can be accurately expressed. It is true
that this can rarely be done completely, so that each proposition
shall precisely indicate its own conditions, but this is the ideal at
which we aim. There is no man now living who can properly be
termed a complete savant, or scientist, in Webster's sense of the
word. There are a few men who are not only thoroughly scientific
in their own special departments, but are also men possessed of
much knowledge upon other subjects and who habitually think
scientifically upon most matters to which they give consideration
;
but these men are the first to admit the incompleteness and super-
ficiality of the knowledge of many subjects which they possess, and
to embrace the opportunity which such a society as this affords of
meeting with students of other branches, and of making that
specially advantageous exchange in which each gives and receives,
yet retains all that he had at first.
Almost all men suppose that they think scientifically upon all
subjects; but, as a matter of fact, the number of persons who are so
free from personal equation due to heredity, to early associations, to
emotions of various kinds, or to temporary disorder of the digestive
or nervous machinery that their mental vision is at all times achro-
matic and not astigmatic, is very small indeed.
Every educated, healthy man possesses some scientific knowledge,
and it is not possible to fix any single test or characteristic which
will distinguish the scientific from the unscientific man. There are
scientific tailors, bankers, and politicians, as well as physicists,
ANNUAL ADDRESS OF THE PRESIDENT. XXXVII
chemists, and biologists. Kant's rule, that in each special branch
of knowledge the amount of science, properly so called, is equal to
the amount of mathematics it contains, corresponds to the definition
of pure science as including mathematics and logic, and nothing
else. It also corresponds to the distinction which most persons,
consciously or unconsciously, make between the so-called physical,
and the natural or biological sciences. Most of us, I presume, have
for the higher mathematics, and for the astronomers and physicists
who use them, that profound respect which pertains to comparative
ignorance, and to a belief that capacity for the higher branches
of abstract analysis is a much rarer mental quality than are those
required for the average work of the naturalist. I do not, however,
propose to discuss the hierarchy of the sciences ; and the term science
is now so generally used in the sense of knowledge, more or less
accurate, of any subject, more especially in the relations of causes
and effects, that we must use the word in this sense, and leave to
the future the task of devising terms which will distinguish the
sciences, properly so called, from those branches of study and occu-
pation of which the most that can be said is that they have a scien-
tific side. It is a sad thing that words should thus become polar-
ized and spoiled, but there seems to be no way of preventing it.
In a general way we may say that a scientific man exercises the
intellectual more than the emotional faculties, and is governed by
his reason rather than by his feelings. He should be a man of both
general and special culture, who has a little accurate information
on many subjects and much accurate information on some one or
two subjects, and who, moreover, is aware of his own ignorance and
is not ashamed to confess it.
We must admit that many persons who are known as scientists
do not correspond to this definition. Have you never heard, and
perhaps assented to, some such statements as these : " Smith is a
scientist, but he doesn't seem to have good, common sense," or " he
is a scientific crank ?
"
The unscientific mind has been defined as one which " is willing
to accept and make statements of which it has no clear conceptions
to begin with, and of whose truth it is not assured. It is the state
of mind where opinions are given and accepted without ever being
subjected to rigid tests." Accepting this definition, and also the
implied definition of a scientific mind as being the reverse of this,
let us for a moment depart from the beaten track which presi-
XXXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
deutial addresses usually follow, and instead of proceeding at once
to eulogize the scientific mind and to recapitulate the wonderful
results it has produced, let us consider the unscientific mind a little,
not in a spirit of lofty coudescension and. ill-disguised contempt,
but sympathetically, and from the best side that we can find. As
this is the kind of mind which most of us share with our neighbors,
to a greater or less degree, it may be as well not to take too gloomy
a view of it. In the first place, the men with unscientific minds
form the immense majority of the human race.
Our associations, habits, customs, laws, occupations, and pleasures
are, ift the main, suited to these unscientific minds ; whose enjoyment
of social intercourse, of the every-day occurrences of life, of fiction,
of art, poetry, and the drama is, perhaps, none the less because
they give and accept opinions without subjecting them to rigid
tests. It is because there are a goodly number of men who do this
that the sermons of clergymen, the advice of lawyers, and the pre-
scriptions of physicians have a market value. This unscientific
public has its uses. We can at least claim that we furnish the ma-
terials for the truly scientific mind to work with and upon ; it is out
of this undifferentiated mass that the scientific mind supposes itself
to be developed by specialization, and from it that it obtains the
means of its own existence. The man with the unscientific mind,
who amuses himself with business enterprises, and who does not
care in the least about ohms or pangenesis, may, nevertheless, be a
man who does as much good in the world, is as valuable a citizen,
and as pleasant a companion as some of the men of scientific minds
with whom we are acquainted.
And in this connection I venture to express my sympathy for two
classes of men who have in all ages been generally condemned and
scorned by others, namely, rich men and those who want to be rich.
I do not know that they need the sympathy, for our wealthy citi-
zens appear to support with much equanimity the disapprobation
with which they are visited by lecturers and writers—a condemna-
tion which seems in all ages to have been bestowed on those who
have by those who have not.
So far as those who actually are rich are concerned, we may, I
suppose, admit that a few of them—those who furnish the money to
endow universities and professorships, to build laboratories, or to
furnish in other ways the means of support to scientific men—are
not wholly bad. Then, also, it is not always a man's own fault that
ANNUAL ADDRESS OF THE PRESIDENT. XXXIX
he is rich ; even a scientist may accidentally and against his will
become rich.
As to those who are not rich, but who wish to be rich, whose chief
desire and object is to make money, either to avoid the necessity for
further labor, or to secure their wives and children from want, or
for the sake of power and desire to rule, I presume it is unsafe to
try to offer any apologies for their existence. But when it is
claimed for any class of men, scientists or others, that they do not
want these things it is well to remember the remarks made by old
Sandy Mackay after he had heard a sermon on universal brotherhood
:
"And so the deevil's dead. Puir auld Nickie ; and him so little ap-
preciated, too. Every gowk laying his sins on auld Nick's back.
But I'd no bury him until he began to smell a wee strong like.
It's a grewsome thing is premature interment."
I have tried to indicate briefly the sense in which the terms "sci-
entist" and "scientific man" are to be used and understood, and
you see it is not an easy matter. The difficulty is less as regards
the term "man of science." By this expression we mean a man who
belongs to science peculiarly and especially, whose chief object in
life is scientific investigation, Avhose thoughts and hopes and desires
are mainly concentrated upon his search for new knowledge, whose
thirst for fresh and accurate information is constant and insatiable.
These are the men who have most advanced science, and whom we
delight to honor, more especially in these later days, by glowing
eulogiums of their zeal, energy, and disinterestedness.
The man of science, as defined by his eulogists, is the beau ideal
of a philosopher, a man whose life is dedicated to the advancement
of knowledge for its own sake, and not for the sake of money or
fame, or of professional position or advancement. He undertakes
scientific investigations exclusively or mainly because he loves the
work itself, and not with any reference to the probable utility of
the results. Such men delight in mental effort, or in the observa-
tion of natural phenomena, or in experimental work, or in historical
research, in giving play to their imagination, in framing hypotheses
and then in endeavoring to verify or disprove them, but always the
main incentive is their own personal satisfaction (with which may
be mingled some desire for personal fame), and not the pleasure or
the good of others. Carried to an extreme, the eulogy of such men
and their work is expressed in the toast of the Mathematical Society
of England: "Pure mathematics; may it never be of use to any
XL PHILOSOPHICAL SOCIETY OF WASHINGTON.
man ! " Now, it is one thing to seek one's own pleasure, and quite
another thing to pride one's self upon doing so. • The men who do
their scientific work for the love of it do some of the best work, and,
as a rule, do not pride themselves on it, or feel or express contempt
for those who seek their pleasure and amusement in other direc-
tions. It is only from a certain class of eulogists of pure science, so
called, that we get such specimens of scientific " dudeism " as the toast
just quoted, opposed to which may be cited the Arab saying that
"A wise man without works is like a cloud without water."
There are other men who devote themselves to scientific work,
but who prefer to seek information that may be useful ; who try to
advance our knowledge of Nature's laws in order that man may
know how to adapt himself and his surroundings to those laws, and
thus be healthier and happier. They make investigations, like the
men of pure science—investigations in which they may or may not
take pleasure, but which they make, even if tedious and disagree-
able, for the sake of solving some problem of practical importance.
These are the men who receive from the public the most honor, for
it is seen that their work benefits others. After all, this is not
peculiar to the votaries of science. In all countries and all times,
and among all sorts and conditions of men, it has always been
agreed that the best life, that which most deserves praise, is that
which is devoted to the helping others, which is unselfish, not stained
by envy or jealousy, and which has as its main pleasure and spriDg
of action the desire of making other lives more pleasant, of bringing
light into the dark places, of helping humanity.
But, on the other hand, the man who makes a profession of doing
this, and who makes a living by so doing, the professional philan-
thropist, whether he be scientist or emotionalist, is by no means to
be judged by his own assertions. Some wise German long ago re-
marked that "Esel singen schlecht, well sie zu hoch anstimmen"— that
is, " asses sing badly because they pitch their voices too high," and
it is a criticism which it is well to bear in mind.
In one of the sermons of Kin O * the preacher tells the story
of a powerful clam who laughed at the fears of other fish, saying
that when he shut himself up he felt no anxiety ; but on trying this
method on one occasion when he again opened his shell he found
himself in a fishmonger's shop. And to rely on one's own talents,
*Cornhill Magazine, August, 1809, p. 196.
ANNUAL ADDRESS OF THE PRESIDENT. XLI
on the services one may have rendered, on cleverness, judgments
strength, or official position, and to feel secure in these, is to court
the fate of the clam.
There are not very many men of science, and there are no satis-
factory means of increasing the number ; it is just as useless to ex-
hort men to love science, or to sneer at them because they do not,
as it is to advise them to be six feet three inches high or to condemn
a man because his hair is not red.
While the ideal man of science must have a " clear, cold, keen
intellect, as inevitable and as merciless in its conclusions as a logic
engine," it would seem that, in the opinion of some, his greatness
and superiority consists not so much in the amount of knowledge
he possesses, or in what he does with it, as in the intensity and
purity of his desire for knowledge.
This so-called thirst for knowledge must be closely analogous to
an instinctive desire for exercise of an organ or faculty, such as
that which leads a rat to gnaw, or a man of fine physique to delight
in exercise. Such instincts should not be neglected. If the rat
does not gnaw, his teeth will become inconvenient or injurious to
himself, but it is not clear that he deserves any special eulogium
merely because he gnaws.
It will be observed that the definition of a scientific man or
man of science, says nothing about his manners or morals. We
may infer that a man devoted to science would have neither time
nor inclination for dissipation or vice ; that he would be virtuous
either because of being passionless or because of his clear foresight
of the consequences of yielding to temptation.
My own experience, however, would indicate that either this
inference is not correct or that some supposed scientific men have
been wrongly classified as such. How far the possession of a scien-
tific mind and of scientific knowledge compensates, or atones for,
ill-bi*eeding or immorality, for surliness, vanity, and petty jealousy,
for neglect of wife or children, for uncleanliness, physical and
mental, is a question which can only be answered in each individual
case ; but the mere fact that a man desires knowledge for its own
sake appears to me to have little to do with such questions. I
would prefer to know whether the man's knowledge and work is of
any use to his fellow-men, whether he is the cause of some happiness
in others which would not exist without him. And it may be noted
that while utility is of small account in the eyes of some eulogist,
37
XLII PHILOSOPHICAL SOCIETY OF WASHINGTON.
of the man of science they almost invariably base their claims for
his honor and support upon his usefulness.
The precise limit beyond which a scientist should not make
money has not yet been precisely determined, but in this vicinity
there are some reasons for thinking that the maximum limit is
about $5,000 per annum. If there are any members of the Philo-
sophical Society of Washington who are making more than this, or
who, as the result of careful and scientific introspection, discover in
themselves the dawning of a desire to make more than this, they
may console themselves with the reflection that the precise ethics
and etiquette which should govern their action under such painful
circumstances have not yet been formulated. The more they
demonstrate their indifference to mere pecuniary considerations the
more creditable it is to them ; so much all are agreed upon ; but
this is nothing new, nor is it specially applicable to scientists. Yet
while each may and must settle such questions as regards himself
for himself, let him be very cautious and chary about trying to
settle them for other people. Denunciations of other men engaged
in scientific pursuits on the ground that their motives are not the
proper ones are often based on insufficient or inaccurate knowledge,
and seldom, I think, do good.
This is a country and an age of hurry, and there seems to be a
desire to rush scientific Avork as well as other things. One might
suppose, from some of the literature on the subject, that the great
object is to make discoveries as fast as possible ; to get all the math-
ematical problems worked out ; all the chemical combinations made
;
all the insects and plants properly labeled ; all the bones and mus-
cles of every animal figured and described. From the point of view
of the man of science there does not seem to be occasion for such
haste. Suppose that every living thing were known, figured, and
described. Would the naturalist be any happier ? Those who wish
to make use of the results of scientific investigation of course
desire to hasten the work, and when they furnish the means we can-
not object to their urgency. Moreover, there is certainly no occa-
sion to fear that our stock of that peculiar form of bliss known as
ignorance will be soon materially diminished.
From my individual point of view, one of the prominent features
in the scientific procession is that part of it which is connected with
Government work. Our Society brings together a large number of
scientific men connected with the various Departments ; some of
ANNUAL ADDRESS OF THE PRESIDENT. XLIII
them original investigators ; most of them men whose chief,
though not only, pleasure is study. A few of them have important
administrative duties, and are brought into close relations with the
heads of Departments and with Congress. Upon men in such posi-
tions a double demand is made, and they are subject to criticism
from two very different standpoints. On the one hand are the sci-
entists, calling for investigations which shall increase knowledge
without special reference to utility, and sometimes asking that em-
ployment be given to a particular scientist on the ground that the
work to which he wishes to devote himself is of no known use, and
therefore will not support him. On the other hand is the demand
from the business men's point of view—that they shall show prac-
tical results ; that in demands for appropriations from the public
funds they shall demonstrate that the use to be made of such appro-
priations is for the public good, and that their accounts shall show
that the money has been properly expended—"properly," not
merely in the sense of usefully, but also in the legal sense—in the
sense which was meant by Congress in granting the funds. Nay,
more, they must consider not only the intentions of Congress but
the opinions of the accounting officers of the Treasury, the comp-
troller and auditor, and their clerks, and not rely solely on their
own interpretation of the statutes, if they would work to the best
advantage, and not have life made a perpetual burden and vexation
of spirit.
There is a tendency on the part of business men and lawyers to
the belief that scientific men are not good organizers or administra-
tors, and should be kept in leading strings ; that it is unwise to
trust them with the expenditure of, or the accounting for, money,
and that the precise direction in which they are to investigate should
be pointed out to them. In other words, that they should be made
problem-solving machines as far as possible.
When we reflect on the number of persons who, like Mark Twain's
cat, feel that they are "nearly lightning on superintending;" on the
desire for power and authority, which is almost universal, the ten-
dency to this opinion is not to be wondered at. Moreover, as re-
gards the man of science, there is some reason for it in the very
terms by which he is defined, the characteristics for which he is
chiefly eulogized.
The typical man of science is, in fact, in many cases an abnor-
mity, just as a great poet, a great painter, or a great musician is
XLIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
apt to be, and this not only in an unusual development of one part
of the brain, but in an inferior development in others. True, there
are exceptions to this rule
—
great and illustrious exceptions ; but I
think we must admit that the man of science often lacks tact, and
is indifferent to and careless about matters which do not concern
his special work, and especially about matters of accounts and
pecuniary details. If such a man is at the head of a bureau, whose
work requires many subordinates and the disbursement of large
sums of money, he may consider the business management of his
office as a nuisance, and delegate as much of it as possible to some
subordinate official, who, after a time, becomes the real head and
director of the bureau. Evil results have, however, been very rare,
and the recognition of the possibility of their occurrence is by no
means an admission that they are a necessity, and still less of the
proposition that administrative officers should not be scientific men.
I feel very sure that there are always available scientific men,
thoroughly well informed in their several departments, who are also
thoroughly good business men, and are as well qualified for admin-
istrative work as any. When such men are really wanted they can
always be found, and, as a matter of fact, a goodly number of them
have been found, and are now in the Government service.
The head of a bureau has great responsibilities; and while his
position is, in many respects, a desirable one, it would not be eagerly
sought for by most scientific men if its duties w7ere fully understood.
In the first place the bureau chief must give up a great part of
his time to routine hack work. During his business, or office, hours
he can do little else than this routine work, partly because of its
amount, and partly because of the frequent interruptions to which
he is subjected. His visitors are of all kinds and come from all
sorts of motives—some to pass away half an hour, some to get infor-
mation, some seeking office. It will not work well if he takes the
ground that his time is too important to be wasted on casual callers
and refers them to some assistant.
In the second place he must, to a great extent at least, give up the
pleasure of personal investigation of questions that specially interest
him, and turn them over to others. It rarely happens that he can
carry out his own plans in his own way, and perhaps it is well that
this should be the case. The general character of his work is usually
determined for him either by his predecessors, or by Congress, or by
the general consensus of opinion of scientific men interested in the
ANNUAL ADDRESS OF THE PRESIDENT. XLV
particular subject or subjects to which it relates. This last has very
properly much weight ; in fact, it has much more weight than one
might suppose, if he judged from some criticisms made upon the work
of some of our bureaus whose work is more or less scientific. In these
criticisms it is urged that the work has not been properly planned and
correlated; that it should not be left within the power of one man to
say what should be done ; that the plans for work should be prepared
by disinterested scientific men—as, for instance, by a committee of
the National Academy—and that the function of the bureau official
should be executive only.
I have seen a good deal of this kind of literature within the last
ten or twelve years, and some of the authors of it are very distin-
guished men in scientific work; yet I venture to question the wis-
dom of such suggestions. As a rule, the plans for any extended
scientific work to be undertaken by a Government department are
the result of very extended consultations with specialists, and meet
with the approval of the majority of them. Were it otherwise the
difficulties in obtaining regular annual appropriations for such work
would be great and cumulative, for in a short time the disapproval
of the majority of the scientific public would make itself felt in
Congress. It is true that the vis inertias of an established bureau
is very great. The heads of Departments change with each new
administration, but the heads of bureaus remain ; and if an unfit
man succeeds in obtaining one of these positions, it is a matter
of great difficulty to displace him ; but it seems to me to be wiser to
direct the main effort to getting right men in right places rather
than to attempt to elaborate a system which shall give good results
with inferior men as the executive agents, which attempt is a waste
of energy.
You are all familiar with the results of the inquiry which has
been made by a Congressional committee into the organization and
work of certain bureaus which are especially connected with scien-
tific interests, and with the different opinions which this inquiry has
brought out from scientific men. I think that the conclusion of the
majority of the committee, that the work is, on the whole, being
well done, and that the people are getting the worth of their money,
is generally assented to. True, some mistakes have been made,
some force has been wasted, some officials have not given satisfac-
tion; but is it probable that any other system would give so much
better results that it is wise to run the risks of change?
XLVI PHILOSOrniCAL SOCIETY OF WASHINGTON.
This question brings us to the only definite proposition which has
been made in this direction, namely, the proposed Department of
Science, to which all the bureaus whose work is mainly scientific,
such as the Coast Survey, the Geological Survey, the Signal Service,
the Naval Observatory, etc., shall be transferred.
The arguments in favor of this are familiar to you, and, as re-
gards one or two of the bureaus, it is probable that the proposed
change would effect an improvement ; but as to the desirability of
centralization and consolidation of scientific interests and scientific
work into one department under a single head, I confess that I have
serious doubts.
One of the strongest arguments in favor of such consolidation
that I have seen is the address of the late president of the
Chemical Society of Washington, Professor Clarke, " On the Re-
lations of the Government to Chemistry," delivered about a year
ago. Professor Clarke advises the creation of a large, completely-
equipped laboratory, planned by chemists and managed by chemists,
in which all the chemical researches required by any department of
the Government shall be made, and the abandonment of individual
laboratories in the several bureaus on the ground that these last are
small, imperfectly equipped, and not properly specialized ; that each
chemist in them has too broad a range of duty and receives too
small a salary to command the best professional ability. He would
have a national laboratory, in which one specialist shall deal only
with metals, another with food products, a third with drugs, etc.,
while over the whole, directing and correlating their work, shall
preside the ideal chemist, the all-round man, recognized as the
leader of the chemists of the United States. And so should the
country get better and cheaper results. It is an enticing plan and
one which might be extended to many other fields of work. Grant-
ing the premises that we shall have the best possible equipment,
with the best possible man at the head of it, and a sufficient corps
of trained specialists, each of whom will contentedly do his own
work as directed and be satisfied, so that there shall be no jealousies,
or strikes, or boycotting, and we have made a long stride toward
Utopia. But before we centralize in this Avay we must settle the
question of classification. Just as in arranging a large library there
are many books Avhich belong in several different sections, so it is in
applied science. Is it certain that the examination of food products
or of drugs should be made under the direction of the national
ANNUAL ADDRESS OP THE PRESIDENT. XLVII
chemist rather than under that of the Departments which are most
interested in the composition and quality of these articles ? This does
not seem to me to be a self-evident proposition by any means.
The opinion of a scientific man as to whether the Government
should or should not undertake to carry out any particular branch of
scientific research and publish the results, whether it should attempt
to do such work through officers of the Army and Navy, or more
or less exclusively through persons specially employed for the pur-
pose, whether the scientific work shall be done under the direction
of those who wish to use, and care only for, the practical results, or
whether the scientific man shall himself be the administrative head
and direct the manner in which his results shall be applied ; the
opinion of a scientific man on such points, I say, will differ accord-
ing to the part he expects or desires to take in the work, according
to the nature of the work, according to whether he is an Army
or Navy officer or not, according to whether he takes more
pleasure in scientific investigations than in administrative prob-
lems, and so forth.
It is necessary, therefore, to apply a correction for personal equa-
tion to each individual set of opinions before its true weight and value
can be estimated, and, unfortunately, no general formula for this
purpose has yet been worked out.
I can only indicate my own opinions, which are those of an Army
officer, who has all he wants to do, who does not covet any of his
neighbors' work or goods, and who does not care to have any more
masters than those whom he is at present trying to serve. You see
that I give you some of the data for the formula by which you are
to correct my statements, but this is all I can do.
I am not inclined at present to urge the creation of a department
of science as an independent department of the Government having
at its head a Cabinet officer. Whether such an organization may
become expedient in the future seems to me doubtful ; but at all
events I think the time has not yet come for it.
I do not believe that Government should undertake scientific
work merely or mainly because it is scientific, or because some
useful results may possibly be obtained from it. It should do, or
cause to be done, such scientific work as is needful for its own in-
formation and guidance when such work cannot be done, or cannot
be done so cheaply or conveniently, by private enterprise. Some
kinds of work it can best have done by private contract, and not by
XLVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
officials ; others, by its own officers. To this last class belong those
branches of scientific investigation, or the means for promoting
them, which require long-continued labor and expenditure on a
uniform plan—such as the work of the Government Observatory,
of the Government surveys, of the collection of the statistics which
are so much needed for legislative guidance, and in which we are at
present so deficient, the formation of museums and libraries, and so
forth.
Considering the plans and operations of these Government insti-
tutions from the point of view of the scientific public, it is highly
desirable that they should contribute to the advancement of abstract
science, as well as to $he special practical ends for which they have
been instituted ; but from the point of view of the legislator, who
has the responsibility of granting the funds for their support, the
practical results should receive the chief consideration, and there-
fore they should be the chief consideration on the part of those who
are to administer these trusts. It must be borne in mind that while
the average legislator is, in many cases, not qualified to judge a
priori as to what practical results may be expected from a given
plan for scientific work, he is, nevertheless, the court which is to
decide the question according to the best evidence which he can get,
or, rather, which is brought before him, and it is no unimportant
part of the duty of those who are experts in these matters to fur-
nish such evidence.
But in saying that practical results should be the chief considera-
tion of the Government and of its legislative and administrative
agents it is not meant that these should be the only considerations.
In the carrying out of any extensive piece of work which involves
the collection of data, experimental inquiry, or the application of
scientific results under new conditions there is more or less oppor-
tunity to increase knowledge at the same time and with compara-
tively little increased cost. Such opportunity should be taken ad-
vantage of, and is also a proper subsidiary reason for adopting one
plan of work in preference to another, or for selecting for appoint-
ment persons qualified not only to do the particular work which is
the main object, but also for other allied work of a more purely
scientific character.
On the same principle it seems to me proper and expedient that
when permanent Government employees have at times not enough
to do in their own departments, and can be usefully employed in
ANNUAL ADDRESS OF THE PRESIDENT. XLIX
scientific work, it is quite legitimate and proper to thus make use
of them. For example, it is desirable that this country should have
such an organization of its Army and Navy as will permit of rapid
expansion when the necessity arises, and this requires that more
officers shall be educated and kept in the service than are needed for
military and naval duty in time of peace. It has been the policy of
the Government to employ some of these officers in work connected
with other departments, and especially in work which requires
such special training, scientific or administrative, or both, as such
officers possess. To this objections are raised, which may be summed
up as follows
:
First, that such officers ought not to be given positions which
would otherwise be filled by civilian scientists, because these places
are more needed by the civilians as a means of earning subsistence,
and because it tends to increase the competition for places and to
lower salaries. Put in other words, the argument is that it is in-
jurious to the interests of scientific men, taken as a body, that the
Government should employ in investigations or work requiring
special knowledge and skill men who have been educated and
trained at its expense, and who are permanently employed and paid
by it. This is analogous to the trades union and the anti-convict
labor platforms.
The second objection is that Army and Navy officers do not, as a
rule, possess the scientific and technical knowledge to properly per-
form duties lying outside of the sphere of the work for which they
have been educated, and that they employ as subordinates really
skilled scientific men, who make the plans and do most of the work,
but do not receive proper credit for it. The reply to this is that it
is a question of fact in each particular case, and that if the officer is
able to select and employ good men to prepare the plans and to do
the work, this in itself is a very good reason for giving him the
duty of such selection and employment.
A third objection is that when an officer of the Army or Navy is
detailed for scientific or other special work the interests of this
work and of the public are too often made subordinate to the
interests of the naval or military service, more especially in the
matter of change of station. For example, civil engineers object to
the policy of placing river and harbor improvements in the hands
of Army engineers, because one of the objects kept in view by the
War Department in making details for this purpose is to vary the
L PHILOSOPHICAL SOCIETY OF WASHINGTON.
duty of the individual officer from time to time so as to give him a
wider experience. Hence it may happen that all officer placed on
duty in connection with the improvement of certain harbors on the
Great Lakes shall, after three or four years, and just as he has gained
sufficient experience of the peculiarities of lake work to make his
supervision there peculiarly valuable, be transferred to work on the
improvement of the Lower Mississippi with which he may be quite
unfamiliar.
In like manner Professor Clarke objects to having a labora-
tory connected with the medical department of the Navy on the
ground that the officer in charge is changed every three years
;
consequently science suffers in order that naval routine may be pre-
served.
There is force in this class of objections, but the moral I should
draw from them is, not that Army and Navy officers should not be
allowed to do work outside their own departments or in science,
but that when they are put upon such duty, the ordinary routine of
change of station every three or four years should not be enforced
upon them without careful consideration of the circumstances of the
case, and satisfactory evidence that the work on which they are en-
gaged will not suffer by the change. And, as a matter of fact, I
believe this has been the policy pursued, and instances could be given
where an officer has been kept twenty years at one station for this
very reason.
I pass over a number of objections that I have heard made to the
employment of Army and Navy officers as administrators, on the
ground that they are too " bumptious," or " domineering," or "super-
cilious," or " finicky," because every one knows what these mean and
their force. An Army officer is not necessarily a polished gentleman
;
neither is a civilian; and a good organizer and administrator,
whether officer or civilian, will at times, and especially to some
people, appear arbitrary and dictatorial.
There is another objection to special details of Army or Navy
officers for scientific duties which comes not so much from outside
persons as from the War Department and the officers themselves,
and it is this : Among such officers there are always a certain num-
ber who not only prefer special details to routine duty, but who
actively seek for such details, who are perpetual candidates for
them.
The proportion of men whose ideas as to their own scientific ac-
ANNUAL ADDRESS OF THE PRESIDENT. LI
quirements, merits, and claims to attention are excessive as com-
pared with the ideas of their acquaintances on the same points is not
greater in the Army than elsewhere, but when an Army officer is
afflicted in this way the attack is sometimes very severe, and the
so-called influence which he brings to bear may cause a good deal
of annoyance to the Department, even if it be not sufficient to obtain
his ends. I have heard officers of high rank, in a fit of impatience
under such circumstances, express a most hearty and emphatic wish
that no special details were possible, so that lobbying for them
should be useless. This, however, seems to me to be too heroic a
remedy for the disease, which, after all, only produces comparatively
trifling irritation and discomfort.
The same evil exists, to a much greater extent, in the civil
branches of the Government. Few persons can fully appreciate
the loss of time, the worry, and the annoyance to which the respon-
sible heads of some of our bureaus for scientific work are subjected
through the desire of people for official position and for mainte-
nance by the Government. They have to stand always at the bat
and protect their wickets from the balls which are bowled at them
in every direction, even from behind by some of their own subor-
dinates.
It is true that a great majority of the balls go wide and cause
little trouble, and a majority of the bowlers soon get tired and
leave the field, but there are generally a few persistent ones who
gradually acquire no small degree of skill in discovering the weak
or unguarded points, and succeed in making things lively for a time.
Considered from the point of view of the public interests, such men
are useful, for although they cause some loss of valuable time, and
occasionally do a little damage by promoting hostile legislation, yet
their criticisms are often worth taking into account ; they tend to
prevent the machine from getting into a rut, and they promote
activity and attention to business on the part of administrative
chiefs. It is a saying among dog fanciers that a few fleas on a dog
are good for him rather than otherwise, as they compel him to take
some exercise under any circumstances.
At all events I think it very doubtful whether the jealousies and
desire for position for one's self or one's friends which exist under
present circumstances would be materially diminished under any
other form of organization, even under a department of science.
Some conflict of interests now exists it is true ; some work is dupli-
LII PHILOSOPHICAL SOCIETY OF WASHINGTON.
cated ; but neither the conflict nor the duplication are necessarily
wholly evil in themselves, nor in so far as they are evil are they
necessary parts of the present system. This system is of the nature
of a growth ; it is organic and not a mere pudding-stoue aggrega-
tion of heterogeneous materials, and the wise course is to correct
improper bendings and twistings gradually, prune judiciously, and
go slow in trying to secure radical changes lest death or permanent
deformity result.
It will be seen that in what I have said I have not attempted to
eulogize science or scientists in the abstract. I should be very
sorry, however, to have given any one the impression that I think
they should not be eulogized. Having read a number of eloquent
tributes to their importance by way of inducing a proper frame of
mind in which to prepare this address, it is possible that I overdid
it a little, and was in a sort of reaction stage when I began to write.
But the more I have thought on the subject, and the more care-
fully I have sought to analyze the motives and character of those of
my acquaintances who are either engaged in scientific work or who
wish to be considered as so doing, and to compare them with those
who have no pretensions to science, and who make none, the more
I have been convinced that upon the Avhole the eulogium is the
proper thing to give, and that it is not wise to be critical as to the
true inwardness of all that we see or hear.
At least nine-tenths of the praises which have been heaped upon
scientific men as a body are thoroughly well deserved. Among them
are to be found a very large proportion of true gentlemen, larger,
I think, than is to be found in any other class of men—men char-
acterized by modesty, unselfishness, scrupulous honesty, and truth-
fulness, and by the full performance of their family and social duties.
Even their foibles may be likable. A little vanity or thirst for
publicity, zeal in claiming priority of discovery, or undue wrath
over the other scientist's theory, does not and should not detract
from the esteem in which we hold them. A very good way of
viewing characteristics which we do not like is to bear in mind that
different parts of the brain have different functions ; that all of
them cannot act at once, and that their tendencies are sometimes
contradictory.
There are times when a scientific man does not think scientifically,
when he does not want to so think, and possibly when it is best that
he should not so think. There is wisdom in Sam. Lawson's remark
ANNUAL ADDRESS OF THE PRESIDENT. LIII
that " Folks that are always telling you what they don't believe are
sort o' stringy and dry. There ain't no 'sorption got out o' not be-
lieving nothing." At one time the emotional, at another the intel-
lectual, side of the scientific man has the ascendency, and one must
appeal from one state to the other. Were scientific thinking rigor-
ously carried out to practical results in every-day life there would
be some very remarkable social changes, and perhaps some very
disagreeable ones.
That scientific pursuits give great pleasure without reference to
their utility, or to the fame or profit to be derived from them ; that
they tend to make a man good company to himself and to bring
him into pleasant associations is certain ; and that a man's own
pleasure and happiness are things to be sought for in his work and
companionship is also certain. If in this address I have ventured
to hint that this may not be the only, nor even the most important,
object in life, that one may be a scientific man, or even a man of
science, and yet not be worthy of special reverence ; because he may
be at the same time an intensely selfish man, and even a vicious
man, I hope that it is clearly understood that it is with no inten-
tion of depreciating the glory of science or the honor which is due
to the large number of scientific gentlemen whom I see around me.
A scientific gentleman—all praise to him who merits this title
—
it is the blue ribbon of our day.
We live in a fortunate time and place; in the early manhood of
a mighty nation, and in its capital city, which every year makes
more beautiful, and richer in the treasures of science, literature, and
art which all the keels of the sea and the iron roads of the land are
bringing to it. Life implies death
;
growth presages decay ; but we
have good reasons for hoping that for our country and our people
the evil days are yet far off. Yet we may not rest and eat lotus
;
we may not devote our lives to our own pleasure, even though it
be pleasure derived from scientific investigation. No man lives for
himself alone ; the scientific man should do so least of all. There
never was a time when the world had more need of him, and there
never was a time when more care was needful lest his torch should
prove a firebrand and destroy more than it illuminates.
The old creeds are quivering; shifting; changing like the colored
flames on the surface of the Bessemer crucible. They are being
analyzed, and accounted for, and toned down, and explained, until
many are doubting whether there is any solid substratum beneath
LIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
but the instinct which gave those creeds their influence is un-
changed.
The religions and philosophies of the Orient seem to have little
in common with modern science. The sage of the east did not try-
to climb the ladder of knowledge step by step. He sought a
wisdom which he supposed far superior to all knowledge of
earthly phenomena obtainable through the senses. The man of
science of the west seeks knowledge by gradual accumulation,
striving by comparison and experiment to eliminate the errors
of individual observations, and doubting the possibility of attain-
ing wisdom in any other way. The knowledge which he has, or
seeks, is knowledge which may be acquired partly by individual
effort and partly by co-operation, which requires material resources
for its development, the search for which may be organized and
pursued through the help of others, which is analogous in some
respects to property which may be used for power or pleasure. The
theologian and the poet claim that there is a wisdom which is not
acquired but attained to, which cannot be communicated or received
at pleasure, which comes in a way vaguely expressed by the words
intuition or inspiration, which acts through and upon the emotional
rather than the intellectual faculties, and which, thus acting, is
sometimes of irresistible power in exciting and directing the actions
of individuals and of communities.
The answer of the modern biologist to the old Hebrew question,
viz., " Why are children born with their hands clenched while men
die with their hands wide open?" would not in the least resemble
that given by the Rabbis, yet this last it is well that the scientist
should also remember : " Because on entering the world men would
grasp everything, but on leaving it all slips away." There exist in
men certain mental phenomena, the study of which is included in
what is known as ethics, and which are usually assumed to depend
upon what is called moral law. Whether there is such a law and
whether, if it exists, it can be logically deduced from observed facts
in nature or is only known as a special revelation, are questions
upon which scientific men in their present stage of development are
not agreed. There is not yet any satisfactory scientific basis for
what is recognized as sound ethics and morality throughout the civil-
ized world ; these rest upon another foundation.
This procession, bearing its lights of all kinds, smoky torches,
clear-burning lamps, farthing rush-lights, and sputtering brimstone
ANNUAL ADDRESS OF THE PRESIDENT. LV
matches, passes through the few centuries of which we have a
record, illuminating an area which varies, but which has been grow-
ing steadily larger. The individual members of the procession come
from, and pass into, shadow and darkness, but the light of the stream
remains. Yet it does not seem so much darkness, an infinite night,
whence Ave come and whither we go, as a fog which at a little dis-
tance obscures or hides all things, but which, nevertheless, gives the
impression that there is light beyond and above it. In this fog we
are living and groping, stumbling down blind alleys, only to find
that there is no thoroughfare, getting lost and circling about on our
own tracks as on a jumbie prairie; but slowly and irregularly we
do seem to be getting on, and to be establishing some points in the
survey of the continent of our own ignorance.
In some directions the man of science claims to lead the way; in
others the artist, the poet, the devotee. Far reaching as the specu-
lations of the man of science may be, ranging from the constitution
and nature of a universal protyle, through the building of a universe
to its resolution again into primal matter or modes of motion, he
can frame no hypothesis which shall explain consciousness, nor has
he any data for a formula which shall tell what becomes of the in-
dividual when he disappears in the all-surrounding mist. Does he
go on seeking and learning in other ways or other worlds ? The
great mass of mankind think that they have some information bear-
ing on these questions ; but, if so, it is a part of the wisdom of the
Orient, and not of the physical or natural science of the Occident.
Whether after death there shall come increase of knowledge, with
increase of desires and of means of satisfying them, or whether there
shall be freedom from all desire, and an end of coming and going
>
we do not know; nor is there any reason to suppose that it is a part
of the plan of the universe that we should know. We do know that
the great majority of men think that there are such things as right
and duty—God and a future life—and that to each man there comes
the opportunity of doing something which he and others recognize
to be his duty. The scientific explanation of a part of the process
by which this has been brought about, as by natural selection,
heredity, education, progressive changes in this or that particular
mass of brain matter, has not much bearing on the practical ques-
tion of " What to do about it ? " But it does, nevertheless, indicate
that it is not a characteristic to be denounced, or opposed, or neg-
lected, since, even in the " struggle-for-existence " theory, it has
I
LVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
been, and still is, of immense importance in human social develop-
ment.
" Four men," says the Talmud, " entered Paradise. One beheld
and died. One beheld and lost his senses. One destroyed the young
plants. One only entered in peace and came out in peace." Many
are the mystic and cabalistic interpretations which have been given
of this saying ; and if for " Paradise " we read the " world of knowl-
edge " each of you can no doubt best interpret the parable for him-
self. Speaking to a body of scientific men, each of whom has, I
hope, also certain unscientific beliefs, desires, hopes, and longings, I
will only say : " Be strong and of a good courage." As scientific
men, let us try to increase and diffuse knowledge ; as men and citi-
zens, let us try to be useful ; and, in each capacity, let us do the
work that comes to us honestly and thoroughly, and fear not the
unknown future.
When we examine that wonderful series of wave marks which we
call the spectrum we find, as we go downwards, that the vibrations
become slower, the dark bands wider, until at last we reach a point
where there seems to be no more movement ; the blackness is con-
tinuous, the ray seems dead. Yet within this year Langley has
found that a very long way lower down the pulsations again appear,
and form, as it were, another spectrum ; they never really ceased,
but only changed in rhythm, requiring new apparatus or new senses
to appreciate them. And it may well be that our human life is only
a kind of lower spectrum, and that, beyond and above the broad black
band which we call death, there are other modes of impulses—another
spectrum—which registers the ceaseless beats of wTaves from the
great central fountain of force, the heart of the universe, in modes
of existence of which we can but dimly dream.
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
GENERAL MEETING.
0)

BULLETIN
GENERAL MEETING.
279th Meeting. January 16, 1886.
President Billings in the Chair.
Thirty-two members and guests present.
Announcement was made of the election to membership of
Messrs. Benjamin Pickman Mann and Charles Cooper Nott.
The following report of the Auditing Committee was presented
by its chairman, Mr. Toner :
December 24, 1885.
The undersigned, a committee appointed at the annual meeting
of the Philosophical Society of Washington, December 19, 1885,
for the purpose of auditing the accounts of the Treasurer, beg
leave to report as follows
:
We have examined the statement of receipts, including annual
dues, sale of Bulletin, and interest on bonds, and find the same to
be correct as stated.
We have examined the statement of disbursements, and com-
pared the same with the vouchers, and find them to agree.
We have examined the returned checks and the bank account
with Puggs & Co., and find the balance, $484.02, to agree with the
statements in the Treasurer's report.
We have examined the U. S. bonds belonging to the Society, and
find them to be in amount and character as represented in the
Treasurer's report, aggregating $2,500.
J. M. Toner,
O. T. Mason,
T. C. Mendenhall,
Committee.
(3)
4 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. J. S. Diller communicated
NOTES ON THE GEOLOGY OF NORTHERN CALIFORNIA.
[Abstract.]
Under the direction of Capt. Dutton I have spent the last three
summers studying the geology of northern California and the ad-
jacent portion of Oregon. The conclusions of a general nature
referring to that region may be briefly summarized as follows
:
In the northern end of the Sierra Nevada and the central por-
tion of the Coast range, among the highly plicated, more or less
metamorphosed strata which are older than those of the Chico group,
there appears to be but one horizon of limestone, and that is of Car-
boniferous age.
The northern end of the Sierra Nevada is made up of three
tilted orographic blocks which are separated from each other by
great faults. The westernmost of these blocks stretching far to the
southeast appears to form the greater portion of the range.
As in the Great Basin region the depressed side of each block
was occupied by a body of water of considerable size. The deposits
formed in these lakes gave rise to the fertile soils of American and
Indian valleys.
The plication of the strata in the Sierra Nevada range took place,
at least in great part, about the close of the Jurassic or beginning
of the Cretaceous period, but the faulting which really gave birth
to the Sierra as a separate and distinct range by differentiating it
from the great platform stretching eastward into the Great Basin
region, did not take place until towards the close of the Tertiary or
the beginning of the Quaternary.
Although the faulting may have commenced earlier, the greater
portion of the displacement has taken place since the deposition of
a large part of the auriferous gravels and the beginning of the
great volcanic outbursts in the vicinity of Lassen's Peak. If we
may accept numerous small earthquake shocks as evidence, the
faulting still continues.
The distribution of the rocks of the Chico group indicates that
the western coast of the continent at that time lay along the western
base of the Sierra extending around the northern end of the range
in the vicinity of Lassen's Peak and stretching far northeasterly
into Oregon.. Off the coast lay a large island which now forms
GENERAL MEETING. 5
northwestern California and the adjacent portion of Oregon. This
island extended as far southeast as the Pit river region where it
was separated from the main land by a wide strait.
All of the ridges developed out of the Cretacean island belong
to the Coast range.
The volcanic ridge of Lassen's Peak lies between the northern
end of the Sierra Nevada and the Coast range. The great volcanic
field of Oregon and Washington Territory, to which Lassen's Peak
and the Cascade range belong, appears in a general way to be out-
lined by the depression between the Cretacean island and the main
land. A general account of the facts from which these conclusions
are drawn will appear in Bulletin of the U. S. Geological Sur-
vey No. 33.
Mr. I. C. Russell read a supplementary paper entitled
NOTES ON THE FAULTS OF THE GREAT BASIN AND OF THE
EASTERN BASE OF THE SIERRA NEVADA.
[Abstract.]
The structure of the Great Basin was systematically studied by
the geologists of the Fortieth Parallel Exploration, and subsequently
by G. K. Gilbert and J. W. Powell. The results of these investiga-
tions, so far as they relate to the faults of the region, are indicated
in the bibliographic list which follows.
The studies here referred to led to the recognition of a type of
mountain structure named the " Great Basin system," which has
been found to prevail over large portions of the United States west
of the Rocky Mountains. A typical mountain of this system is a
long, narrow orographic block, upraised along one edge, i. e. a mono-
clinal ridge. A mountain range having this structure usually
presents an abrupt scarp, formed of the edges of broken strata,
on -the side bordered by the fault, and slopes much more gently
in the opposite direction.
Mountain ranges of this character occupy the greater part of the
area of interior drainage, known as the Great Basin, and at times
overlap its borders. An older structure in which corrugation plays
an important part has been recognized by several geologists in the
desert ranges of Nevada and Utah, but these disturbances were
produced previous to the faulting which gave origin to the present
topographic relief.
6 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The writer has observed Great Basin structure to extend through-
out Western Utah, Northern Nevada, and into' Oregon as far as
Malheur Lake. On the west side of the Great Basin, at the imme-
diate base of the Sierra Nevada, there is an immense compound
displacement that can be followed all the way from Honey Lake on
the north to beyond Owen's Lake on the south, a distance of over
350 miles. Along many of the faults composing this belt the
records of a post-Quaternary movement may be clearly recognized.
Fault scarps produced by recent movement have been observed in
Eagle and Carson Valleys, south of Carson City, in Bridgeport
Valley, and on the west side of Mono Lake. The earthquake in
Owen's Valley in 1872, was caused by a movement along one of
the faults of this series.
The eastern face of the Sierra Nevada is extremely abrupt and
its western slope is gentle. Corrugations of older date than the
faults which determine the present relief of the mountains may be
observed at many localities. It thus agrees in its general features
with many of the Basin ranges. The Sierra Nevada is essentially
monoclinal in structure, but is traversed from north to south by
faults which divide it into separate ranges, as may be seen in the
neighborhood of Lake Tahoe and in the elevated region west of
Mono Lake. The Great Basin structure here extends beyond the
borders of the area of interior drainage, and is probably limited on
the west by the great valley of California. How far north of Lake
Tahoe the secondary faults that divide the mountain mass may be
traced is unknown, but they can certainly be followed to where the
Central Pacific railroad crosses the mountains.
The following list indicates where observations on the faults of
the Great Basin system may be found
:
Clarence King: Reports of the Fortieth Parallel Exploration.
Vol. 1, 1878, pp. 735, 744-746; Vol. Ill, 1870,
p. 451.
J. D. Whitney : The Owens Valley earthquake. Overland
Monthly, Aug. and Sept., 1872.
Joseph Le Conte: On the Structure and Origin of Mountains, with
special reference to recent objections to the
"Contraction Theory." American Journal of
Science, Vol. XVI, '1878, pp. 95-112.
u " A theory of the formation of the great features
of the earth's crust. American Journal of
Science, Vol. IV, 1872, pp. 345-355, 460-472.
GENERAL MEETING. 7
G. K. Gilbert : Progress report upon Geographical and Geological
Explorations and Surveys West of the 100th
Meridian, in 1872. Washington, 1874. p. 50.
" " Report upon Geographical and Geological Explo-
rations and Surveys west of the 100th Meri-
dian. Washington, 1875. Vol. Ill, Geology,
pp. 21-42.
" " Contributions to the history of Lake Bonneville.
In Second Annual Report of the U. S. Geo-
logical Survey. Washington, 1882. pp. 192
-200.
" " A theory of the earthquakes of the Great Basin
with a practical application. American
Journal of Science, Vol. XXVII, 1884, pp.
49-53.
J. W. Powell : Basin Range System. See Report on Lands of
the Arid Region of the United States.
Washington, 1879. pp. 94-95.
"
" Basin Range Province. See Report on the
Geology of the eastern portion of the Uinta
Mountains. Washington, 1876. pp. 6-7, 23-
25.
C. E. Dutton : Geology of the High Plateaus of Utah. Washing-
ton, 1880. pp. 51-53.
I. C. Russell : Sketch of the Geological History of Lake Lahon-
tan. Third Annual Report of the U. S.
Geological Survey. Washington, 1883. p.
202.
" " A Geological Reconnoissance in Southern Oregon.
Fourth Annual Report of the U. S. Geologi-
cal Survey. Washington, 1884. pp. 442-453.
" " Lake Lahontan. Monograph No. XI, U. S.
Geological Survey, pp. 24-28, 274-284.
Mr. Gilbert remarked that the section exhibited by Mr.
Diller appeared to demonstrate a history comprising (1) the folding
of the slates and the formation of several faults and associated
monoclines, (2) the general degradation of the country until the
monoclinal ridges were approximately obliterated, and (3) a re-
newal of movement on the old fault lines, giving rise to the exist-
ing topography.
8 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Willis remarked that in 1883 he had had opportunity to
study the Cascade Mountains north of the region described by Mr.
Diller. The Sierra structure is apparently not found in the north-
ern part of Washington Territory, and the eastern face of the
Cascade range is probably not characterized like the Sierra by a
great fault.
Mr. Diller concurred in the statement that the Cascade range
is built essentially of igneous rocks, and is not characterized by
great faults, at least along its eastern base.
The topography of the Sierra has entirely changed since the
deposition of the auriferous gravels, and some of the fault move-
ments are so recent that the stream terraces to which they have
given rise are still preserved.
Mr. G. K. Gilbert made a communication on
RECENT CHANGES OF LEVEL IN THE BASIN OF LAKE ONTARIO.
[The substance of this communication was presented to the
American Association for the Advancement of Science at Ann
Arbor, and appears in abstract in Science, Vol. VI, p. 222.]
Remarks were made by Mr. E. Farquhar.
280th Meeting. January 30, 1886
The President in the Chair.
Fifty-five members and guests present.
The Chair announced the appointment of the Committee on
Communications.
Mr. George E. Curtis made a communication on
lieutenant lockwood's expedition to farthest north.
[Abstract.]
The paper opened with a reference to the statement in the Ency-
clopaedia Britannica (article, Polar Regions, p. 326,) that " all this
region [the northern coast of Greenland and the interior of Grinnell
GENERAL MEETING. 9
Land] had already been explored and exhaustively examined by
the English expedition of 1875-76." A refutation of this state-
ment was not now necessary inasmuch as a retraction had already
been made ; but an impartial examination of Lieut. Lockwood's
observations was still required as a basis for our own confidence in
the latitude attained.
A description of the equipment of the expedition was given, with
a sketch of the events of the journey, and extracts from the narra-
tive report. The weights of the food and equipments drawn by the
dog team furnished the basis of a discussion as to the value of dogs
in arctic sledging. The weight of food taken for the support of
each man was about twice that taken for each dog. Now if a man
can drag a sufficiently greater amount to compensate for the greater
weight of his food, it is immaterial whether the motive force used
be dogs or men. On this expedition the dog sledge was actually
loaded so as to give a weight of about 100 lbs. to each dog ; but the
maximum weight that can be advantageously drawn by a man is
only 125 or, perhaps, 150 lbs. The ratio of effective work performed
to the weight of food consumed is, therefore, materially greater for
dogs than for men, so that a substantial economical advantage is
obtained by using dogs instead of men for sledge dragging. This
advantage seems not to have been appreciated by the English ex-
pedition of 1875'-76, whose heavy sledges and equipments were all
drawn by hand. In addition to the more conspicuous causes of
the failure of Lieut. Beaumont's expedition on the Greenland coast,
the neglect to make use of dogs must be added as an important
element.
The sextant observations made by Lieut. Lockwood for determin-
ing the position of his farthest north were shown to be highly
satisfactory. Sets of circum-meridian observations for latitude were
made at midnight of May 14th and at noon of May 15th. The
conditions of observation offer no sufficient reason for giving more
weight to one set than to the other. The mean of these results
gives 83° 24' as the latitude attained by Lieut. Lockwood, and an
uncertainty not greater than 1' represent the accuracy of its deter-
mination.
The paper closed with the following tribute to the character of
Lieut. Lockwood as an arctic explorer
:
I cannot close this review of Lieut. Lockwood's expedition to
farthest north without turning from the cold discussion of the astro-
10 PHILOSOPHICAL SOCIETY OP WASHINGTON.
nomical and geographical records to speak of him of whose life and
labors they constitute an imperishable memorial.'
The success of the expedition was not the result of chance, but
was due to Lieut. Lockwood's thorough knowledge of the details
of such an undertaking, and to his indomitable energy in its execu-
tion. During the preceding winter he had devoted himself to
preparation for the work; had made a careful study of the man-
agement and equipment of previous sledging expeditions—especially
those of the English in 1875-76—and profiting by the experience
of his predecessors was able to avoid their mistakes. Lieut. Beau-
mont's journey on the Greenland coast was impeded by the heavy
sledge, and the heavier equipments with which it was weighted.
Lieut. Lockwood's extraordinary distance was attained with a light
sledge drawn by dogs and loaded with nothing but food and the
barest necessities of a camp. Regardless of all personal comforts,
everything was sacrificed to the objects of the expedition.
Under the instruction of Mr. Israel, the young astronomer*
Lieut. Lockwood had familiarized himself during the winter with
all the astronomical observations necessary to be made by an ex-
plorer, and with the return of the spring sun applied himself to
practical observations with the sextant until he became an expert
in its use. So good was his astronomical work that the accuracy
of his observations is dependent only on the variability of the in-
strument and the difficulty of the conditions of observation.
In addition to a practical knowledge of arctic sledging, the expe-
dition was undertaken with a determined energy of purpose, those
qualities expressively termed " grit" and " pluck," which no obstacle
could defeat. Retaining only two companions at Cape Bryant, he
sent back his supporting party and continued his advance over an
unknown coast. Suffering continuously from cold, hunger, or
fatigue, he pushed on with unflinching perseverance until one hun-
dred and fifty miles of new coast were traversed and the national
colors unfurled in the highest latitude ever attained by man.
Simply to go a little nearer the pole than his predecessors was
not, however, the controlling object of this expedition. Lieut.
Lockwood's own motives, as we read them in his journal, were
these: "My great wish is to accomplish something on the north
coast of Greenland that will reflect credit on myself and on the ex-
pedition." Inspired by this praiseworthy ambition, his skillful
management resulted in its most successful realization. His mo-
GENERAL MEETING. 11
tives were not those of the visionary and enthusiast who " knows
nothing and fears nothing," but of an earnest practical explorer
whose ambition is to add something to the world's knowledge of
the planet on which we live. The literal fidelity of his narrative,
its freedom from an exaggeration that has too often marred the
records of previous Arctic explorers, the exact and painstaking
descriptions, and the careful distinction between what is seen and
what is inferred, all bear witness to his conscientiousness in the
search for truth.
As an important element in the success of Lieut. Lockwood's ex-
peditions, due recognition must be given to the cordial, sympathetic
and able co-operation of Sergeant Brainard. Chosen by Lieut.
Lockwood to continue the journey to Cape Bryant, when all the
remainder of the party returned, it was Brainard who pushed
onward with him over one hundred and fifty miles of that desolate
coast and reached the farthest north. It was likewise Lockwood
and Brainard who a year later, in May, 1883, explored the interior
of Grinnell Land and looked out on the shores of the western polar
sea.
But only one of these companions in exploration was destined
.to reach home to receive the honor due to their heroic achieve-
ments—honor due, but, as yet, awarded neither to the living nor
the dead. The story of the return is known to all, but perhaps not
Lieut. Lockwood's wonderful cheerfulness of spirit through that last
terrible winter at Cape Sabine with death staring him in the face
Lieut. Lockwood died on April 9, 1884, "from action of water on
the heart induced by insufficient nutrition "—the official euphemism
for starvation. This record of indescribable suffering, privation
and death, following that of two years of heroic endeavor and
achievement, is a tragedy which appeals to human hearts with, a
force unequalled by any story of fiction or by any drama of the
stage.
To Lieut. Lockwood's achievements are applicable the familiar
lines of Horace :
" Exegi rnonumentum aere perennius
Regalique situ pyramidum altius,
Quod non imber edax, non Aquilo impotens
Possit diruere, aut innumerabilis
Annorum series et fuga temporum."
Woven into the history of arctic discovery and engraven on our
12 PHILOSOPHICAL SOCIETY OF WASHINGTON.
maps, the substantial results of Lieut. Lockwood's explorations form
a tablet more enduring than brass, which the corroding storm, the
fierce north wind, and the flight of ages cannot efface.
In reply to a question by Mr. Mussey, Mr. Curtis stated that the
time for longitude determination was obtained from one ordinary
watch of good quality, and one pocket chronometer. Messrs. Dall
and Robinson discussed the advantages and disadvantages of the
use of dogs in arctic sledging, and attention was called to the im-
portance of using snow shoes, and of coating the sledge runners
with ice.
Mr. O. T. Mason made a communication on
TWO EXAMPLES OF SIMILAR INVENTIONS IN AREAS WIDELY APART.
[Abstract.]
Anthropologists assign similar inventions observed in different
parts of the world to one of the following causes
:
1. The migration of a certain race or people who made the in-
vention. Upon this theory similar inventions argue the presence of
the same people or race.
2. The migration of ideas—that is, an invention may be made by
a certain race or people and taught or loaned to peoples far removed
in time and place. Upon this theory similar inventions argue iden-
tity of origin, but not necessarily the consanguinity of those who
practice them.
3. In human culture, as in nature elsewhere, like causes produce
like effects. Under the same stress and resources the same inven-
tions will arise.
Now, the question arises, which of these causes shall be invoked
in specific cases to account for resemblances.
We must first examine the word resemblance.
Taking Aristotle's four causes
:
The material cause, ex qua aliquid fit.
The formal cause, per quam.
The efficient cause, a qua.
The final cause, propter quam.
We must enlarge upon them as follows : Every human activity
involves six fundamental considerations.
1. The agent, or efficient cause.
GENERAL MEETING. ' 13
2. The material cause.
3. The implemental cause.
4. The formal cause.
5. The processive cause—that is, the exact order and method of
the action.
6. The motive or function.
We might, also, include a series of concomitants, such as techni-
cal vocabulary, all sorts of traditional lore and myths, social or-
ganization, and even religious rites.
Again, some of the six causes are themselves generally the out-
come of other causes, so that we have concatenations and genealo-
gies of causes.
Now for the application. Most men, when they say this thing
resembles that, have reference only to one of our six causes. They
mean simply that there is resemblance in form, or material, or
technical method, or function. My plan would be to submit such
resemblances to scrutiny to ascertain how far they extend, and, also,
to examine resemblances known to be consanguine, or borrowed,
or independent, to ascertain which of our characteristics are pecu-
liar to them. In that way an inductive system of rules would be
adduced.
The two independent inventions which I exhibit are a beginning
in that direction. One is a stitch in basketry, found only at Cape
Flattery and on the Congo. This stitch is common enough in fish-
traps, wattling fences, and cages, but in only these two areas have
people thought to apply it to close basketry. It consists of vertical
warp, a horizontal second warp, laid behind the first, and a coiling
or sewing of these two together, so as to show a diagonal stitch in
front and a vertical stitch in the rear. Here the resemblance is in
method alone. In all other respects the inventions diner.
The other invention referred to is the throwing-stick of Austra-
lians, Puru Purus, and Eskimo. These agree, in motive or func-
tion and in the fundamental idea of a staff and a hook. Beyond
this the Eskimo have invented a dozen additional attachments
never dreamed of by the others.
Mr. Murdoch supplemented the enumeration of throwing sticks
by describing an undeveloped form used by the Siberian Eskimo.
In reply to a question by Mr. Goode, Mr. Mason stated that he
had not seen the Brazilian sticks ; they are mentioned by many
14 PHILOSOPHICAL SOCIETY OF WASHINGTON.
travelers. Mr. Mann and Mr. Murdoch described the manner in
which the throwing stick is used by Eskimo in kyaks. The motion
centers in the wrist and not the elbow or shoulder.
281st Meeting. February 13, 1886.
The President in the Chair.
Fifty-five members and guests present.
Mr. J. H. Kidder communicated an
HISTORICAL SKETCH OF DEEP SEA TEMPERATURE OBSERVATIONS,
illustrating the subject by numerous diagrams and by a collection
of deep sea thermometers.
Mr. E. B. Elliott made a communication on the
ANNUAL PROFIT TO BANKS OF NATIONAL BANK NOTE CIRCULATION,
and a second communication on the
QUANTITY OF UNITED STATES SUBSIDIARY SILVER COIN EXISTING
AND IN CIRCULATION.
In these papers he developed the formulae used in computing cer-
tain tables embodied in the report of the Comptroller of the
Currency.
Remarks were made by Messrs. Mussey and Lawrence.
Mr. Asaph Hall read a paper on
THE NEW STAR IN THE NEBULA OF ANDROMEDA,
giving an historical account of its discovery, growth and decadence.
[This paper is printed in the American Journal of Science, 3d se-
ries, vol. xxxi, p. 299.]
general meeting. 15
282d Meeting. February 27, 1886.
The President in the Chair.
Fifty-six members and guests present.
The Chair announced the election to membership of Mr. George
JOTHAM CUMMINGS.
Mr. Asaph Hall made a communication on
THE IMAGES OF STARS,
which was discussed by Messrs. Eastman, Curtis, and Paul.
[This paper is published in the Sidereal Messenger, April, 1886.]
Mr. R. S. Woodward made a communication
ON THE CHANGES OF TERRESTRIAL LEVEL SURFACES DUE TO
VARIATIONS IN DISTRIBUTION OF SUPERFICIAL MATTER.
[To appear as a Bulletin of the U. S. Geological Survey.]
He was followed by Mr. G. K. Gilbert with a paper
ON THE OBSERVED CHANGES OF LEVEL SURFACES IN THE BONNE-
VILLE AREA, AND THEIR EXPLANATION
;
and Mr. T. C. Chamberlin then began a paper
ON THE VARYING ATTITUDES OF FORMER LEVEL SURFACES IN
THE GREAT LAKE REGION AND THE APPLICABILITY OF PRO-
POSED EXPLANATIONS.
283d Meeting. March 13, 1886.
Vice-President Harkness in the Chair.
Thirty-nine members and guests present.
The Secretary read a letter from the Secretary of the Council of
the Anthropological Society, inviting the members of the Philo-
sophical Society and their friends to attend the annual meeting of
16 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the Anthropological Society and listen to an address by its president,
Major J. W. Powell.
The Chair announced the election to membership of Messrs. Car-
los Albert Kenaston, Roland Duer Irving and Artemas
Martin.
Mr. T. C. Chamberlin completed his communication
ON THE VARYING ATTITUDES OF FORMER LEVEL SURFACES IN
THE GREAT LAKE REGION AND THE APPLICABILITY OF
PROPOSED EXPLANATIONS.
Remarks were made by Mr. Dutton.
Mr. R. D. Irving made a communication on
THE ENLARGEMENT OF MINERAL FRAGMENTS AS A FACTOR IN
ROCK ALTERATION,
which was discussed by Messrs. Iddings, Diller, Dutton, and
Lawrence.
284th Meeting. March 27, 1886.
The President in the Chair.
Thirty-three members and guests present.
Mr. I. C. Russell made a communication on
THE SUBAERIAL DECAY OF ROCKS AND THE ORIGIN OF THE RED
CLAY OF CERTAIN FORMATIONS.
This was discussed by Prof. John S. Newberry, of New York
city, and by Messrs. Goode, Darton, Irving, and Chamberlin.
Mr. Romyn Hitchcock made a communication on
RECENT IMPROVEMENTS IN MICROSCOPIC OBJECTIVES, WITH DEMON-
STRATION OF THE RESOLVING POWER OF A NEW 1-16TH INCH.
Remarks were made by the President.
GENERAL MEETING. 17
Mr. Henry Farquhar read a communication on
A FONETIK ^ELFABET.
[^Ebstraekt.]
Ais selfabet cendoerteyks tu repriz6nt de sawndz av I^glic spiytc
sez yuwjuwali hoard, bai twenti-nain letoerz. Av <5iyz b, d, f, g, h,
1c, I, m, n, p, r, s, t, v, w, y send z hsev der koestomeri sawndz ; c hsez
its sawnd sez in benificieri [beneficiary] — a sawnd akeyjoenali given
tu s or t or ch, or mooer ofen tu sh ; j iz kanfamd tu its Frentc
sawnd— hwitc iz ool dset iz left tu it hwen kambaind wi<J d in I/'glic,
sez in ozdjutcent [adjutant] ; hwail de neyzal yuwjuwali riten ng, de
ih flset send th carp, ar given bai de I6tcerz y, 8 send ft, barod fram de
Griyk selfabet. Av de vawels, a iz sez in wad or bar, e sez in pet, i
sez in pit, o sez in on or or, u sez input; hwail de daigrsefs ce send 02
ar yuwzd for de vawel sawndz hoard in bozt [bat] send in beet [but
;
won, burr, stir, herd, heard, word, etc.]. Doeblld letoerz indikeyt
proloo/'d sawndz: I in doebll [double], m in prizmm [prism], a in
stdari [starry], in doon [dawn]. (Edcer lo^ vowels ar rigarded sez
impyuoer sawndz ; send sloerz bifocer r ar dinowted bai 02, tendensi
tu klowz wi<5 de lips bai w, send wi<S de toe^ bai y, falowi^ a cort vawel
does wiy hsev eoe, ice, oce, uce in bear, bicer, bocer, bucer [bear, beer,
bore, boor], atv, ow, uw in haivs, flow, buwt [house, flow, boot], ey, iy,
ay in beyt, biyt, bayt [bait, beat, bite]. Mz egzsempllz av ce^oer kam-
bineycoenz, oil, ivain, yuwz, tenyur, kyuozr [oil, wine, use, tenure, cure]
mey biy given. iEksented vawelz ar markt, sekanderi seksents
(sez on de foerst silabll av veriabiliti) hsevif de greyv sain, prinsipal
woenz de sekyuwt.
Omy tu de pawcerful influwens av <5e skuwlz in kiypij' cep sen ek-
sesiv revcerens for de kanvenccenal stsendard av speli^, send tu de
fsekt dset de msedjdxiti av de woerdz av awcer lseygwedj ar nown tu
oes bai <?er sepicerens sez printed or riten rsedcer <?sen bai der sawnd
sez spowken, <Jer iz litll imiydiet praspekt av scekses in de " speli^-
riform" muwvment, hwitc eymz tu divelap iiweer spelif intu woen
mooer nicerli fonetik. N&vcer<Jeles, der ar prsektikal yiiwsez for a
39
18 PHILOSOPHICAL SOCIETY OF WASHINGTON.
gud fonetik selfabet. Foerst, it kud foernic a stsendard av proncensiey-
coen in dikcceneriz av ool sorts— huvvz riydoerz wud «5oes biy seyvd
de tsesk av lcerni^ a difoerent sistem for iytc dikcoeneri, sez set prez-
ent. Sekand, it kud send cud form a regyular brsentc av instrcek-
coen in skuwlz, send does assist in sikyucerb/ yuwniform proncen-
sieycoen. 6*cerd, soem soetc divays iz olmowst a nisesiti, if wiy wud
bri^ ordoer intu a biznes naw oltuge'5oer keyatik ; trsenslitoereycoen av
neyniz fram <Je Riiwcan, iErabik send ce^cer lse^gwedjez nat yuwziy
oe Rowman selfabet. iEz wiy falo now rne#ad kansistentli set prez-
ent, <?er wud poerhseps biy now greyt difikcelti in estseblicb/ woen
;
especaii if bai it <Je sayt av a neym kud giv sen sepraksimet aidia
haw it iz pronawnst bai 5owz mowst fserniliar wW it.
Mr. Mussey said that the principal difficulty in all phonetic
alphabets was not in the alphabets themselves, but in the existing
variety of pronunciation and the disagreements as to the true
pronunciation of words. Pitman's phonetic system—little short
of an inspiration—was to his mind the best ever devised for
practical use, though Bell's system of visible speech enabled a
person familiar with it to correctly pronounce words and sentences
in any language whatever.
Mr. Mallery said that he had been connected with the prepa-
ration of a phonetic alphabet by the Bureau of Ethnology, with
the object of collecting and recording the vocabularies of the
languages of the North American Indians. In addition to the
requisite that there should be a distinct character for every sound,
it was made a fundamental rule that the characters should be
limited to those in an ordinary font of English type, embracing
however not only the Roman alphabet but such characters and dia-
critical marks as the printers' cases of average newspapers could
furnish. This was accomplished so as to provide for many more
sounds than are included in Mr. Farquhar's scheme, yet without
resort to the Greek letters used by him in several instances. It
was done by the simple device of reversing the large number of
letters in the Roman alphabet which present a markedly different
appearance when so reversed, from their erect position. This is
entirely convenient to the printer and does not occasion awkward-
ness in the current script to the recorder or writer for the press, as
GENERAL MEETING. 19
it is only necessary to mark the letter intended to be reversed, after
writing it in the normal manner, and to notify the printer accord-
ingly. In practice the letters intended to be reversed are marked
by a cross beneath them, though a still more current method of
distinction would be by the cedilla in using which the pen or pencil
is not removed from the letter as formed. This is however more
convenient to the writer than to the printer.
The result of this scheme in practice has solved one part of the
problem of a universal phonetic alphabet. Vocabularies and
chrestomathies of unwritten languages have been recorded and
printed, upon which grammars and dictionaries have also been pre-
pared and printed, and from them the languages can be learned so
as to be spoken intelligibly without oral instruction. The possibility
of the use of such an alphabet with only such modification as would
increase its simplicity, in the reform of the English literation, is not
to be doubted, in view of its success under more difficult conditions.
The actual obstacles to phonetic reform of fixed alphabets are,
though perhaps insuperable, non-essential in the scientific view of
the question.
Concerning the gliding sounds mentioned by Mr. Farquhar, Mr.
Doolittle remarked that some of these appeared to be essential,
while others were only accidental.
285th Meeting. April 10, 1886.
The President in the Chair.
Fifty-nine members and guests present.
The Chair announced the election to membership of Messrs.
Alexander George McAdie and Robert Thomas Hill.
Mr. Mallery read a communication on
CUSTOMS OF EVERY-DAY LIFE.
[Abstract.]
The scope of the paper excluded the more commonly noted cere-
monial institutions, such as appear in regal courts, courts of justice,
and legislative bodies, and embraced the ordinary modes of behavior
among civilized people. These all have history and significance,
20 PHILOSOPHICAL SOCIETY OF WASHINGTON.
are not the result of deliberate invention or convention, and in their
present shape clearly exhibit the laws of evolution, though not always
in the directions set forth in text-books and treatises on sociology.
Comment was made upon the topics of social etiquette, precedence,
titles, grammatical forms of personalty, the address and signatures
of letters, forms and practices relating to written invitations and to
social visits, and formularies of oral greeting, with examples or
illustrations under each topic.
Fashion was distinguished from custom as being imitative and
transitory, although in some few instances genuine merit in a fashion
led to its permanent adoption under the same law with which the
convenient and useful portions of old customs have survived in
modifications.
Two points on which the paper specially declared disagreement
with Herbert Spencer relate to the bow in salutation and to the
hand-shake or grasp. The bow Mr. Spencer regards as but modi-
fied from the natural expressions of physical fear and bodily subjec-
tion noticed among sub-human animals and the lowest tribes of men,
originating in actual prostration and groveling to which crawling
and kneeling succeed, and the bow is but a simulated and partial
prostration. A large class of obeisances doubtless had their origin
in the attitudes of fear, and several were adduced in addition to
those mentioned by Mr. Spencer, but it was contended that the sub-
ject of the bow is much more complex than as presented by him,
a separate and independent course of evolution being suggested.
Evidence was collected from many sources, and especially from ges-
ture speech, relating to the concepts of, and expressions for, higher
and lower, superior and inferior, assent, submission and respect, all
connected with the forward and downward inclination of the head
in salutation. Regarding the uncovering of the head as a part of
the masculine bow, the paper offered to Mr. Spencer a new illustra-
tion of militancy, too often insisted upon in his Synthetic Philosophy
but not definitely in this connection. The voluntary deprivation of
removable head gear—once defensive—is often a mark of defeat and
subjection. The modern formal military and naval salutes contain
the same idea that the saluter is actually or symbolically powerless.
Therefore the action of the removal of the hat, the present repre.
sentative of the casque, helmet, or morion, is better adapted to a
"surrender" theory than to that of pretended "beggary" advocated
by Mr. Spencer.
GENERAL MEETING. 21
That great writer believes that the hand-shake originated in a
struggle, first real, afterwards fictitious, in which each of the per-
formers attempted to kiss the hand of the other, which was resisted,
thus producing a reciprocating movement of the joined hauds. In
examining this explanation the antiquity and prevalence of the kiss
in salutation was questioned. The mutual kiss of affection or pas-
sion by the lips between opposite sexes is not found among the lower
tribes and is probably not of great antiquity. It was preceded
without reference to sex by patting, stroking or rubbing different
parts of the body—smelling and'snifning being also common. The
kiss of the hand is undoubtedly ancient and gestural, and is ap-
parently not derived from that of the lips, which is gustatory. In-
stances were admitted of the identical friendly contest for priority
in kissing hands relied on by Mr. Spencer, but they were consid-
ered to be connected with the topic of precedence as secondary, the
joining of hands being primary and wholly unconnected with a
"shake" or any motion after junction. Evidence was presented
that the junction of hands in testimony and in expression of agree-
ment and friendship is of too high antiquity and universality to be
derived from a pantomimic contest about precedence for the compara-
tively modern and limited kiss.
Mr. Mason expressed the opinion that not all customs are indi-
rectly derived, and cited the innovations of the day as instances of
customs deliberately assumed for a definite purpose.
Mr. Mendenhall referred to the numerous ways in which Jap-
anese customs are the inverse of ours. In beckoning, the fingers are
turned clown instead of up, and this is probably explained by the fact
that in Japan those who are beckoned—namely, inferiors—are by
custom or in theory prostrate. The kitchen of a hotel is placed at
the front against the street. A horse is backed into the stable and
led out. It is a matter of etiquette, and modesty also, that ladies
turn their toes in. The Japanese do not shake hands ; the bow is
very low, and is begun twenty feet away. There is no kiss of cere-
mony or friendship, but the kiss exists as an expression of passion.
Japanese children play all the common games of our children in
some modified form, except marbles.
In reply to a question by Mr. Mason, Mr. Mendenhall said
that a Japanese does not shake his own hands as a salutation to
22 PHILOSOPHICAL SOCIETY OF WASHINGTON.
another, but may join them in bowing as a merely accidental atti-
tude. Messrs. E. Farquhar and Mussey spoke* of the antiquity
of kissing as indicated by Hebrew and Greek literature. Other
remarks were made by the President and by Mr. Clarke.
Mr. R. D. Mussey made a communication entitled
WHEN I FIRST SAW THE CHOLERA BACILLUS.
286th Meeting. April 24, 1886.
The President in the Chair.
Thirty members present.
The President communicated an invitation from the American
Historical Association to attend its sessions of April 27-29.
Mr. G. Brown Goode and Mr. T. H. Bean made a joint com-
munication on
THE DISTRIBUTION OF FISHES IN THE OCEANIC ABYSSES AND
MIDDLE STRATA.
Remarks were made by Messrs. Paul, Harkness, Billings,
Doolittle, Goode, Welling, and Taylor, and by Prof.
Edward D. Cope, of Philadelphia.
Mr. Gilbert Thompson made a communication on
THE PHYSICAL-GEOGRAPHICAL DIVISIONS OF THE SOUTHEASTERN
PORTION OF THE UNITED STATES AND THEIR CORRESPONDING
TOPOGRAPHICAL TYPES.
[Abstract.]
Having charge of the geographical work carried on by the U. S.
Geological Survey in that portion of the Appalachian region south
of Pennsylvania and the Ohio river, I have had occasion to con-
sider the classification of the region from the point of view of the
geographer. It has previously been divided by many authors and
into numerous sections, the basis of classification being geological
botanical, agricultural, or commercial, and usually from a local
standpoint. For my purposes the principal basis of classification
is the character of the topographic relief, but this is so closely
GENERAL MEETING. 23
related to the features controlling other classifications that a large
share of the boundaries coincide with lines previously drawn and
the selection of appropriate designations is little more than a choice
between names previously given.
There are some parts of the United States where the drainage
basin affords the best unit for the purposes of the physical geo-
grapher. This holds for the basin of the Laurentian lakes, the basin
of the Red River of the North, and the great Interior basin. But in
the Appalachian region the drainage cannot be used. There is how-
ever in this region a remarkable line of demarcation, known as the
fall line, which finds its manifestation in connection with the drain-
age, and is the natural boundary of an important division. If we
follow the course of any river in the eastern part of the United
States, south of New England, from its source to the sea, we discover
that at a certain point it ceases to be rapid and turbulent, and
becomes broad and slow-moving, and in many cases an estuary of
the sea. At the point where this change occurs there is usually
a fall or rapid. The familiar local example is the Potomac at
Little Falls. I have traced this fall line from near Troy, N. Y.,
southward by the interior cities of Washington, Richmond, Colum-
bia, and Montgomery, and thence to the Muscle Shoals of the
Tennessee river. It is always the lower limit of water power
and often the upper limit of navigation, and is therefore marked,
and destined to be marked, by cities and towns of importance. In
its northern portion it is at the head of tide, and nowhere does it
exceed an altitude of 200 feet. It may yet be determined that it
crosses the Saint Lawrence at the Lachine rapids and the Missis-
sippi above Cairo, although no rapid exists at that point. Whether
it may be traced farther and into Mexico remains to be determined.
From the fall line to the shore of the sea there is a region having
a gentle slope, traversed by slow-moving rivers, and fringed at al-
most a dead level by deltas, swamps and everglades. This I have
entitled the coastal plains, including as subdivisions the Atlantic
plains and the Gulfplains.
The area bounded by the fall line and by the Mississippi and
Ohio rivers and a part of the drainage divide of the Laurentian
lakes, might be taken as a whole as the Appalachian region, but it
includes three sections so distinct in topographic type as to warrant
separate designations.
From the Ohio river southeastward and from the Mississippi
24 PHILOSOPHICAL SOCIETY OF WASHINGTON.
eastward the country gradually rises until it reaches an altitude of
about 2500 feet above sea level, where it is geneually cut off by an
escarpment facing to the southeast aud about 1200 feet in height.
The composite name of Cumberland- Allegheny -Catskill plateau
would serve to define it, but for brevity I have designated the whole
as the Cumberland plateau. Its general topographic character is
that of a table land deeply cut by a system of ramifying drainage.
At the north the surface is somewhat rolling, and the plateau ends
at the south in long, finger-like spurs. Its rivers and streams rise
generally near the edge of the escarpment and flow toward the
northwest. The Potomac however breaks across the edge and flows
eastward, while the New and Tennessee rivers enter the plateau
from the east and flow westward.
From the Cumberland plateau eastward to the eastern foot of
the Blue Ridge lies a belt to which the name of Appalachian re-
gion is applied in a restricted and definite sense. It is characterized
by numerous long, narrow mountain ridges, closely parallel to
each other and bending in sympathy with the local curvature
of the belt. Through large areas they are approximately uniform
in height, but elsewhere they are unequal. In a notable belt, every-
where recognized in the local nomenclature as a valley, and travers-
ing the region from north to south, the ridges are so low that they
rank only as hills. At the north the principal mountain area lies
west of the great valley and only the Blue Ridge on the east. At
the south the valley lies close to the Cumberland plateau, and the
Blue Ridge is expanded into a broad mountain district, culminating
in Mt. Mitchell (6711 feet), the highest summit east of the Rocky
Mountains.
The remaining area is the Piedmont region, an undulating plain,
diversified by low spurs from the mountain region, and occasional
isolated hills of considerable elevation. The streams are rapid, and
the topographic relief gradually diminishes toward the fall line.
The communication was fully illustrated by maps and topographic
sketches, and by a profile from Louisville, Kentucky, to Charleston,
South Carolina. Remarks were made by Messrs. Gilbert, Hark-
nes8 and Cope.
general meeting. 25
287th Meeting. May 8, 1886.
The President in the Chair.
Thirty-five members present.
The Chair announced the election to membership of Messrs.
Joseph Hammond Bryan and Merwin Marie Snell.
Mr. Thomas Russell made the following communication on
temperatures at which differences between mercurial
and air thermometers are greatest.
Glass and mercury do not expaud uniformly. An increase in
temperature of one degree at one hundred degrees causes greater
changes of volume than the same increase at zero. (In all refer-
ences here to degrees and temperatures the centigrade scale is to be
understood.) Normal mercurial thermometers, when corrected for
their various errors of construction, differ among themselves and
also from the air-thermometer.
At 40° the mercurial thermometer reads about 0.°2 higher than
the air-thermometer. At— 38. °8, the melting point of mercury, it
reads about 0.°2 lower. The quality of mercury in a thermometer
has an influence on its reading. A thermometer containing unj
of lead in the mercury will read 0.°5 lower at 50° than if the
mercury is pure. [H. J. Green.]
Comparisons have been made at the Signal Office between an air-
thermometer and a number of mercurials. Some deductions have
been made from the results of this work as to the temperatures at
which the differences between the two thermometers are greatest.
From the same results there have also been derived values of the
coefficients of expansion of glass dependent on the second and third
powers of the temperatures. It is to these I wish to call your at-
tention.
The air-thermometer used was of the kind that measures tem-
peratures by the varying pressure of a quantity of air kept at a
constant volume. Five Tounelot mercurial thermometers were
compared with this air-thermometer at temperatures from 0° to
55°. Two Baudin thermometers were compared with it from 0°
to— 38.°8.
The freezing points of mercurial thermometers rise with age. A
few days after a thermometer is filled this rise may amount to a
26 PHILOSOPHICAL SOCIETY OF WASHINGTON.
whole degree. In a year after that it may rise an additional five-
tenths of a degree; with succeeding years the 'change is less and
less.
When a thermometer is raised to a high temperature its freezing
point is depressed. The average depression for 100° is about 0.°2.
On raising to a temperature lower than 100° the freezing point is
also depressed, but not so much. For 50° the depression is about
O.°05. For temperatures as high as 100° the depressions are about
proportional to the squares of the temperatures by which they are
produced.
The cause of these changes of freezing point is in the nature of
the glass. The mercury in the thermometer has nothing to do with
them ; neither has the atmospheric pressure.
The amount of the changes depends on the composition of the
glass in the thermometer-bulb. It has been recently ascertained by
H. F. Wiebe that the change is greatest for glass containing equal
quantities of potash and soda. A thermometer made of a variety
of glass containing 14 per cent, of potash, 14 per cent, of soda, the
remainder silica and oxide of lead, was found to have its freezing
point depressed 0.°84 on raising it to 100°. Thermometers in which
the potash or soda in the glass was replaced by lime were found
to have the freezing points depressed only 0.°07 for the tempera-
ture of 100°.
To produce the maximum depression of freezing point peculiar
to any temperature requires that the thermometer be kept at that
temperature for a certain length of time. For a temperature of
100° a half hour suffices ; for 50° two hours are required.
If the thermometer is kept at 100° longer than half an hour
the depressed freezing point after that time begins to rise. If con-
tinued at the higher temperature for two weeks the freezing point at
the end of that time will be found to have risen about one degree.
This fact is taken advantage of by some makers of thermometers
to produce an instrument whose freezing point "will vary but little
in years subsequent to its manufacture.
The depression of freezing point produced by high temperature
is only temporary. The thermometer in the course of time regains
the reading of its freezing point corresponding to ordinary tempera-
tures. The more quickly the depression is produced the more
slowly the reading is regained.
After a thermometer has been subjected to a temperature of 100°
GENERAL MEETING. 27
it will regain its ordinary freezing point reading in one month.
The change in the first part of this period is much more rapid than
towards the end. To recover the depression caused by 50° re-
quires only two days. The older a thermometer the more quickly
it gains its freezing point corresponding to ordinary temperatures.
An instrument forty years old will regain its freezing point after
exposure to 100° in one week while an instrument three years old
requires a month.
The more alternations of temperature a thermometer is subjected
to the more quickly its freezing point rises.
A thermometer subjected to a very high temperature, as 350°, will
will have its freezing point raised from 12° to 20°. This rise is
not due to softness of the glass at the high temperature and a con-
sequent diminution in the volume of the bulb by the atmospheric
pressure. This is shown by experiments with weight-thermometers.
In these the tubes are open to the pressure of the air and there is
as much pressure inside as outside the bulb.
As heating to 100° depresses the freezing point while heating to
350° raises it there must be some intermediate temperature for
which there is no change. This point is usually at the tempera-
ture of about 160° to 180°, but varies widely with thermometers
made of different kinds of glass.
When a thermometer is subjected to a very low temperature a
temporary rise in its freezing point is produced. To produce an
appreciable rise requires a long-continued exposure. After being
kept twenty-four hours at— 30° the freezing point is found to be
about 0.05° higher than at first.
One hundred degrees on the centigrade scale is taken as the tem-
perature of steam from pure water boiling under a normal barometric
pressure equal to 760 mm. of mercury. A variation of 1 mm.
in the pressure will change the temperature 0.04°.
Zero is taken as the temperature at which pure ice melts when
subject to an atmosphere of pressure. An increase of a whole at-
mosphere lowers the temperature of the melting point of ice 0.008°.
This is to be distinguished from the effect of an atmosphere of
pressure on the reading of a thermometer ; by compressing the bulb
it causes the thermometer to read about 0.°2 higher than if there
was no pressure.
The fundamental distance on a normal thermometer is taken as
the reading it would have at a true temperature of exactly 100°
28 PHILOSOPHICAL SOCIETY OF WASHINGTON.
minus the reading of its depressed freezing point. This, which
should be exactly one hundred degrees, rarely is so. When the fun-
damental distance is taken iu this way it is invariable with age. It
is the same forty years after the thermometer is made as four hours
after, provided the thermometer is kept at ordinary temperatures.
The fundamental distance is not invariable when the raised freez-
ing point is used in forming it instead of the depressed freezing
point. In this case there is a constant diminution with age as the
raised freezing point rises more rapidly than the boiling point.
There is not uniformity of practice in the matter of forming the fun-
damental distance, but it is greatly to be desired.
Pleating a thermometer to 350° causes a permanent increase in
its fundamental distance between depressed freezing point and boil-
ing, varying from 0.°4 to 0.°9. An increase of 0.°4 in the funda-
mental distance corresponds to a decrease of fo part in the coeffi-
cient of expansion of the glass.
The total correction of a mercurial normal thermometer for
errors in its construction is composed of three parts
:
1st. The correction for erroneous fundamental distance. For
any temperature this is a proportional part of the differ-
ence between the fundamental distance and 100°.
2nd. The calibration correction. This is the correction to the
scale marks considered as subdividing the capacity of the
tube from 0° to 100° into one hundred equal parts. It
involves variations in the bore of the tube as well as irreg-
ularities in the placing of the marks.
3rd. The correction at freezing point. This is the amount the
thermometer reads in melting ice above or below 0°. At
any time it is the observed reading of the thermometer in
melting ice immediately after exposure to the temperature
measured. Sometimes it is impossible and it is almost
always inconvenient to observe the freezing point of the
thermometer immediately after observing a temperature.
In such a case the position of the depressed freezing point
for that temperature must be computed from the law of
the variation of the freezing point. It is always prefera-
ble however when the highest accuracy is required to ac-
tually observe the freezing point.
When a thermometer is put in ice this is what happens : The
column falls rapidly at first, then more slowly. Presently it be-
. GENERAL MEETING. 29
comes stationary ; finally it begins to rise. Fifteen minutes after
the thermometer reaches its lowest reading this rise is about 0.°01.
It is best in observing the freezing point of a thermometer to put it
in ice thoroughly saturated with water. The ice should be con-
tained in a vessel from which the water cannot flow off. A ther-
mometer put in ice in this condition takes on the temperature of
0° more quickly than if put in dry ice containing a good deal of
air. This method of observing the freezing point was introduced
by Baudin of Paris.
There is another correction to a normal thermometer which is
little known and rarely applied. Let
:
V= volume of bulb at 0°.
v ss volume of tube from 0° to 100° at temperature 0°.
/? = coefficient of cubical expansion of glass.
Y = coefficient of expansion of mercury.
T= thermometer-reading corrected for calibration, etc.
t = true temperature.
A consideration of the construction of the thermometer leads to
this equation
:
7(1 4- m + • (1+00^ = F(l + yt). (1)
The volume of the bulb at t°, plus the volume of that part of the
tube corresponding to the thermometer reading, is equal to the
volume of the mercury at 2°. For t = 100 the equation becomes
:
V (1 + /3100) + v (1 + ,3100) = 7(1 + rl00). (2)
v
Eliminating
-y from (2) by means of its value found from (1)
we have
:
rp__ t 1 + 100/? f o,
• 1 + Ui '
(3)
Taking as the coefficient of cubical expansion of glass, /5, the
quantity 0.000026, the following values are found for T— t, for
the various readings of the thermometer from — 40° to + 100°.
T
30 PHILOSOPHICAL SOCIETY OF WASHINGTON.
These are known as the Poggendorf corrections. They are due
to the capacity of the tube from the zero to the one-lumdrod degree
mark, being different at different temperatures.
In the following table are shown the results of the comparisons
of a certain mercurial thermometer, Tounelot No. 4207, with the
air-thermometer
:
Touncloi Xo. 4207.
GENERAL MEETING. 31
powers of the temperatures in changing the capacity of the tube
from 0° to 100° are neglected. The capacity of the tube is only -^
part of that of the bulb.
@v ft2 , t33 are the coefficients of expansion for glass for the first,
second, and third powers of the temperature. yv y2 , y3 are the
same for mercury.
To make an adjustment of the differences between the mercurial
and air-thermometers equation (4) can be put in the form
(100*- ?) x+ (10000*— f)y+ 0.000026?— 0.0026* 4- a =0 (5)
in which x = r* ~ f
2
, y =
Yz ~
'} and A = T— I This is less ap-
proximate than (4) but still sufficiently rigorous for the purpose
intended.
Forming observation-equations on this model with the observed
differences a, as the absolute terms, and solving by the method of
least squares, the values of x and y are found to be
x = - 0.0001391
y = + 0.000000863
Substituting these in (5) it becomes
- 0.00788* + 0.000165? - 0.000000863? + a = 0. (6)
Differentiating (6) with respect to t and A, and putting -r- = 0,
the following quadratic-equation is found
0.000002589? - 0.000330* + 0.00788 = 0, (7)
the solution of which gives for the temperatures at which the differ-
ences between the mercurial and air-thermometer are greatest * =
31.8 and * = 95.8. To find the temperatures at which the mercurial
and air-thermometer agree, put A = in (6) ; the values of * that
then satisfy the equation are * = 0, * = 100, and * = 91.
At 32° the mercurial thermometer reads higher than the air-
thermometer, at 96°, it reads lower. A curve representing the
differences has the following form :
/W 35° 50" 75' IW -200*
Fig. 1.
—
T 4207 minus Air-thermometer. Abscissas = Temperatures.
Centigrade. Ordinates = Differences.
32 PHILOSOPHICAL SOCIETY OF WASHINGTON.
This agrees with what has been observed by Dr. Gruumaeh of
the Berlin Aichungs Commission. Pie found the maximum differ-
ence on a certain thermometer to be + 0.°12 at 29.°8, and another
secondary maximum of — 0.°04 at 82°.
A slight change in the values of x and y will make a large
change in the position of the secondary maximum. For another
thermometer investigated at the Signal Office this point was found
to be at 130°.
The values of x and y can be analyzed still further to ascertain
whether consistent with known physical properties of glass and
mercury.
Taking Broch's values for the expansion of mercury, which are
based on a re-reduction of Regnault's observations, it is founds
adapting the figures to the notation used here, that:
7l
= + 0.000181792
7a
=
-f- 0.000000000175
73 = + 0.000000000035116
Substituting these values of y x and y2 iu the equations
„_ 72 —
&
_
fs — ft
n - h J Yi — Pi
and aking $ = 0.000026 we get
/S, = + 0.000000021859
l33
= + 0.000000000099512
The linear coefficient of expansion of a specimen of glass, such
as is used in barometer-tubes and thermometers, has been very care-
fully determined by Dr. Benoit of the International Bureau of
Weights and Measures. Deriving from this the cubical coefficient,
in the notation used here, we have Dr. Benoit's values
£ = + 0.0000252
/32
= + 0.0000000144
It will thus be seen that there is a good agreement between the
two values of pt found by the two different processes.
Remarks were made by Messrs. Gilbert, Harkness, and.
Paul.
GENERAL MEETING. 33
Mr. J. H. Kidder made a communication on
THE GILDING OF THERMOMETER BULBS,
and was followed by Mr. H. Allen Hazen on
EFFECTS OF SOLAR RADIATION UPON THERMOMETER BULBS
HAVING DIFFERENT METALLIC COVERINGS.
[Abstract.]
After showing the importance of shielding from or measuring the
effects of solar radiation upon thermometer bulbs used in determin-
ing the air temperature and indicating the attempts that have been
made in obtaining satisfactory results in the past, Mr. Hazen
explained the most recent work of Prof. Wild, of St. Petersburg.
Prof. Wild had a bulb coated with copper by the galvanoplastic
method, then the copper with gold, which latter was highly polished.
From theoretical considerations he established a formula as follows
:
in which i
a
= temperature of air sought ; tm = that of the metallic-
covered bulb ; t3 = that of a black bulb ; and c is a constant which
he assumed at .15. The published observations indicated a very
high reading of the metal-covered bulb, even higher than would
have been obtained with a bare glass bulb.
Mr. Hazen's own experiments consisted in comparisons between
bulbs as follows:- (1) black, (2) bright, (3, 4) with silver and gold
deposited in an exceedingly thin layer and giving a most admirable
surface, and (5, 6) with silver and gold deposited on copper as nearly
as possible as suggested by Prof. Wild. These thermometers were
exposed in sunshine in the open air as well as indoors. It was very
difficult to shield from other radiations, dark heat, etc., but it was
found that an exposure of two feet from a window pane gave fairly
good results. The results are given in the accompanying table. In
computing the actual value of t& from the formula it was found
necessary to take the readings of the black and bright bulbs at each
set and compute the t% by using .6 as the constant. It was found
that the black and bright bulbs were the only ones that did not de-
teriorate from day to day. All the metal-covered bulbs were
carefully polished each day.
40
34 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Comparison of various coverings of thermometer bulbs (out of doors).
Date.
Apr. 14, '86.
Apr. 19
Apr. 20
May 3
Mean
general meeting. 35
288th Meeting. May 22, 1886.
Vice-President Harkness in the Chair.
Forty-eight members and visitors present.
Mr. Newton L. Bates read a communication entitled
ORGANIC CELLS OF UNKNOWN ORIGIN AND FORM FOUND IN
HUMAN FAECES (TWO CASES),*
illustrating his remarks by specimens exhibited under the microscope.
Referring to the composition of these cells, reported to contain four
per cent, of silica, Mr. Clarke called attention to the desirability
of testing for other inorganic substances. In reply to a question as
to where in the intestinal canal the cells ha'd been found, Mr. Bates
replied that the evidence in the case indicated the lower part of
the canal.
i
Mr. J. S. Billings made a communication
ON MUSEUM SPECIMENS ILLUSTRATING BIOLOGY.
[Abstract.]
After referring to the increasing interest on the part of the pub-
lic in Biology and Natural History, as theories of evolution, natural
selection, etc., are becoming better understood, and to the conse-
quent increasing importance of museums or parts of museums in-
tended to illustrate the structure and functions of animals, several
types of museums were briefly described, including the collection at
Florence, the Hunterian Museum, the average Medical School Mu-
seum, the museums proposed by Drs. Roberts, Wilder, and Shu.
feldt, etc.
The special scope and purposes of the Army Medical Museum
were stated to be to illustrate: 1. The effects, immediate and remote,
of wounds and of those diseases most prevalent in the army, i. c,
* These cells are now believed to have come from the banana. If a trans-
verse slice of banana is placed in a watch glass and covered with strong
nitric acid, two rows of cells become colored and are apparent to the naked
eye. A note on the subject may be found in the Boston Medical and Surgi-
cal Journal, March 10th, 1883, p. 446. Similar changes doubtless take
place by prolonged stay in the intestine, and when found clean and free
from vegetable fiber these cells are likely to deceive expert microscopists.
36 PHILOSOPHICAL SOCIETY OF WASHINGTON.
the diseases and injuries of adult males. 2. The work of the
medical department of an army, modes of transporting sick and
wounded, hospitals, medical supplies, instruments, etc. 3. Human
anatomy and pathology of both sexes and all ages. This requires
many specimens in comparative anatomy and pathology, which are
indispensable for a correct understanding of the structure, develop-
ment, abnormalities and diseases of man. It is not however proposed
to form a museum of comparative anatomy—that belongs to the
functions of the National Museum. 4. To show the morphologi-
cal basis, or want of such basis, for ethnological classification, more
especially of the native races of America. This includes anthro-
pometry and craniology. 5. To illustrate for medical investiga-
tors and teachers the latest methods, the newest apparatus, etc., for
biological investigation, and various modes of preparing and mount-
ing specimens. In connection with this it is hoped to induce origi-
nal workers to deposit in the museum type specimens or series of
specimens illustrating their discoveries and methods.
The classification and arrangement of specimens which it is pro-
posed to carry out in the new Museum building were then briefly
described.
Various modes of preparing specimens were shown, including
dissections under spirit, frozen and tinted sections, injections by cor-
rosion, etc., and the difficulties in making and preserving such
specimens were explained.
A second communication on the same subject was made by Mr.
G. Brown Goode, and a third, by request, by Mr. Frederick A.
Lucas, of the National Museum, who spoke more especially of
osteological specimens. The papers were all fully illustrated by
specimens from the Medical and National Museums.
Mr. George P. Merrill made a communication
ON GEOLOGICAL MUSEUMS.
Remarks were made on the general subject of museums and their
management by Prof. Edward Morse, of Salem, Mass.
GENERAL MEETING. 37
289th Meeting. October 9, 1886.
The President in the Chair.
Seventy-eight members and guests present.
The Chair announced the election to membership of Messrs.
Cooper Curtice, Henry Mitchell, Henry Gustav Beyer,
and Newton Lemuel Bates.
The subject for the evening was
THE CHARLESTON EARTHQUAKE,
which was discussed by Messrs. T. C. Mendenhall andW J Mc-
Gee and Prof. Charles G. Rockwood of Princeton, N. J.
Mr. Mendenhall spoke of the odor observed on Sullivan's
Island previous to the shock, of the time of the clock-stopping
shock in Charleston, of the detonations accompanying the various
shocks and heard in Charleston, Summerville, and elsewhere, of the
torsional movements of monuments, and of the directions in which
various structures were thrown down. He exhibited an isoseismal
map compiled from data gathered by the U. S. Signal Service. He
also stated at second hand a novel theory for the origin of the earth-
quake, and spoke of the convergence of opinion of geologists and
physicists in regard to the condition of the interior of the earth.
He accepted as the time of the clock-stopping shock in Charleston
9h. 51' 20" p. m.
Mr. McGee described the geological relations of Charleston,
showing that a depth of 2,000 feet of clastic rocks had been demon-
strated beneath the city, and that the total depth to the crystalline
rocks might be as much as one mile. He described the pheno-
mena of deformation of rails and other railway structures, gave in
detail an observation of a severe shock at Summerville, described the
detonations, and exhibited numerous photographs illustrating the
destructive work of the earthquake and the formation of craterlets
and sinks.
Prof. Rockwood exhibited an isoseismal map compiled from data
gathered by the Earthquake Commission, and characterized by far
greater irregularities in the form of contours than were shown by
Mr. Mendenhall's map. He called attention to the fact that nearly
all the isoseismal curves show salient angles toward the northwest.
He dwelt upon the exceptional nature of this opportunity for earth-
quake investigation, and urged that the utmost advantage be taken
38 PHILOSOPHICAL SOCIETY OF WASHINGTON.
of it. He spoke also of the complexity of earthquake movements,
and the difficulties to be overcome in analysing them. He thought
that the conspicious inequality in the violence of the shocks at lo-
calities not widely separated was to be ascribed to the intersection
and combination of rock waves deflected by reflection and refrac-
tion. Two intersecting waves would be especially destructive at
their nodal points, and comparatively harmless at their points of
interference.
It was announced by the President that the discussion would be
continued at the next meeting.
290th Meeting. October 23, 1886.
The President in the Chair.
Sixty-seven members and guests present.
The discussion of
THE CHARLESTON EARTHQUAKE
was resumed, the principal speakers being Mr. Everett Hayden
and Mr. H. M. Paul. Remarks were made by Messrs. McGee,
Billings, Robinson, Dutton, Bell, Clarke, and Gilbert, and
by Dr. E. P. Howland, who was present by invitation.
Mr. Hayden first discussed a chart on which were plotted the
areas disturbed by earthquakes in the southeastern United States
from 1874 to 1885, compiled from Rockwood's Notes in the Ameri-
can Journal of Science. This indicated two earthquake belts, one
along the Appalachians, the other along the coast. In the former
28 shocks are recorded, in only 3 of which the area is as great as
1,000 square miles (2 in central Virginia, and 1 in western North
Carolina and northern Georgia) ; in the latter 5 are recorded,
only 1 of which (that of 1879 in Florida and Georgia) was at all
severe. So far as this evidence goes, therefore, we should have ex-
pected a severe shock like that of August 31st to have originated
in the Appalachians and to have been orogenic in character, an
accompaniment of the gradual elevation of the range.
He then proceeded to give a summary of the information which
had reached the Geological Survey up to date, illustrating by charts
of isoseismal and coseismal lines. The geologic and physical phe-
nomena in the region of greatest intensity having been already dis-

THE
CHARLESTON EARTHQUAKE
\
from datn in the hands of the
D. S. GEOLOGICAL SURVEY
I let, 23, 1SSG.
' Everett Hnydcn, AsA Geol..
GENERAL MEETING. 39
cussed at the last meeting were not touched upon. The data used
came for the most part from correspondence with private parties,
although some valuable information had been received from the
Signal Service, Light-House Board, and Hydrographic Office—only
a small portion, however, of what they would eventually furnish.
The State Department had reported that the shock was felt very
slightly in Bermuda, and would report later as to Cuba and the
Bahamas.
The isoseismals were plotted on an enlarged photograph of the
relief model of the eastern United States in the Coast Survey Office,
which illustrated the general topographic features more graphically
than an ordinary map. In the discussion special attention was paid
to explaining their irregular shapes by reference to the surface con-
figuration as well as the geologic structure of the country. The
inclosed area, marked 4, in West Virginia and Kentucky, well
illustrates the fact that a shock may be felt with greater severity
beyond a mountain range than in its midst. The similar isolated
areas of less intensity in Iudiana and Illinois are also typical of
variations due to local conformations ; were it possible to plot inten-
sities in still greater detail there would doubtless be hundreds of
such isolated districts all through the disturbed area. Other points
dwelt upon were the unobstructed transmission of the vibrations
along the parallel ridges of the range and up the valleys of the
Connecticut and Hudson rivers ; the obstruction offered by ridges,
valleys, and strike of strata transverse to the direction of propaga-
tion; and the rapid loss of energy in the sands and alluvial deposits
of the northeast coast and lower Mississippi valley. The total
land area included within the outer isoseismal is 774,000 square
miles, and if we add only half as much more for ocean area it
closely approximates to that given by Reclus for the great Lisbon
earthquake. Special acknowledgement was made for valuable
positive and negative reports received from members of the New
England Meteorological Society through their secretary, Prof. W.
M. Davis ; they accurately fixed the limits of the disturbed area
in New England.
1 The coseismals were plotted from the most reliable and consist-
ent among a hundred or more good time observations, and special
care was taken to make them conform to the actual facts, unin-
fluenced by any preconceived theoretical ideas. Attention was
called to certain peculiarities of these lines, such as their noticeable


40 PHILOSOPHICAL SOCIETY OF WASHINGTON.
prolongation to the northward and southwestward ; the narrow inter-
vals where they run along the western flanks of. the Appalachians
and across the Florida peninsula ; and the wide intervals in the
Ohio and upper Mississippi valleys. The following considerations
were offered as helping to explain these apparently anomalous fea-
tures : The crystalline Archean rocks and parallel ridges of the
mountain chain favor a rapid axial transmission of the vibrations.
The first tremors spreading to the northwestward, however, are cut
off and deadened by the mountains, so that it is a later phase of the
wave which is felt and recorded beyond ; having passed the range
it then spreads with little obstruction and high velocity through
comparatively level strata. Similarly in the littoral and alluvial
deposits to the northeast, south, and southwest the earlier tremors
are lost and later phases of the wave are successively recorded.
It is especially to be remembered that all these times are from non-
instrumental observations ; an exact instrumental observation made
at Toronto, Ontario, by Prof. Chas. Carpmael (9: 54: 50 p. m.),
could not be used here because so early as to be wholly inconsistent
with all other reliable but non-instrumental observations.
The epicentrum, or point on the surface directly above that part
of the deep-lying fissure where the earliest vibrations originated, is
placed by these coseismals about a hundred miles north of Charles-
ton, which is not at all inconsistent with the fact that the greatest
damage was caused in that city. In fact, it is to be expected that
the destruction of buildings should be greater at a distance, where
the angle of emergence is less. Moreover, 'most of the evidence
seems to point to a very deep-lying origin, in which case one can-
not but attribute much of the local damage, as well as the continu-
ance of shocks of considerable intensity but small area, to the
character of the recent geologic formations in that region. Borings
for artesian wells at Charleston indicate that the Tertiary and
Cretaceous strata are very heterogeneous in character—sands,
clays, limestone-marls, and imperfectly consolidated beds of con-
glomerate, with occasional cavities containing running water—and
much of the city is built upon made land. Such considerations
may explain the extremely local character of many of the shocks
which have been felt at various points in the State of South
Carolina since August 31st, as well as the great intensity of the
shock at Charleston on that date. Local sinks in the ground are re-
ported even in northern Florida, far from the origin of the disturb-
GENERAL MEETING. 41
ance. An analogous case is seen in the fact that the great destruc-
tion of life and property at Lisbon, in 1755, occurred in those por-
tions of the city built on weak Tertiary formations, while houses on
the firmly consolidated Secondary rocks suffered little damage.
The following velocities of wave transmission are indicated :
To
—
Feet per second. Miles per minute.
Toronto, Ontario 15,000 170
Washington, D. C 13,000 148
Prairie du Chien, Wise 9,300 106
Average 12,400 141
By way of comparison the following recorded velocities are of
interest: Lisbon, 1755, 2,000 feet per second; Naples, 1857, 1775;
St. Lawrence valley, 1870, 12,000 ; England, 1884, 9,200.
Reported directions of transmission, while very often what we
should expect, are yet generally so contradictory as to be of little
value. Similarly the number of shocks felt is recorded so differently
by different observers as to be very confusing ; the occurrence of
two shocks at a point at some distance from the origin is explained
by the hypothesis that the first traveled rapidly through the hard
under-lying rocks, and the second more slowly through the softer
and more recent strata above. The shock is reported as accom-
panied by sounds of greater or less intensity all along the extent
of Archean rocks from northern Alabama to Connecticut, and at
points on the coastal plain within a radius of about 300 miles from
the origin.
The coincidence of an unusually high tide is worthy of remark
;
the moon was near perigee, and there had been an eclipse of the
sun only three days previously. The fact that no sea-wave was
caused by the shock confirms the, conclusion that the origin was in-
land. The weather is generally reported to have been very still
and sultry, although there were no unusual barometric conditions.
The summer had been an unusually dry one.
Only two other recorded earthquakes in North America can be
compared with this in either area or intensity : that at New Madrid,
Missouri, in 1811, which was probably fully its equal, and that in
the St. Lawrence valley in 1870, equal possibly in area but not in
intensity.
Mr. Paul explained the generally received classification of earth-
quake waves, described some of the results of the Tokio earthquake
42 PHILOSOPHICAL SOCIETY OF WASHINGTON.
studies, discussed the relation of destructiveness to amplitude of
vibration and to rate of acceleration, and requested Mr. McGee to
describe more specifically than at the last meeting the phenomena
observed by him in connection with a severe shock in Summerville.
Mr. McGee said that during the tremor the bedstead upon which
he lay left the floor from fifteen to thirty times, the departures
being roughly estimated at three per second. The clear ascent, as
judged from the force of the return blow, ranged from one-fourth
inch to two or three inches. The bed stood on the ground floor
of a wooden house, supported on piers. Earlier shocks had crushed
or driven down the piers under the heavier parts of the house, so
that the weight was borne in large part by piers under verandas, etc.
Mr. Paul said that if the floor in descending separated from the
legs of the bedstead its acceleration of motion must exceed that due
to gravitation. The fall of the earth manifestly could not be faster
than that of the bedstead. Assuming the accuracy of the observa-
tion the only possible explanation would seem to be that the floor
had behaved as an elastic spring.
Dr. Howland described a shock observed by himself, and said
that of some hundreds of chimneys observed by him in Charleston
75 per cent, had fallen to the west.
The President spoke of the bearing of the earthquake upon sani-
tary matters. The water mains in Charleston had been run in
some places through sewers, and there is no assurance that these
mains are now in such condition as to render contamination im-
possible.
Mr. Dutton inferred from the magnitude of the area through
which the shock was felt, as compared with its moderate destruc-
tiveness in the central region, that the centrum lay at great depth.
Mr. Bell was much interested in the statement that, even at
considerable distances from the centre of disturbance, the noise ac-
companying the earthquake either preceded the shock or was per-
ceived simultaneously with it. This, he thought, indicated that the
sound was of local origin. The great velocity with which the
earthquake disturbance had been propagated seemed to him to pre-
clude the idea of a sound-wave from the centre of disturbance as
the cause of the noise perceived. Any sound due to this cause
should, he thought, at considerable distances, have been observed
after the experience of the shock.
He also spoke of the worthlessness of testimony regarding the
GENERAL MEETING. 43
direction of sounds proceeding from points below the observer. In
this connection he directed attention to experiments relating to
Binaural Audition which he had communicated to the American
Association for the Advancement of Science in 1879;* and he
recommended any one who placed reliance on the testimony that
had been adduced relating to the direction of the earthquake noises
to try the following experiment
:
To one end of a long pole attach an ordinary electric call-bell,
and at the other end place a push-knob, by means of which the ex-
perimenter can at will ring the bell. Let the person whose credi-
bility as a witness is to be tested stand with his feet considerably
apart, with his eyes closed and head still. The experimenter can
then silently move the call-bell into any desired position before
ringing, and the observer can indicate his appreciation of the direc-
tion of the sound by pointing to the place from whence he conceives
it to have emanated,
Such being the disposition of the parties the experiment Mr. Bell
would recommend is the following: Carefully and silently intro-
duce the end of the pole between the legs of the observer so that
the bell is directly underneath him. Now ring and ask your wit-
ness to indicate by pointing the position of the bell. He had tried
the experiment many times, and had been surprised, and even
startled, by the result. The observer usually formed a distinct
judgment as to the direction of the sound, but the one feature that
was common to all the experiments was that the indicated direction
was wrong.
Mr. Gilbert remarked that the simultaneous occurrence of deto-
nations and tremors indicated that the sound waves were identical
with some at least of the waves constituting the earthquake. It was
therefore legitimate to compare the velocity of transmission of the
earthquake waves with the velocity of transmission of sound in vari-
ous media, and such comparison indicates that the portion of the
crust traversed by the earthquake waves was characterized by an
elasticity between that of gold and that of iron.
Mr. Bell thought that deductions based upon the assumption
that the disturbance had been propagated with the velocity of
* The paper was published in extenso in the American Journal of Otology
for July, 1880, vol. II, p. 169. See also Nature, vol. XXI, p. 310, and vol.
XXII, pp. 586-7.
44 PHILOSOPHICAL SOCIETY OF WASHINGTON.
sound should be received with caution ; for it is well known that
very great and sudden disturbances may be propagated through a
medium with a greater velocity than the normal velocity of sound
in that medium. In Captain Parry's Arctic expedition it was
noticed that distant observers heard the report of cannon before
hearing the command to fire.
The President announced that Mr. T. C. Mendenhall, having
removed from the city, had resigned his position on the General
Committee of the Society, and that the committee had filled the
vacancy by the election of Mr. "William B. Taylor.
291st Meeting. November 6, 1886.
Vice-President Mallery in the Chair.
Twenty-three members and guests present.
Mr. O. T. Mason made a communication on
BOWYERS AND FLETCHERS.
[Abstract.]
Whatever may be our theory of creation, the arts of mankind
proceed from the same sources as the genera and species of natural
objects. The design 'of this paper is to demonstrate, by means of
an art almost universally dispersed in time and place, that we may
regard the implements and products of human industry in the light
of biological specimens. They may be divided into families, genera,
and species. They may be studied in their several ontogenies (that
is, we may watch the unfolding of each individual thing from its
raw material to its finished production). They may be regarded as
the products of specific evolution out of natural objects serving
human wants and up to the most delicate machine performing the
same function. They may be modified by their relationship, one to
another, in sets, outfits, apparatus, just as the insect and flower are
co-ordinately transformed. They observe the law of change under
environment and geographical distribution.
The bow, at first, was only an elastic limb or branch transformed
little or none at all. From this parent form have developed three
GENERAL MEETING. 45
types under the control of the material, namely, the perfect, simple
bow, in lands where elastic woods abound ; the compound bow, in
localities where, by choice or necessity, horn, bone, and antler are
preferred as material ; and the sinew-backed bow, with its two sub-
types of the corded back and the solid back. Each one of these
types may be subdivided indefinitely by ethnic marks.
The arrow, at first a reed or twig unmodified, was only a shaft
with merely an indication of a head as in some of the lower forms.
From this, by a normal evolution, have come the feather, fore-shaft,
head, and barbs, differentiating into endless varieties under the stress
of material, definite functions, and the thousand and one forces
which together we may call its environment.
A large collection of bows and arrows varying in material, form,
and origin was exhibited to exemplify the theory set forth.
The communication was discussed by Messrs. Taylor, E. Far-
quhar, Riley, Harkness, Dall, and Elliott. Mr. Taylor
called attention to the break in the evolutionary history of the bow
at its very beginning. The stride from the elastic throwing-stick
to the bow is immense. The discussion turned chiefly upon the
proper basis for museum classification of ethnological material,
Messrs. Riley, Dall, and Elliott advocating a classification primarily
by peoples or races, and Mr. Mason defending the evolutionary
system, Avhere classification by races is supplemented and traversed
by a classification in which articles of a kind are placed together.
Mr. G. K. Gilbert began a communication on
CERTAIN NEW AND SMALL MOUNTAIN RANGES,
which was unfinished when the hour for adjournment arrived.
292d Meeting. November 20, 1886.
The President in the Chair.
Forty-two members and guests present.
Mr. G. K. Gilbert completed his communication
ON CERTAIN NEW AND SMALL MOUNTAIN RANGES,
and remarks were made by Messrs. Billings and Hazen.
46 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Thomas Russell presented a communication on
NORMAL BAROMETERS,
which was discussed by Messrs. Billings and Harkness.
Mr. N. H. Darton read a paper
ON THE OCCURRENCE OF COPPER ORE IN THE TRIAS OF THE
EASTERN UNITED STATES,
and Mr. J. S. Diller followed with a communication on
THE LATEST VOLCANIC ERUPTION IN NORTHERN CALIFORNIA AND
ITS PECULIAR LAVA.
[Published in Am. Jour. Sci., 3d series, vol. xxxiii.]
Remarks on the last paper were made by Mr. Iddings.
293d Meeting. December 4, 1886.
By courtesy of the trustees of the Columbian University the meet-
ing was held in the law lecture-room of the University building.
Invitation to attend the meeting was extended to the members of
the Anthropological, Biological, and Chemical societies and of the
Cosmos Club. Two hundred and two persons were present.
Vice-President Mallery presided.
The Chair read a letter from the secretary of the Chemical Society
inviting the members of the Philosophical Society to listen, on the
evening of Dec. 9, to an address by Prof. H. W. Wiley, retiring
president of the Chemical Society, on " Our Sugar Supply."
President Billings then presented his annual address, the sub-
ject being
scientific men and their duties.
[Printed in full on pp. xxxv-lvi of this volume.]
A vote of thanks for the address was passed by the audience.
general meeting. 47
294th Meeting. December 18, 1886.
the sixteenth annual meeting.
The President in the Chair.
The minutes of the 292d and 293d meetings were read and ap-
proved.
The Chair read the order of business as prescribed by the Stand-
ing Rules.
The Secretary read the minutes of the fifteenth annual meeting.
The Chair announced the election to membership of Messrs.
Joseph Claybaugh Gordon, Nelson Horatio Darton, Mar-
shall McDonald, "William Lee Trenholm, and William
Francis Hillebrand.
The annual report of the Secretaries was read. [See page xxix.]
The annual report of the Treasurer was read [see page xxx] and
referred to an Auditing Committee, consisting of Messrs. R. S.
Woodward, S. M. Burnett, and J. H. Kidder.
The Treasurer read the list of members entitled, under Standing
Rule 14, to vote for officers.
After a recess of five minutes, the Society proceeded to the elec-
tion of officers for the year 1887. [The result of the election ap-
pears on page xv.]
The following amendment to the Constitution was offered by
Mr. W. H. Dall, and laid on the table, as required by Article VI
of the Constitution.
In Article III insert, after " consisting of," the words the ex-presi-
dents of the Society.
In Article IV insert, before " other members," the word nine.
[The effect of the amendment is to make ex-presidents of the Society
permanent members of the General Committee.]
The rough minutes of the meeting were then read, and the Society
adjourned.

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
MATHEMATICAL SECTION.
41 49

STANDING RULES
MATHEMATICAL SECTION,
1. The object of this Section is the consideration and discussion
of papers relating to pure or applied mathematics.
2. The special officers of the Section shall be a Chairman and a
Secretary, who shall be elected at the first meeting of the Section
in each year, and discharge the duties usually attaching to those
offices.
3. To bring a paper regularly before the Section it must be sub-
mitted to the Standing Committee on Communications for the
stated meetings of the Society, with the statement that it is for the
Mathematical Section.
4. Meetings shall be called by the Standing Committee on Com-
munications whenever the extent or importance of the papers sub-
mitted and approved appear to justify it.
5. All members of the Philosophical Society who wish to do so
may take part in the meetings of this Section.
6. To every member who shall have notified the Secretary of the
General Committee of his desire to receive them, announcements of
the meetings of the Sections shall be sent by mail.
7. The Section shall have power to adopt such rules of procedure
as it may find expedient.
51
OFFICERS
MATHEMATICAL SECTION FOR 1886.
Chairman, Wm. B. Taylor. Secretary, Marcus Baker.
LIST OF MEMBERS WHO RECEIVE ANNOUNCEMENT OF THE
MEETINGS.
Abbk, C.
Avert, E. S.
Baker, M.
Bates, H. H.
Billings, J. S.
Burgess, E. S.
Christie, A. S.
Coffin, J. H. C.
Curtis, G. E.
DeLand, T. L.
DOOLITTLE, M. H.
Eastman, J. K.
Eimbeck, W.
Elliott, E. B.
Farquhar, H.
Elint, A. S.
Gilbert, G. K.
Gore, J. H.
Green, B. B.
Hall, A.
Harkness, W.
Hazen, H. A.
Hill, G. W.
Hodgkins, H. L.
King, A. P. A.
KUMMEL, C. H.
Lefavour, E. B.
McGee, W J
Martin, A.
Newcomb, S.
Paul, H. M.
Bitter, W. P. M'K.
Bobinson, T.
Smiley, C. W.
Stone, O.
Taylor, W. B.
Upton, W. W.
Winlock, W. C.
Woodward, R. S.
Ziwet, A.
52
BULLETIN
OP THE
MATHEMATICAL SECTION.
22d Meeting. March 24, 1886.
The Chairman, Mr. G. W. Hill, presided.
Present, fourteen members and one invited guest.
Election of officers of the section for the year 1886 was conducted
by ballot, and resulted in the choice of Mr. W. B. Taylor as chair-
man and Mr. Marcus Baker as secretary.
Mr. Henry Farquhar made a communication on
a comparison of the boss and auwers declination
standards,
in which the systematic difference between the standard of Dr.
Auwers' "Fundamental-Catalog" and the "Normal System of Prof.
Boss was considered as a function of declination, and shown to be
almost completely explained by the supposition of a tube-flexure
inadequately allowed for, in the observations on which one or other
standard depends.
[A paper covering the same ground was afterward read by Mr.
Farquhar before the American Association for the Advancement
of Science, and an abstract of it will appear in the proceedings of
that body for the Buffalo meeting, 1886.] *
The paper was briefly discussed by Messrs. Hall, Hill, and
Woodward.
Mr. R. S. Woodward then read a paper entitled
ON THE POSITION AND SHAPE OF THE GEOID AS DEPENDENT ON
LOCAL MASSES.
[This will be published as a Bulletin of the United States Geo-
logical Survey.]
54 philosophical society op washington.
23d Meeting. April 14, 1886.
The Chairman, Mr. William B. Taylor, elected at the last
meeting, presided, and upon taking the chair offered a few remarks
expressive of his appreciation of the honor conferred upon him and
of his desire for the prosperity of the Section.
Present, seventeen members and one guest.
Mr. R. S. Woodward recited, in abstract, the principal points of
his paper of the preceding meeting, and there ensued a general dis-
cussion of the subject, in which Messrs. Baker, Doolittle, Hill,
Paul, Thomas Russell, Stone, Taylor, aND Woodward par-
ticipated.
Mr. C. H. Kummell then presented a paper
on the use of somoff's theorem for evaluation of the
elliptic integral of the third species.
[This paper will appear in full in Annals of Mathematics, vol. 2,
Nos. 4 and 5.]
Remarks were made by Mr. Hill.
INDEX.
Address of the President xxxv, 46
Administration of research xlii
Amendment to the constitution 47
American Historical Association, Invitation
from the 22
Annual meeting 47
Anthropological Society, Invitation from the 15
Appalachian region, Physical divisions of
the 22
Arctic exploration 8
Arrow, Development of the 44
Auditing committee, Appointment of 47
Report of. 3
Bates, Newton L. : communication on or-
ganic cells of unknown origin and form
found in human faeces 35
— election to membership — 37
Bean, T. H. : communication on the distri-
bution of fishes in the oceanic abysses
and middle strata (Title) 22
Bell, A. Graham : remarks on aural determi-
nation of the direction of sound 42
— remarks on identity of sound and earth-
quake-waves 43
Beyer, H. G., Election to membership of 37
Bibliography of faults of the Great Basin.... 6
Billings, J. 8.: annual address as Presi-
dent xxxv, 46
— communication on museum specimens
illustrating biology 35
— remarks on the Charleston earthquake... 42
Bowyers and fletchers 44
Bryan, J. H., Election to membership of 25
Bulletin, Rules for publication of. xiii
Calendar xxviii
California, Notes on geology of northern 4
Cells, Problematic 35
Ceremonial institutions _ 19
Chamberlin, T. C. : communication on the
varying attitudes of former level sur-
faces in the Great Lake region and the
applicability of proposed explanations
(Title) 15,10
Charleston earthquake 37, 38
Chemical Society of Washington, Invitation
from the ^ 46
Page.
Clarke, F. W. : cited on the relations of Gov-
ernment to chemistry xlvi, 1
— remarks on problematic cells 35
Committee on communications xiv, xv
publications xiv, xv
— Report of auditing 3
— Rules of the general xii
Comparison of the Boss and Auwers declina-
tion standards 53
Constitution vii
Constitution, Proposed amendment to 47
Cummings, G. J., Election to membership of 15
Curtice, Cooper, Election to membership of. 37
Curtis, George E. : communication on Lieut.
Lockwood's expedition to farthest north 8
Customs of every day life 19
Dall, W. H. : offers amendment to the con-
stitution of the Society „ 47
— remarks on museum classification 45
Darton, N. H. : communication on the oc-
currence of copper ore in the Trias of
the eastern United States (Title) 46
— Election to membership of. 47
Deceased members xxvi
Declination standards 53
Diller, J. S. : communication on the geology
of northern California 4, 8
latest volcanic eruption in north-
ern California and its peculiar lava (Title) 46
Doolittle, M. H. : remarks on a phonetic
alphabet 19
Duties of scientific men xxxv
Earthquakes 37,38
Effects of solar radiation upon thermometer
bulbs having different metallic coverings. 33
Election of officers 47
Elliott, E. B.: communication on the annual
profit to banks of national bank note cir-
culation (Title) 14
quantity of United States subsid-
iary silver coin existing and in circula-
tion (Title) 14
— remarks on museum classification 45
Farquhar, Henry: communication on acom-
parison of the Boss and Auwers declina-
tion standards 53
(55)
56 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Farquhar, Henry : communication on a pho-
netic alphabet 17
Faults of the Great Basin and Sierra Nevada 5
Fletchers and bowyers 44
General committee, Rules of xii
— meeting, Minutes of .*. 3
Geology of northern California 4
Gilbert, G. K. : communication on certain
new and small mountain ranges (Title).. 45
the observed changes of level sur-
faces in the Bonneville area, and their
explanation (Title) 15
recent changes of level in the basin
of Lake Ontario (Title) 8
— remarks on geology of Sierra Nevada 7
the Charleston earthquake 43
Goode, G. Brown : communication on the dis-
tribution of fishes in the oceanic abysses
and middle strata (Title) 22
museum specimens illustrating bi-
ology (Title) 36
Gordon, J. C , Election to membership of. 47
Governmental administration of research... xlii
Great Basin, Faults of the 5
Hall, Asaph: communication on the images
of the stars (Title) 15
new star of Andromeda (Title) 14
Hayden, Everett: communication en the
Charleston earthquake 38
Hazen, H. Allen: communication on effects
of solar radiation upon thermometer
bulbs having different metallic coverings 33
Hill, R. T., Election to membership of 19
Hillebrand, W. F., Election to membership of 47
Hitchcock, Romyn : communication on re-
cent improvements in microscopic ob-
jectives, with demonstration of the re-
solving power of a new 1-1G inch (Title)„ 16
Howland, Dr. E. P. : remarks on the Charles-
ton earthquake 38
Irving, R. D. : communication on the en-
largement of mineral fragments as a
factor in rock alteration (Title) 16
— election to membership 16
Institutions, Ceremonial 19
Kenaston, C. A., Election to membership of. 16
Kidder, J. H. : communication entitled, his-
torical sketch of deep sea temperature
observations (Title) 14
the gilding of thermometer bulbs
(Title) 33
Kummell, C. H. : communication on the use
of Somoff' s theorem for the evaluation
of the elliptic integral of the third
species 54
Page.
Lucas, Frederick A. : communication on
museum specimens illustrating biology
(Title) 36
McAdie, A. G., Election to membership of... 19
BlcDonald, Marshall, Election to member-
ship of. 47
McGee, W.J: communication on the Charles-
ton earthquake 37
— remarks on the Charleston earthquake.... 42
Mallery, Garrick : communication on cus-
toms of every day life 19
— remarks on phonetic alphabets 18
Mann, B. Pickman : election to membership 3
— remarks on throwing sticks 14
Martin, Artemas, Election to membership of 16
Mason, O. T. : communication on bowyers
and fletchers 44
two examples of similar inventions
in areas widely apart 12
— remarks on derivation of social customs.. 21
Mathematical section, Members of. 52
Minutes of '. 53
Officers of 52
Rules of 51
Members, Deceased xxvi
— List of xvi
— New xxix, 3, 15,16, 19, 25, 37, 47
Mendenhall, T. C. : communication on the
Charleston earthquake 37
— remarks on Japanese customs 21
— resignation from General Committee 44
Merrill, George P. : communication on geo-
logical museums (Title) 3ft
Metallic coverings of thermometer bulbs.... 33
Minutes of the General Meeting 3
Mitchell, Henry, Election to membership of 37
Murdoch, John : remarks on throwing
sticks 13, 14
Museum classification 45
Museum specimens illustrating biology 35
Mussey, R. D. : communication entitled,
when I first saw the cholera Bacillus
(Title) 22
— remarks on phonetic alphabets 18
New members xxix, 3, 15, 16, 19, 25, 37, 47
Notes on the faults of the Great Basin and of
the eastern base of the Sierra Nevada... 5
geology of northern California 4
Nott, C. C, Election to membership of 3
Officers of Army and Navy in relation to
scientific work xlix
— elected December, 1885 xiv
1886 XV
Organic cells of unknown origin and form
found in human freces 35
INDEX. 57
Page.
Paul, H. M. : communication on the Charles-
ton earthquake 41, 42
Phonetic alphabet 17.
Physical-geographical divisionsof the south-
eastern portions of the United States and
their corresponding topographical types 22
President's address xxxv, 46
Report, Annual, of the secretaries xxix, 47
treasurer xxx, 47
— of auditing committee 3
Riley, C. V. : remarks on museum classifica-
tion 45
Rockwood, Prof. Charles G. : communication
on the Charleston earthquake 37
Rules for publication of Bulletin xiii
— of the General Committee xii
Mathematical Section 51
Society ix
Russell, I. C. : communication on faults of
the Great Basin and the eastern base of
the Sierra Nevada 5
the subaerial decay of rocks and the
origin of the red clay of certain forma-
tions (Title) 1G
Russell, Thomas : communication on nor-
mal barometers (Title) 4G
temperatures at which differences
between mercurial and air thermometers
are greatest 25
Scientific men and their duties xxxv
Secretaries, Annual report of xxix, 47
Sierra Nevada, Faults of the 4, 5
Similar inventions in areas widely apart 12
Snell, M. M., Election to membership of 25
Page.
Spencer, Herbert: cited on ceremonial in-
stitutions 20
Standing committees '. xiv, xv
Standing rules of the General Committee.... xii
Mathematical Section 51
Society
,
ix
Stitch in basketry 13
Taylor, W. B.: appointment to vacancy in
General Committee 44
— remarks as chairman of Mathematical
Section 54
on the evolution of the bow 15
Temperatures at which differences between
mercurial and air thermometers are
greatest 25
Thermometry 25, 33
Thompson, Gilbert: communication on the
physical-geographical divisions of the
southeastern portion of the United
States and their corresponding topo-
graphical types 22
Throwing sticks 13
Treasurer, Annual report of xxx, 47
Trenholm, W. L. : election to membership... 47
Two examples of similar inventions in areas
widely apart 12
Willis, Bailey : remarks on geology of Cas-
cade Mountains 7
Woodward, R. S. : communication on the
changes of terrestrial level surfaces due
to variations in distribution of super-
ficial matter (Title) 15
position and shape of the geoid as
dependent on local masses (Title) 53, 54

BULLETIN
PHILOSOPHICAL SOCIETY
OF
WASHINGTON.
VOL. X.
1887.
Containing the Minutes of the Society and of the Mathematical
Section for the year 1887; together with the pro-
ceedings of the Baird Memorial Meeting
AND
AN INDEX TO THE FIRST TEN VOLUMES.
PUBLISHED BY THE CO-OPERATION OF THE SMITHSONIAN INSTITUTION.
WASHINGTON:
1888.

CONTENTS.
Constitution Vii
Standing Rules of the Society ix
Standing Eules of the General Committee xu
Rules for the Publication of the Bulletin xiii
Officers elected December 18, 1S8G xiv
Officers elected December 21, 1887 xv
List of Members xvn
List of Deceased Members xxvin
Summary of Membership xxix
Calendar I xxxi
Annual Report of the Secretaries xxxn
Annual Report of the Treasurer ... xxxiv
Annual Address of the President, William Harkness xxxix
Bulletin of the General Meetings 1
Report of the Auditing Committee 3
Graphic methods in research, G. K. Gilbert 4
Geologic ao;e of the lowest formation of Emmon's Taconic sys-
tem, C. D. Walcott, {Title only) 5
Present status of mineralogy, F. W. Clarke, [Title only) 6
Topography and geology of the cross timbers of Texas, R. T.
Hill, {Title only) _.__ 6
Sky glows of 1883, H. A. Hazen, {Title only) 6
Topography and structure in the Bays Mountains, Tennessee,
Bailey Willis, {Title only) 7
Geographical distribution of scientific men and institutions in
the "United States, G. Brown Goode, {Title only) 7
Our city shade trees, their foes and their future, C. V. Riley,
{Title only) 7
Frequency of coincidences, Lester F. Ward 8
Theory of the wind-vane, G. E. Curtis, {Title only) 9
Electrometer as used in observations of atmospheric electricity,
C. F. Marvin, {Title only).... 9
Development of perspective map from contour map, Bailey
Willis, {Titleonly) 9
Plane table exhibited and explained, W. D. Johnson 9
Relation between wind velocity and pressure, H. A. Hazen,
{Titleonly) .._. 10
Mt. Rainier and its glaciers, Bailey Willis 10
What is a topographic map? Marcus Baker 11
Counting-out rhymes of children, H. C. Bolton, {Title only) 13
On a device for viewing the sun by light of any desired wave
length, William Harkness 13
What is topography? by M. H. Doolittle, W. D. Johnson, H.
G. Ogden, Gilbert Thompson 14, 15
The Muir glacier, Alaska, J. W. Chickering, {Titleonly) 15
Economic phase of the English sparrow question, C. Hart
Merriam, {Titleonly) 16
The quaternary deposits and the great displacement of the
middle Atlantic slope, W J McGee, {Title only) __. 16
Visit to scene of Charleston earthquake and resulting conclu-
sions, C. E. Dutton, {Titleonly) 16
iii
IV CONTENTS.
Page.
South Florida notes, W. H. Dall, (Title only) 16
Depth of earthquake foci, C. E. Dutton • 17
Manchester meeting of the British Association for the advance-
ment of Science, 188^7, F. W. Clarke, (Title only) 19
Signal Service bibliography of meteorology, 0. Abbe 20
Geographical distribution of fossil plants, L. F. Ward, (Title
only) 28
Speed of propagation of the Charleston earthquake, C. E.
Dutton and Simon Newcomb, (Title only) 28
Representation of comet orbits by models, William Harkness,
(Title only) 28
Statistics of the Philosophical Society, G. K. Gilbert 29
Newton's via, M. H. Doolittle, ( Title only) 38
Reference indexing, B: Pickman Mann 38
Presentation of the annual address 39
Annual meeting 39
Proceedings at the Baird memorial meeting 41
Introduction 43
Relation of Professor Baird to participating societies, Garrick
Mallery 45
Professor Baird as administrator, Wm. B. Taylor 49
Professor Baird in science, W. H. Dall 61
Personal characteristics of Professor Baird, J. W. Powell 71
Bulletin of the Mathematical Section 79
Standing rules of the section 81
List of officers and members of the section 82
Association ratios, M. H. Doolittle 83
The rotten apple problem, a question in probabilities, Marcus
Baker, M. H. Doolittle, G.W. Hill, G. E. Curtis, E. B. Elliott,
Henry Farquhar, Artemas Martin, Alex. S. Christie, Ormond
Stone 87-89
Free cooling of a homogeneous sphere, R. S. Woodward, (Title
only) 90
Brachisthode on the helicoid, C. H. Kummell 90
Motion of Hyperion, G. W. Hill 90
Parallax of a Tauri, Asaph Hall 91
Most probable value of latitude from entangled observations
in use of Talcott's method, A. S. Flint 91
Mutual action of elements of electric currents, E. B. Elliott.. 92
Association ratios, M. H. Doolittle 93
Solution of a problem in Science, Henry Farquhar, (Title only). 96
Solutions of the trisection problem, Marcus Baker, G. E. Curtis. 96, 98
Integration of differential equations admitting periodic inte-
grals, G. W. Hill 100
Euler's theorem (generally called Lambert's), Asaph Hall 101
New form of computing machine, E. B. Elliott 102
The constant P in observations of terrestrial magnetism, Wm.
Harkness 102
Conditioned cooling of a homogeneous sphere, R. S. Woodward. 103
The orbit of Hyperion, Ormond Stone 104
Quotients of space-directed lines, E. B. Elliott 105
Methods of finding »th power numbers whose sum is an nth
power, Artemas Martin 107
Committees on mathematical communications 111
Note on the publications of the Society 113
Index to Volumes I-X 117
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
CONSTITUTION, RULES,
LISTS OF
OFFICERS AND MEMBERS,
CALENDAR,
AND REPORTS OF
SECRETARIES AND TREASURER.

CONSTITUTION
OF
THE PHILOSOPHICAL SOCIETY OF WASHINGTON.
Article I. The name of this Society shall be The Philosophi-
cal Society of Washington.
Article II. The officers of the Society shall be a President,
four Vice-Presidents, a Treasurer, and two Secretaries.
Article III. There shall be a General Committee, consisting of
the ex-Presidents of the Society, the officers of the Society, and nine
other members.*
Article IV. The officers of the Society and the nine other mem-
bers of the General Committee shall be elected annually by ballot
;
they shall hold office until their successors are elected, and shall
have power to fill vacancies.*
Article V. It shall be the duty of the General Committee to
make rules for the government of the Society, and to transact all
its business.
Article VI. This constitution shall not be amended except by
a three-fourths vote of those present at an annual meeting for the
election of officers, and after notice of the proposed change shall
have been given in writing at a stated meeting of the Society at
least four weeks previously.
* Amended December 21, 1887.
42

STANDING RULES
FOR THE GOVERNMENT OF THE
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The Stated Meetings of the Society shall be held at 8 o'clock
p. m. on every alternate Saturday; the place of meeting to be
designated by the General Committee.
2. Notice of the time and place of meeting shall be sent to each
member by one of the Secretaries.
When necessary Special Meetings may be called by the President.
3. The Annual Meeting for the election of officers shall be the
last stated meeting in the month of December.
The order of proceedings (which shall be announced by the
Chair) shall be as follows
:
First, the reading of the minutes of the last Annual Meeting.
Second, the presentation of the annual reports of the Secretaries,
including the announcement of the names of members elected since
the last Annual Meeting.
Third, the presentation of the annual report of the Treasurer.
Fourth, the announcement of the names of members who, having
complied with section 14 of the Standing Rules, are entitled to vote
on the election of officers.
Fifth, the election of President.
Sixth, the election of four Vice-Presidents.
Seventh, the election of Treasurer.
Eighth, the election of two Secretaries.
Ninth, the election of nine members of the General Committee.
Tenth, the consideration of Amendments to the Constitution of
the Society, if any such shall have been proposed in accordance
with Article VI of the Constitution.
Eleventh, the reading of the rough minutes of the meeting.
4. * Elections of officers are to be held as follows:
In each case nominations shall be made by means of an informal
*Amended May 7, 1887.
X PHILOSOPHICAL SOCIETY OF WASHINGTON.
ballot, the result of which shall be announced by the Secretary;
after which the first formal ballot shall be taken.
In the ballot for Vice-Presidents, Secretaries, and members of the
General Committee, each voter shall write on one ballot as many
names as there are officers to be elected, viz., four on the first ballot
for Vice-Presidents, two on the first fcr Secretaries, and nine on the
first for members of the General Committee; and on each subse-
quent ballot as many names as there are persons yet to be elected
;
and those persons who receive a majority of the votes cast shall be
declared elected ; Provided that the number of persons receiving a
majority does not exceed the number of persons to be elected, in
which case the vacancies shall be filled by the candidates receiving
the highest majorities.
If in any case the informal ballot result in giving a majority for
any of the candidates, it may be declared formal by a majority vote.
5. The Stated Meetings, with the exception of the Annual Meet-
ing, shall be devoted to the consideration and discussion of scientific
subjects.
The Stated Meeting next preceding the Annual Meeting shall be
set apart for the delivery of the President's Annual Address.
6. Sections representing special branches of science may be
formed by the General Committee upon the written recommenda-
tion of twenty members of the Society.
7. Persons interested in science, who are not residents of the Dis-
trict of Columbia, may be present at any meeting of the Society,
except the Annual Meeting, upon invitation of a member.
8. On request of a member, the President or either of the Secre-
taries may, at his discretion, issue to any person a card of invitation
to attend a specified meeting. Five cards of invitation to attend a
meeting may be issued in blank to the reader of a paper at that
meeting.
9. Invitations to attend during three months the meetings of the
Society and participate in the discussion of papers, may, by a vote
of nine members of the General Committee, be issued to persons
nominated by two members.
10. Communications intended for publication under the auspices
.
of the Society shall be submitted in writing to the General Com-
mittee for approval.
STANDING RULES. XI
11. Any paper read before a Section may be repeated, either
entire or by abstract, before a general meeting of the Society, if
such repetition is recommended by the General Committee of the
Society.
12. It is not permitted to report the proceedings of the Society or
its Sections for publication, except by authority of the General
Committee.
13. *New members may be proposed in writing by three mem-
bers of the Society for election by the General Committee ; but no
person shall be admitted to the privileges of membership unless he
signifies his acceptance thereof in writing, and pays his dues to the
Treasurer, within two months after notification of his election.
14. Each member shall pay annually to the Treasurer the sum
of five dollars, and no member whose dues are unpaid shall vote at
the Annual Meeting for the election of officers, or be entitled to a
copy of the Bulletin.
In the absence of the Treasurer, the Secretary is authorized to
receive the dues of members.
The names of those two years in arrears shall be dropped from
the list of members.
Notice of resignation of membership shall be given in writing to
the General Committee through the President or one of the Secre-
taries.
15. The fiscal year shall terminate with the Annual Meeting.
16. Any member who is absent from the District of Columbia
for more than twelve consecutive months may be excused from
payment of dues during the period of his absence, in which case he
will not be entitled to receive announcements of meetings or current
numbers of the Bulletin.
17. Any member not in arrears may, by the payment of one
hundred dollars at any one time, become a life member, and be
relieved from all further annual dues and other assessments.
All moneys received in payment of life membership shall be in-
vested as portions of a permanent fund, which shall be directed
solely to the furtherance of such special scientific work as may be
ordered by the General Committee.
^Amended Oct. 9, 1886.
STANDING RULES
OF THE
GENERAL COMMITTEE OF THE PHILOSOPHICAL
SOCIETY OF WASHINGTON.
1. The President, Vice-Presidents, and Secretaries of the Society
shall hold like offices in the General Committee.
2. The President shall have power to call special meetings of the
Committee, and to appoint Sub-Committees.
3. The Sub-Committees shall prepare business for the General
Committee, and perform such other duties as may be entrusted to
them.
4. There shall be two Standing Sub-Committees ; one on Com-
munications for the Stated Meetings of the Society, and another on
Publications.
5. The General Committee shall meet at half-past seven o'clock
on the evening of each Stated Meeting, and by adjournment at
other times.
6. For all purposes, except for the amendment of the Standing
Rules of the Committee or of the Society, and the election of mem-
bers, six members of the Committee shall constitute a quorum.
7. The names of proposed new members recommended in con.
formity with Sectionl3 of the Standing Rules of the Society, may
be presented at any meeting of the General Committee, but shall
lie over for at least four weeks before final action, and the concur-
rence of twelve members of the Committee shall be necessary to
election.
The Secretary of the General Committee shall keep a chronologi-
cal register of the elections and acceptances of members.
8. These Standing Rules, and those for the government of the
Society, shall be modified only with the consent of a majority of
the members of the General Committee.
ZE^TTXjIES
PUBLICATION OF THE BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
1. The President's Annual address shall be published in full.
2. The annual reports of the Secretaries and of the Treasurer
shall be published in full.
3. When directed by the General Committee, any communication
may be published in full.
4. Abstracts of papers and remarks on the same will be pub-
lished, when presented to the Secretary by the author in writing
within two weeks of the evening of their delivery, and approved by
the Committee on Publications. Brief abstracts prepared by one
of the Secretaries and approved by the Committee on Publications
may also be published.
5. If the author of any paper read before a Section of the
Society desires its publication, either in full or by abstract, it shall
be referred to a committee to be appointed as the Section may
determine.
The report of this committee shall be forwarded to the Publica-
tion Committee by the Secretary of the Section, together with any
action of the Section taken thereon.
6. Communications which have been published elsewhere, so as
to be generally accessible, will appear in the Bulletin by title only,
but with a reference to the place of publication, if made known in
season to the Committee on Publications.
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 18, 1886.
President
Vice-Presidents
Treasurer
Secretaries
.William Harkness.
.Garrick Mallery.
J. R. Eastman.
.Robert Fletcher.
Marcus Baker.
C. E. Dutton.
G. K. Gilbert.
J. H. Kidder.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates.
W. H. Dall.
G. B. Goode.
H. M. Paul.
F. W. Clarke.
E. B. Elliott.
C. V. Riley.
W. C. "WlNLOCK.
R. S. Woodward.
STANDING COMMITTEES.
On Communications :
J. R. Eastman, Chairman. Marcus Baker. J. H. Kidder.
On Publications:
Marcus Baker, Chairman. Robert Fletcher. J. H. Kidder.
S. F. Baird.
xiv
OFFICERS
PHILOSOPHICAL SOCIETY OF WASHINGTON
Elected December 21, 1887.
President
Vice-Presidents
Treasurer
Secretaries
.Garrick Mallery.
.J. R. Eastman.
G-. K. Gilbert.
.Kobert Fletcher.
.Marcus Baker.
C. E. Dutton.
G. Brown Goode.
W. C. Winlock.
MEMBERS AT LARGE OF THE GENERAL COMMITTEE.
H. H. Bates.
W. H. Dall.
J. H. Kidder.
H. M. Paul.
F. W. Clarke.
E. B. Elliott.
S. P. Langlet.
C. V. Rilet.
R. S. Woodward.
PAST PRESIDENTS OF THE SOCIETY AND ex-Officio MEM-
BERS OF THE GENERAL COMMITTEE.
J. S. Billings, 1886. Simon Newcomb, 1879, 1880.
Asaph Hall, 1885. J. W. Powell, 1883.
Wm. Harkness, 1887. W. B. Tatlor, 1882.
J. C. Welling, 1884.
STANDING COMMITTEES.
On Communications :
G. K. Gilbert, Chairman. J. R. Eastman. G. Brown Goode.
On Publications :
Marcus Baker, Chairman. Robert Fletcher.
S. P. Langley.
W. C. Winlock.

LIST OF MEMBERS
PHILOSOPHICAL SOCIETY OF WASHINGTON;
TOGETHER WITH
TEAR OF ADMISSION TO THE SOCIETY, POST-OFEICE
ADDRESS, AND RESIDENCE.
Corrected to December 31, 1887.
1871. Abbe, Prof. Cleveland,
Signal Office, War Department. 2017 I street.
1875. Abert, Mr. S. T. (Sylvanus Thayer)
1881. Adams, Mr. Henry,
1873. Aldis, Hon. A. O. (Asa Owen),
810 19th street.
1603 H street.
1765 Mass. avenue.
1871. Antisell, Dr. Thomas {Founder),
Patent Office. 1311 Q street.
1879. Avery, Mr. Robert S. (Robert Stanton),
320 A street se.
1887. Babcock, Mr. Wm. H. (William Henry),
P. O. Box 220.
1881. Baker, Prof. Frank,
1315 Corcoran street.
1876. Baker, Mr. Marcus,
Geological Survey. 1125 17th street.
1875. Bancroft, George,
1623 H street; in summer, Newport, R. I.
1885. Barus, Dr. Carl,
Geological Survey. 2750 Q street.
1871. Bates, Mr. H. H. (Henry Hobart,)
Patent Office. The Portland.
1886. Bates, Dr. N. L. (Newton Lemuel), U. S. K,
283 Henry street, Brooklyn, N. Y.
1884. Bean, Dr. T. H. (Tarleton Hoffman),
National Museum. 1616 19th street
XVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
1875. Beardslee, Capt. L. A. (Lester Anthony), U. S. N. (Absent),
^Little Falls, N. Y.
1879. Bell, Mr. A. Graham (Alexander Graham),
1336 19th street.
1881. Bell, Dr. C. A. (Chichester Alexander) (Absent),
University College. London, England.
1871. Benet, Gen. S. V. (Stephen Vincent), U. S. A. (Founder),
Ordnance Office, War Dept. 1717 I street.
1875. Bessels, Dr. Emil,
Glenn Dale, Md.
1886. Beyer, Dr. H. G. (Henry Gustav) (Absent),
Navy Department.
1871. Billings, Dr. John S. (John Shaw), U. S. A. (Founder),
Army Medical Museum. 3027 N street.
1876. Birnie, Capt. Rogers, Jr., U. S. A.,
Office Chief of Ordnance, U. S. A. 1341 N. H. avenue.
1883. Bodfish, Mr. S. H. (Sumner Homer),
Geological Survey. 807 H street.
1884. Boutelle, Capt. C. O. (Charles Otis),
Coast and Geodetic Survey.
1884. Bowles, Asst. Nav. Constr. Francis T. (Francis Tiffany),
U. S. N. (Absent),
Navy Department.
1884. Brown, Prof. S. J. (Stimson Joseph), U. S. N. (Absent),
Washburn Observatory. Madison, Wis.
1883. Browne, Dr. J. Mills (John Mills), U. S. N.,
Navy Department. The Portland.
1886. Bryan, Dr. J. H. (Joseph Hammond),
1644 Connecticut avenue.
1883. Burgess, Mr. E. S. (Edward Sandford),
High School. 1120 13th street.
1879. Burnett, Dr. Swan M. (Swan Moses),
1734 K street.
1874. Busey, Dr. Samuel C. (Samuel Clagett),
901 16th street.
1871. Casey, Col. Thomas Lincoln, U. S. A. (Founder, absent),
Army Building, cor. Green and Houston Sts., New York city.
1882. Caziarc, Lieut. L.V. (Louis Vasmer), U. S. A. (Absent),
Fortress Monroe, Va.
1883. Chamberlin, Pres. T. C. (Thomas Crowder) (Absent),
Madison, Wis.
1885. Chatard, Dr. Thomas M. (Thomas Marean),
Geological Survey. Cosmos Club.
1874. Chickering, Prof. J. W., Jr. (John White),
Deaf Mute College, Kendall Green.
1880. Christie, Mr. Alex. S. (Alexander Smyth),
Coast and Geodetic Survey. 204 4th street se.
LIST OF MEMBERS. XIX
1877. Clark, Mr. Edward,
Architect's Office, Capitol. 417 4th street.
1874. Clarke, Prof. F. W. (Frank Wigglesworth),
Geological Survey. 1425 Q street.
1871. Coffin, Prof. J. H. C. (John Huntington Crane), U. S. N.
(Founder),
1901 I street.
1880. Comstock, Prof. J. H. (John Henry) (Absent),
Cornell University, Ithaca, N. Y.
1874. Coues, Prof. Elliott,
Smithsonian Institution. 1726 N street.
1873. Craig, Lieut. Robert, U. S. A. (Absent),
War Department.
1879. Craig, Dr. Thomas (Absent),
Johns Hopkins University, Baltimore, Md.
1886. Cummings, Prof. G. J. (George Jotham),
Howard University.
1886. Curtice, Dr. Cooper,
Agricultural Department.
1884. Curtis, Mr. Geo. E. (George Edward) (Absent),
"Washburn College, Tbpeka, Kansas.
1871. Dall, Mr. Wm. H. (William Healey) (Founder),
Smithsonian Institution. 1119 12th street.
1886. Darton, Mr. N. H. (Nelson Horatio),
Geological Survey. 1412 N street.
1880. Davis, Commander C. H. (Charles Henry), U. S. N.,
Navy Department.
1872. Dean, Dr. R. C. (Richard Crain), U. S. K (Absent),
Navy Department. 45 Lafayette Place, N . Y. city.
1881. De Caindry, Mr. Wm. A. (William Augustin),
War Department. 1014 17th street.
1884. Dewey, Mr. Fred. P. (Frederic Perkins),
National Museum. Lanier Heights.
1884. Diller, Mr. J. S. (Joseph Silas),
Geological Survey. 1804 16th street.
1876. Doolittle, Mr. M. H. (Myrick Hascall),
Coast and Geodetic Survey. 1925 I street.
1873. Dunwoody, Lt. H. H. C. (Henry Harrison Chase), U. S. A.
(Absent),
War Department.
1872. Dutton, Capt. C. E. (Clarence Edward), U. S. A.,
Geological Survey. 2119 H street.
1884. Earll, Mr. R. Edward (Robert Edward),
National Museum. 1336 T street.
1871. Eastman, Prof. J. R. (John Robie), U. S. N.,
Naval Observatory. 1905 N street.
1884. Eimbeck, Mr. William,
Coast and Geodetic Survey.
XX PHILOSOPHICAL SOCIETY OF WASHINGTON.
1871. Eldredge, Dr. Stewart (Absent),
Yokohama, Japan.
1871. Elliott, Mr. E. B. (Ezekiel Brown) (Founder),
Gov't Actuary, Treas. Dept. 1210 G street.
1883. Emmons, Mr. S. F. (Samuel Franklin),
Geological Survey. 1708 H street.
1873. Endltch, Dr. F. M. (Frederic Miller) (Absent),
Reading, Pa.
1874. Ewing, Gen. Hugh (Absent),
Lancaster, Ohio.
1876. Farquhar, Mr. Edward,
Patent Office Library. 1915 H street.
1881. Farquhar, Mr. Henry,
Coast and Geodetic Survey. Brooks Station, D. C.
1887. Fernow, Mr. B. E. (Bernhard Eduard),
Department of Agriculture. Cor. 8th and B streets sw.
1872. Ferrel, Prof. William,
1641 Broadway, Kansas City, Mo.
1873. Fletcher, Dr. Robert,
Army Medical Museum. The Portland.
1882. Flint, Mr. A. S. (Albert Stowell),
Naval Observatory. 1441 Chapin street.
1881. Flint, Dr. J. M. (James Milton), U. S. N.,
Smithsonian Institution. The Portland.
1873. Fristoe, Prof. Edward T,
Columbian University, cor. 15th and H streets.
1875. Gallaudet, President E. M. (Edward Miner),
Deaf Mute College, Kendall Green.
1874. Gannett, Mr. Henry,
Geological Survey. 1881 Harewood ave., LeDroit Park.
1873. Gilbert, Mr. G. K. (Grove Karl),
Geological Survey. 1424 Corcoran street.
1879. Godding, Dr. W. W. (William Whitney),
Government Hospital for the Insane.
1885. Gooch, Dr. F. A. (Frank Austin) (Absent),
Yale College, New Haven, Connecticut.
1874. Goode, Mr. G. Brown (George Brown),
Smithsonian Institution. 1203 N. H. ave.
1875. Goodfellow, Mr. Edward,
Coast and Geodetic Survey.
1886. Gordon, Prof. J. C. (Joseph Claybaugh),
Deaf Mute College, Kendall Green.
1880. Gore, Prof. J. H. (James Howard),
Columbian University. 1305 Q street.
1878. Graves, Mr. Walter H. (Walter Hayden) (Absent),
Denver, Colorado
1880. Greely, Gen. A. W. (Ad.)lphus Washington), U. S. A.,
Signal Office, War Department. 1914 G street.
LIST OF MEMBERS. XXI
1879. Green, Mr. Bernard R. (Bernard Richardson),
Office of Building for State, War, and
Navy Departments. 1738 N street.
1875. Green, Commander F. M. (Francis Mathews), U. S. N.
{Absent),
Navy Department.
1871. Greene, Prof. B. F. (Benjamin Franklin), U. S. N. (Founder,
absent),
West Lebanon, N. H.
1875. Greene, Francis V. (Francis Vinton) (Absent),
No. 1, Broadway, New York city.
1884. Gregory, Dr. J. M. (John Milton) (Absent),
45 Albert st., Kegent's Park, London, England.
1879. Gunnell, Surg. Gen'l F. M. (Francis M.), U. S. N.,.
Navy Department. 600 20th street.
1879. Hains, Lt.-Col. P. C. (Peter Conover), U. S. A.,
Engineer's Office, Potomac River Improve-
ment, 2136 Pa. ave. 1824 Jefferson place.
1871. Hale, Prof. Asaph, U. S. N. (Founder),
Naval Observatory. 2715 N street.
1884. Hall, Mr. Asaph, Jr. (Absent),
Yale Observatory, New Haven, Conn.
1885. Hallock, Dr. William,
Geological Survey. 2923,} M street.
1885. Hampson, Mr. Thomas,
Geological Survey. Lanier avenue.
1871. Harkness, Prof. William, U. S. N. (Founder),
Naval Observatory. Cosmos Club.
1880. Hassler, Dr. F. A. (Ferdinand Augustus) (Absent),
Santa Aria, Los Angeles Co., Cal.
1886. Hayden, Lieut. Everett, U. S. N.,
Hydrographic Office.
1882. Hazen, Prof H. A. (Henry Allen),
P. O. Box 427. 1416 Corcoran street.
1884. Heap, Major D. P. (David Porter), U. S. A. (Resigned),
Engineer 3d and 4th Light House District, Tompkins-
ville, N. Y.
1874. Henshaw, Mr. H. W. (Henry Wetherbee),
Bureau of Ethnology. 13 Iowa Circle.
1879. Hill, Mr. G. W. (George William),
Nautical Almanac Office. 314 Indiana ave.
1886. Hill, Mr. R. T. (Robert Thomas),
Geological Survey. 1626 15th street.
1886. Hillebrand, Dr. W. F. (William Francis),
Geological Survey.' 506 Maple ave., Le Droit Park.
1884. Hitchcock, Mr. Romyn,
National Museum. Osaka, Japan.
1885. Hodgkins, Prof. H. L. (Howard Lincoln),
Columbian University. 1532 19th street.
XXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
1873. Holden, Prof. E. S. (Edward Singleton) {Absent),
Lick Observatory, San Jose, Cal.
1887. Holmes, Mr. J. H. (Jesse Herman),
1811 I street.
1879. Holmes, Mr. W. H. (William Henry),
Geological Survey. 1444 Stoughton street.
1874. Howell, Mr. E. E. (Edwin Eugene) (Absent),
48 Oxford street, Rochester, N. Y.
1885. Iddings, Mr. J. P. (Joseph Paxson),
Geological Survey. 1028 Vermont ave.
1886. Irving, Prof. R. D. (Roland Duer),
Geological Survey. Madison, Wis.
1880. James, Rev. Owen (Absent),
Scran ton, Pa.
1871. Jenkins, Rear Admiral T. A. (Thornton Alexander),U.S.N.
(Founder),
2115 Pennsylvania ave.
1878. Johnson, Mr. A. B. (Arnold Burges),
Light House Board, Treas. Dept. 601 Maple ave.,
Le Droit Park.
1879. Johnson, Dr. Joseph Taber,
Private Hospital, 1728 K street.
1884. Johnson, Mr. Willard D. (Willard Drake),
Geological Survey. 501 Maple ave., Le Droit Park.
1873. Johnston, Dr. W. W. (William Waring),
1603 K street.
1884. Kauffmann, Mr. S. H. (Samuel Hay),
1000 M street.
1886. Kenaston, Prof. C. A. (Carlos Albert),
Howard University.
1884. Kerr, Mr. Mark B. (Mark Brickell),
Geological Survey. 2104 H street.
1880. Kidder, Dr. J. H. (Jerome Henry),
Smithsonian Institution. 1606 N. H. ave.
1880. Kilbourne, Lieut. C. E. (Charles Evans), U. S. A. (Absent),
War Department.
1875. King, Dr. A. F. A. (Albert Freeman Africanus),
726 13th street.
1887. King, Mr. Harry,
Geological' Survey. 1319 Q street.
1887. Knight, Mr. Fred J. (Fred Jay),
Geological Survey.
1874. Knox, Hon. John Jay (Absent),
Prest. Nat. Bank Republic, New York city.
19 E. 41st street.
1887. Knowlton, Mr. F. H. (Frank Hall),
National Museum. 202 5th street se.
1882. Kummell, Mr. C. H. (Charles Hugo),
Coast and Geodetic Survey. 608 Q street.
LIST OF MEMBERS. XXIII
1887. Langley, Prof. S. P. (Samuel Pierpont),
Secretary Smithsonian Institution.
1884. Lawrence, Mr. William,
Bellefontaine, Ohio.
1874. Lee, Dr. William,
2111 Penna. ave. 1821 I street.
1882. Lefavour, Mr. E. B. (Edward Brown) (Absent),
Cambridge, Mass.
1871. Lincoln, Dr. N. S. (Nathan Smith),
1514 H street.
1880. Loomis, Mr. E. J. (Eben Jenks),
Nautical Almanac Office. 1443 Stoughton street.
1886. McAdie, Mr. A. G. (Alexander George),
U. S. Signal Office, St. Paul, Minn.
1886. McDonald, Col. Marshall,
TJ. S. Fish Commission. 1515 K street.
1883. McGee, Mr.W J,
Geological Survey.
1879. McGuire, Mr. Fred. B. (Frederick Bauders),
1416 F street. 614 E street.
1876. McMurtrie, Prof. William (Absent),
University of Illinois, Champaign, 111.
1884. Maher, Mr. James A. (James Arran),
Geological Survey. 15 Grant Place.
1875. Mallery, Col. Garrick, TJ. S. A.,
Bureau of Ethnology. 1323 N street.
1885. Mann, Mr. B : Pickman (Benjamin Pickman),
Patent Office. 1918 Sunderland Place.
1886. Martin, Mr. Artemas,
Coast and Geodetic Survey. 55 C street se.
1885. Marvin, Prof. C. F. (Charles Frederick),
Signal Office, War Department. 1736 13th street.
1878. Marvin, Mr. Jos. B. (Joseph Badger),
Lock Box 379.
1875. Mason, Prof. 0. T. (Otis Tufton),
.
National Museum. 1305 Q street.
1884. Matthews, Dr. W. (Washington), U. S. A.,
Army Medical Museum. 1262 New Hampshire ave.
1871. Meigs, Gen. M. C. (Montgomery Cunningham), U. S. A.
(Founder),
1239 Vermont avenue.
1885. Mendenhall, Prof. T. C. (Thomas Corwin) (Absent),
Terre Haute, Ind.
1886. Merriam, Dr. C. Hart (Clinton Hart),
Department of Agriculture. 1919 16th street.
1884. Merrill, Mr. George P. (George Perkins),
National Museum. 1602 19th street.
1886. Mitchell, Prof. Henry,
43 Coast and Geodetic Survey. 1331 L street.
XXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
1883. Morgan, Dr. E. Carroll (Ethelbert Carroll),
918 E street.
1885. Moser, Lieut. J. F. (Jefferson Franklin), U. S.K (Absent),
Navy Department.
1884. Murdoch, Mr. John,
Smithsonian Institution. 1429 Stoughton street.
1881. Mussey, Gen. R. D. (Reuben Delavan),
P. O. Box 618.
1871. Newcomb, Prof. Simon, U. S. K (Founder),
Navy Department.
1872. Nichols, Dr. C. H. (Charles Henry) (Absent),
Bloomingdale Asylum, Boulevard and 117th street,
New York city, N. Y.
1871. Nicholson, Mr. W. L. (Walter Lamb) (Founder),
2222 G street.
1879. Nordhoff, Mr. Charles,
1732 H street.
1884. Norris, Dr. Basil, U. S. A. (Absent),
Vancouver Barracks, Wash. Ter.
1885. Nott, Judge C. C. (Charles Cooper),
Court of Claims. 826 Connecticut ave.
1884. Ogden, Mr. H. G. (Herbert Gouverneur),
Coast and Geodetic Survey. 1324 19th street.
1878. Osborne, Mr. J. W. (John Walter),
212 Delaware ave ne.
1871. Parke, Gen. John G. (John Grubb), U. 8. A. (Founder),
West Point, N. Y.
1871. Parker, Dr. Peter (died Jan. 10, 1888) (Founder),
1871. Parry, Dr. C. C. (Charles Christopher) (Absent),
Davenport, Iowa.
1877. Paul, Mr. H. M. (Henry Martyn),
Naval Observatory. 1915 G street.
1874. Peale, Dr. A. C. (Albert Charles),
Geological Survey. 1446 Stoughton street.
1873. Poe, Gen. O. M. (Orlando Metcalfe), U. S. A. (Absent),
34 West Congress street, Detroit, Mich.
1884. Poindexter, Mr. W. M. (William Mundy),
1505 Pennsylvania ave. 1227 15th street.
1882. Pope, Dr. B. F. (Benjamin Franklin), U. S. A. (Absent),
Surg. General's Office, U. S. A.
1874. Powell, Major J. W. (John Wesley),
Geological Survey. 910 M street.
1880. Prentiss, Dr. D. W. (Daniel Webster),
1101 14th street.
1879. Pritchett, Prof. H. S. (Henry Smith) (Absent),
Director of Observatory, Washington University.
St. Louis, Mo.
LIST OF MEMBERS. XXV
1882. Rathbun, Mr. Richard,
National Museum.. 1622 Massachusetts ave.
1884. Ray, Lieut. P. H. (Patrick Henry), U. S. A.,
Fort Gaston, Cal.
1883. Renshawe, Mr. Jno. H. (John Henry),
Geological Survey. 1215 L street.
1884. Ricksecker, Mr. Eugene,
Geological Survey. 904 14th street.
1878. Riley, Dr. C. V. (Charles Valentine),
Department of Agriculture. 1700 13th street.
1879. Ritter, Mr. W. F. McK. (William Francis McKnight)
(Absent),
P. O. Box 50, Milton, Pa.
1884. Robinson, Mr. Thomas,
U. S. Engineer Service. Vienna, Va.
1872. Rogers, Mr. Joseph A. (Joseph Addison) (Absent),
Naval Observatory.
1882. Russell, Mr. Israel C. (Israel Cook),
Geological Survey. 42 B street ne.
1883. Russell, Mr. Thomas,
Signal Office, "War Department. 1344 Wallach Place.
1883. Salmon, Dr. D. E. (Daniel Elmer),
Agricultural Department. 1716 13th street.
1883. Sampson, Commander W. T. (William Thomas), U. S. N.
(Absent),
Naval Academy, Annapolis, Md.
1871. Saville, Mr. J. H. (James Hamilton),
1419 F street. 1315 M street.
1871. Schott, Mr. Charles A. (Charles Anthony) (Founder),
Coast and Geodetic Survey. 212 1st street se.
1887. Seely, Col. F. A. (Franklin Austin),
Patent Office.
1875. Shellabarger, Hon. Samuel,
Room 31 Kellogg Building. 812 17th street.
1874. Sherman, Hon. John,
U. S. Senate. 1319 K street.
1881, Shufeldt, Dr. R. W. (Robert Wilson), U. S. A. (Absent),
Care Smithsonian Institution.
1879. Sigsbee, Commander C. D. (Charles Dwight), U. S. H*.
(Absent),
Naval Academy, Annapolis, Md.
1883. Skinner, Dr. J. O. (John Oscar), U. S. A. (Absent),
Surg. General's Office, U. S. A.
1882. Smiley, Mr. Chas. W. (Charles Wesley),
U. S. Fish Commission. 943 Massachusets ave.
1876. Smith, Chf. Eng. David, U. S. N.,
Navy Department.
XXVI PHILOSOPHICAL SOCIETY OP WASHINGTON.
1880. Smith, Mr. Edwin,
Coast and Geodetic Survey. 2024 Hillyer Place.
1887. Smyth, Mr. H. L. (Henry Lloyd),
Geological Survey.
1886. Snell, Mr. Merwin M. (Merwin-Marie),
National Museum. 732 6th street.
1887. Spencer, Dr. J. W. (Joseph William),
1012 17th street.
1872. Spofford, Mr. A. R. (Ainsworth Rand),
Library of Congress. 1621 Massachusetts ave.
1884. Stearns, Mr. R. E. C. (Robert Edwards Carter),
Geol. Survey ; Smithsonian Institution. 1213 12th St.
1874. Stone, Prof. Ormond (Absent),
Leander McCormick Observatory, Univ. of Virginia.
1887. Symons, Capt. T. W. (Thomas William), U. S. A.,
District Building. 1727 De Sales street.
1881. Taylor, Mr. F. W. (Frederick William) (Absent),
Smithsonian Institution.
1871. Taylor, Mr. William B. (William Bower) (Founder),
Smithsonian Institution. 306 C street.
1875. Thompson, Prof. A. H. (Almon Harris),
Geological Survey.
1884. Thompson, Mr. Gilbert,
Geological Survey. 1448 Q street.
1878. Todd, Prof. David P. (David Peck) (Absent),
Amherst College Observatory, Amherst, Mass.
1873. Toner, Dr. J. M. (Joseph Meredith),
615 Louisiana ave.
1886. Trenholm, Hon. W. L. (William Lee),
Comptroller of the Currency. 1815 M street.
1882. True, Mr. F. W. (Frederick William),
National Museum. 1101 14th street.
1882. Upton, Mr. Wm. W. (William Wirt),
1416 F street. 1746 M street.
1880. Upton, Prof. Winslow (Absent),
Brown University, Providence, E. I.
1883. Walcott, Mr. C. D. (Charles Doolittle),
Geological Survey ; National Museum.
1881. Waldo, Prof. Frank (Absent),
Forest ave., Cincinnati, Ohio.
1872. Walker, Mr. F. A. (Francis Amasa) (Absent),
Massachusetts Institute of Technology, Boston, Mass.
1883. Walling, Mr. H. F. (Henry Francis) (Absent),
Mass. Trigonometrical Survey, Cambridge, Mass.
1876. Ward, Mr. Lester F. (Lester Frank),
Geological Survey. 1464 Khode Island ave.
LIST OF MEMBERS. XXVII
1882. Webster, Mr. A. L. (Albert Lowry) (Absent),
107 Drexel Building, Broad street, New York city;
West New Brighton, Staten Island, N. Y.
1885. Weed, Mr. W. H. (Walter Harvey),
Geological Survey. 825 Vermont ave.
1882. Welling, Mr. J. C. (James Clarke),
1302 Connecticut ave.
1873. Wheeler, Capt. Geo. M. (George Montague), U. S. A.,
Lock Box 93. 930 16th street.
1876. White, Dr. C. A. (Charles Abiathar),
Geological Survey. 312 Maple ave., Le Droit Park.
1884. White, Dr. C. H. (Charles Henry), U. S. N.,
Museum of Hygiene.
1887. Whiting, Mr. H. L. (Henry Laurens),
Coast and Geodetic Survey. West Tisbury, Mass.
1885. Willis, Mr. Bailey,
Geological Survey. 1739 G street.
1887. Wilson, Mr. H. C. (Herbert Couper) (Absent),
Carleton College Observatory, Northfield, Minn.
1885. Wilson, Mr, H. M. (Herbert Michael),
Geological Survey. 1715 G street.
1873. Wilson, Mr. J. Ormond (James Ormond),
1439 Massachusetts ave.
1880. Winlock, Mr. W. C. (William Crawford),
Naval Observatory. 1923 H street.
1875. Wood, Mr. Joseph (Absent),
Pittsburgh, Penn.
1871. Wood, Lieut. W. M. (William Maxwell), U. S. N. (Absent),
Navy Department.
1883. Woodward, Mr. R. S. (Robert Simpson),
Geological Survey. 1804 Columbia road.
1885. Wortjvian, Dr. J. L. (Jacob Lawson),
Army Medical Museum. 1711 13th street.
1885. Wright, Mr. Geo. M. (George Mitchell) (Absent),
Akron, Ohio.
1887. Wurdemann, Mr. H. V. (Harry Vanderbilt),
Geological Survey. 1235| 5th street.
1874. Yarrow, Dr. H. C. (Harry Crecy),
Army Medical Museum. 814 17th street.
1884. Yeates, Mr. W. S. (William Smith),
Smithsonian Institution. 631 T street.
1885. Ziwet, Mr. Alexander,
64 Sibley street, Detroit, Mich.
XXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
LIST OF DECEASED MEMBERS.
Name.
Benjamin Alvord
Orville Elias Babcock .
Theodorus Bailey
Spencer Fullerton Baird
Joseph K. Barnes
Henry Wayne Blair
Horace Capron
Salmon Portland Chase .
Frederick Collins
Benjamin Faneuil Craig
Charles Henry Crane
Josiah Curtis
Kichard Dominicus Cutts .
Charles Henry Davis
Frederick William Dorr
Alexander B. Dyer
Amos Beebe Eaton .
Charles Ewing .
Elisha Foote .
John Gray Foster
Leonard Dunnell Gale
Isaiah Hanscom .
William Babcock Hazen
Joseph Henry
Franklin Benjamin Hough .
Andrew Atkinson Humphreys
Ferdinand Kampf .
Washington Caruthers Kerr
Jonathan Homer Lane
Edward Phelps Lull
Oscar A. Mack
Archibald Kobertson Marvine
Fielding Bradford Meek
James William Milner .
Albert James Myer
George Alexander Otis .
Peter Parker
.
Carlile Pollock Patterson
Titian Ramsay Peale
Benjamin Peirce
John Campbell Riley
John Rodgers .
LIST OF MEMBERS. XXIX
Name.
Benjamin Franklin Sands .
George Christian Shaeffer
Henry Eobinson Searle
William J. Twining
Joseph Janvier Woodward .
John Maynard Woodworth
Mordecai Yarnall
Admitted.
Founder
Founder
1877
1878
Founder
1874
1871
Active members
Absent members
SUMMARY.
182
58
Total .
Deceased members
,
240
49

PHILOSOPHICAL SOCIETY OP WASHINGTON. XXXI
XXXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL REPORT OF THE SECRETARIES.
Washington, D. C, December 21, 1887.
To the Philosophical Society of Washington :
We have the honor to present the following statistical data for
1887:
The last Annual Report brought the record of membership
down to December 18, 1886. The number of active mem-
bers was then ......... 183
This number has been increased by the addition of 14 new
members, by the return of 1 absent member, and by the
reinstatement of 2 members previously dropped. It has
been diminished by the departure of 7 members, by the
resignation of 1, and by the death of 3 members. The net
increase of active members has thus been ... 6
And the active membership is now 189
The roll of new members is
:
W. H. Babcock. F. H. Knowlton. T. W. Symons.
Everett Hayden. S. P. Langley. H. L. Whiting.
J. H. Holmes. F. A. Seely. H. C. Wilson.
Harry King. H. L. Smyth. H. V. Wurdeman.
F. J. Knight. J. W. Spencer.
The roll of deceased members is
:
S. F. Baird. W. B. Hazen. E. P. Lull.
There have been 16 meetings, of which 14 have been for the pre-
sentation and discussion of papers, 1 for the President's Annual
Address, and 1 for the Annual Reports and election of officers
;
the average attendance (at the 14 meetings for presentation of
papers), has been 49. There have been 12 meetings of the Mathe-
matical Section ; average attendance 17.
The first 5 meetings of the year were held in the library of the
Surgeon General's Office, at which meetings the average attendance
was 40 ; the 9 remaining meetings were held in the Assembly Hall
of the Cosmos Club, at which the average attendance was 54.
In the general meetings 37 communications have been presented
in the Mathematical Section 20. Altogether 57 communications
secretaries' REPORT. XXXIII
have been made by 37 members and 1 guest. The number of
members and guests who have participated in the discussions is 40.
The total number who have contributed to the scientific proceed-
ings is 47, or 25 per cent, of the present active membership.
The General Committee has held 16 meetings ; average attend-
ance 13, the smallest attendance at any meeting being 11 and the
largest 15.
Of the present active membership 146, or 77 per cent., are em-
ployed in the service of the Government, and 44, or 23 per cent.,
are not so employed.
Marcus Baker,
J. H. Kidder,
Secretaries.
XXXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
REPORT OF THE TREASURER.
Mr. President and Gentlemen:
The report which I shall presently have the honor to submit to
you exhibits the total receipts and disbursements for the fiscal year
ending with this meeting.
The receipts, however, include amounts received for outstanding
dues of previous years, and it is, therefore, proper to say that the
income belonging to the year 1887 was $1,035.75, and the expendi-
ture $568.22, leaving a net surplus for the year of $467.53.
The unpaid dues of former years which have been collected in
1887 amount to $120.
The assets of the Society consist of
:
2 Government bonds, $1,000 and $500, at 4 per cent., $1,500 00
1 " bond, 1,000, « 4* " 1,000 00
6 Cosmos Club mortgage bonds, " 5 « 600 00
Cash with Riggs & Co ' . . 942 05
Unpaid dues 265 00
Total $4,307 05
The removal of the Society from its old place of meeting at the
Army Medical Museum made it nececessary to provide certain
articles of furniture and equipment for use in its new quarters.
The ninth volume of the Bulletin was duly issued in January to
all members entitled to receive it, and to the societies and scientific
journals with which it is customary for the Philosophical Society to
exchange publications.
TREASURERS REPORT. XXXV
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BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
ANNUAL ADDRESS OF THE PRESIDENT.

ANNUAL ADDRESS OF THE PRESIDENT,
William Harkness.
Delivered December 10, 1887.
THE PROGRESS OF SCIENCE AS EXEMPLIFIED IN
THE ART OF WEIGHING AND MEASURING.
Two centuries ago the world was just beginning to awaken from an
intellectual lethargy which had lasted a thousand years. During all
that time the children had lived as their parents before them, the
mechanical arts had been at a standstill, and the dicta of Aristotle
had been the highest authority in science. But now the night of
medievalism was approaching its end, and the dawn of modern
progress was at hand. Galileo had laid the foundation for accurate
clocks by discovering the isochronism of the simple pendulum
;
had proved that under the action of gravity light bodies fall as
rapidly as heavy ones ; had invented the telescope and with it dis-
covered the spots on the sun, the mountains on the moon, the sat-
ellites of Jupiter, and the so-called triple character of Saturn ; and
after rendering himself immortal by his advocacy of the Copernican
system, had gone to his grave, aged, blind, and full of sorrows. His
contemporary, Kepler, had discovered the laws which, while history
endures, will associate his name with the theory of planetary motion,
and he also had passed away. The first Cassini was still a young
man, his son was a little child, and his grandson and great-grand-
son, all of whom were destined to be directors of the Paris Observa-
tory, were yet unborn. The illustrious Huyghens, the discoverer
of Saturu's rings and the father of the undulatory theory of light,
was in the zenith of his powers. The ingenious Hooke was a little
younger, and Newton, towering above them all, had recently in-
vented fluxions, and on the 28th of April, 1686, had presented his
Principia to the Royal Society of London and given the theory
of gravitation to the world. Bradley, who discovered nutation and
44 xxxix
XL PHILOSOPHICAL SOCIETY OF WASHINGTON.
the aberration of light ; Franklin, the statesman and philosopher,
who first drew the lightning from the clouds ; Doilond, the inventor
of the achromatic telescope ; Euler, the mathematician who was
destined to accomplish so much in perfecting algebra, the calculus,
and the lunar theory; Laplace, the author of the Mecanique
Celeste ; Rumford, who laid the foundation of the mechanical
theory of heat ; Daltou, the author of the atomic theory upon which
all chemistry rests ; and Bessel, the greatest of modern astrono-
mers—these and others almost as illustrious, whom we cannot even
name to-night, were still in the womb of time.
Pure science first felt the effects of the new intellectual life and
it was more than a century later before the arts yielded to its influ-
ence. Then came Hargreaves, the inventor of the spinning-jenny;
Arkwright, the inventor of the cotton-spinning frame; Watt, who
gave us the condensing steam engine; Jacquard, the inventor of
the loom for weaving figured stuffs ; Murdock, the originator of gas
lighting; Evans, the inventor of the high-pressure steam engine;
Fulton, the father of steam navigation; Trevithick, who ranks
very near Watt and Evans in perfecting the steam engine ; and
Stephenson, the father of railroads. If now we add the names
of those who have given us the telegraph, to wit: Gauss, the emi-
nent physicist and the greatest mathematician of the present cen-
tury ; Weber, Wheatstone, and Henry—all famous physicists—and
Morse, the inventor and engineer ; we have before us the demi-gods
who have transformed the ancient into the modern world, given us
machinery which has multiplied the productive power of the human
race many fold, annihilated time and space, and bestowed upon
toiling millions a degree of comfort and luxury which was unknown
to kings and emperors of old.
The discoveries and inventions of the last two centuries have so
far exceeded all others within historic times that we are amply jus-
tified in calling this an age of phenomenal progress, and under the
circumstances a little self-glorification is pardonable
—
perhaps even
natural. The weekly and monthly records of scientific events
which appear in so many newspapers and magazines are the imme-
diate result of this, and the great increase of ephemeral scientific
literature has led multitudes of educated people to believe that
such records represent actual progress. The multiplication of
bricks facilitates the building of houses, but does not necessarily
ANNUAL ADDRESS OP THE PRESIDENT. XLI
improve architecture. Similarly, the multiplication of minor inves-
tigations improves our knowledge of details, but rarely affects the
great philosophic theories upon which science is founded. The im-
portance of human actions is measured by the degree in which they
affect human thought, and the only way of permanently affecting
scientific thought is by modifying or extending scientific theories.
The men who do that are neither numerous, nor do they require
weekly paragraphs to record their deeds ; but their names are hon-
ored by posterity. Even in this golden age the advance of science
is not steady, but is made by spasmodic leaps and bounds. Mere
scientific brick making, commonly called progress, is always the
order of the day until some genius startles the world by a discovery
affecting accepted theories. Then every effort is directed in the
new line of thought until it is measurably worked out, and after
that brick making again resumes its place. While the progress in
two centuries has been immense, the progress in a week or a month
is usually almost nil. Optimism has its uses in many departments
of human affairs, but science should be cool and dispassionate,
having regard only for the truth. To make a trustworthy estimate
of the actual state of the whole vast realm of science would be a
task beyond the powers of any one man ; but perhaps it will not
be amiss to spend the time at our disposal this evening in briefly
reviewing the recent progress and present condition of the funda-
mental processes upon which the exact sciences rest—I allude to
the methods of weighing and measuring.
Physical science, deals with many quantities, but they are all so
related to each other that almost every one of them can be ex-
pressed in terms of three fundamental units. As several systems
of such units are possible, it is important to select the most con-
venient, and the considerations which guide us in that respect are
the following:
1. The quantities selected should admit of very accurate com-
parison with other quantities of the same kind.
2. Such comparisons should be possible at all times, and in all
places.
3. The processes necessary for making such comparisons should
be easy and direct.
XLII PHILOSOPHICAL SOCIETY OF WASHINGTON.
4. The fundamental units should be such as to admit of easy defi-
nitions and simple dimensions for the various derived units.
Scientific men have long agreed that these requirements are best
fulfilled by adopting as the fundamental units, a definite length, a
definite mass, and a definite interval of time. Length is an element
which can be very accurately measured and copied, but it must be
defined by reference to some concrete material standard, as for
example, a bar of metal, and as all substances expand and contract
with changes of temperature, it is necessary to state the temperature
at which the standard is correct. A standard of mass, consisting
of a piece of platinum, quartz, or other material not easily affected
by atmospheric influences, probably fulfills the conditions set forth
above better than any other kind of magnitude. Its comparison
with other bodies of approximately equal mass is effected by weigh-
ing, and as that is among the most exact of all laboratory operations,
very accurate copies of the standard can be made, and they can be
carried from place to place with little risk of injury. Time is also
an element which can be measured with extreme precision. The
immediate instruments of measurement are clocks and chronometers,
but their running is checked by astronomical observations and the
ultimate standard is the rotation of the earth itself.
It is important to note that the use of three fundamental units is
simply a matter of convenience and not a theoretical necessity, for
the unit of mass might be defined as that which at unit distance
would generate in a material point unit velocity in unit time ; and
thus we should have a perfectly general system of measurement
based upon only two fundamental units—namely, those of space and
time. Such a system is quite practicable in astronomy, but cannot
yet be applied with accuracy to ordinary terrestrial purposes. Ac-
cording to the law of gravitation
Mass = Acceleration X (Distance)2
and as in the case of the earth we can measure the quantities on
the right-hand side of that equation with considerable accuracy, we
can satisfactorily determine the earth's mass in terms of the supposed
unit. That suffices for the needs of astronomy, but for other scien-
tific and commercial purposes a standard of mass having a magni-
tude of about a pound is necessary, and as two such masses can be
compared with each other from five to ten thousand times more
ANNUAL ADDRESS OF THE PRESIDENT. XLIII
accurately than either of them can be determined in terms of the
supposed unit, three fundamental units are preferable to two.
The Chaldeans, Babylonians, Persians, Greeks, and Romans all
seem to have had systems of weights and measures based upon toler-
ably definite standards, but after the decline of the Roman Empire
these standards seem to have been forgotten, and in the beginning
of the sixteenth century the human body had so far become the
standard of measurement that the units in common use, as for ex-
ample, the foot, palm, etc., were frequently taken directly from it.
The complete table of measures of length was then as follows : the
breadth (not the length) of four barley corns make a digit, or finger
breadth; four digits make a palm, (measured across the middle
joints of the fingers ;) four palms are one foot ; a foot and a half
is a cubit ; ten palms, or two feet and a half, are a step ; two steps,
or five feet, are a pace ; ten feet are a perch ; one hundred and
twenty-five paces are an Italic stadium ; eight stadia, or one thousand
paces, are an Italic mile ; four Italic miles, are a German mile ; and
five Italic miles are a Swiss mile. It was then the practice to fur-
nish standards of length in books by printing in them lines a foot or
a palm long, according to the size of the page, and from these and
other data it appears that the foot then used on the continent of
Europe had a length of about ten English inches.
In England the first attempts at scientific accuracy in matters of
measurement date from the beginning of the seventeenth century,
when John Greaves, who must be considered as the earliest of the
scientific metrologists, directed attention to the difference between the
Roman and English foot by tolerably accurate determinations of
the former, and also attempted the investigation of the Roman
weights. He was followed by Dr. Edward Bernard, who wrote a
treatise on ancient weights and measures about 1685, and towards
the end of the century the measurements of the length of a degree
by Picard and J. D. Cassini awakened the attention of the French
to the importance of rigorously exact standards. In considering
the progress of science with respect to standards of length we may
safely confine our inquiries to the English yard and the French
toise and meter, for during the last two hundred years they have
been almost the only standards adopted in scientific operations.
The English measures of length have come down from the Saxons,
but the oldest standards now existing are the Exchequer yards of
XLIV PHILOSOPHICAL SOCIETY OP WASHINGTON.
Henry VII (1490) 1 and Elizabeth (1588).2 These are both brass end
measures, the former being an octagonal rod about half an inch in
diameter, very coarsely made, and as rudely divided into inches on
the right hand end and into sixteenths of a yard on the left hand
end ; the latter a square rod with sides about half an inch wide,
also divided into sixteenths of a yard and provided with a brass bed
having end pieces between which the yard fits. One end of the bed
is divided into inches and half inches. Francis Baily, who saw this
Elizabethan standard in 1836, speaks of it as " this curious instru-
ment, of which it is impossible, at the present day, to speak too much
in derision or contempt. A common kitchen poker, filed at the ends
in the rudest manner by the most bungling workman, would make
as good a standard. It has been broken asunder ; and the two pieces
have been dove-tailed together: but so badly that the joint is nearly
as loose as that of a pair of tongs. The date of this fracture I could
not ascertain, it having occurred beyond the memory or knowledge
of any of the officers at the Exchequer. And yet, till within the
last 10 years, to the disgrace of this country, copies of this measure
have been circulated all over Europe and America, with a parch-
ment document accompanying them (charged with a stamp that
costs £3. 10s. exclusive of official fees) certifying that they are true
copies of the English standard."3
In the year 1742 certain members of the Royal Society of Lon-
don, and of the Royal Academy of Sciences of Paris, proposed that,
in order to facilitate a comparison of the scientific operations car-
ried on in the two countries, accurate standards of the measures
and weights of both should be prepared and preserved in the ar-
chives of each of these societies. This proposition having been
approved, Mr. George Graham at the instance of the Royal Society
had two substantial brass rods made, upon which he laid off, with
the greatest care, the length of three English feet from the stan-
dard yard kept at the Tower of London. These two rods, together
with a set of troy weights, were then sent over to the Paris Acad-
emy, which body, in like manner, had the measure of a French half
toise set off upon the rods, and keeping one, as previously agreed,
returned the other, together with a standard weight of two marcs,
to the Royal Society. In 1835, Baily declared this copy of the half
1 43, p. 34, and 44, pp. 51-2. (See Bibliography on page lxxix.)
2 43, p. 25.
3 34, p. 146.
ANNUAL ADDRESS OF THE PRESIDENT. XLV
toise to be of little value because the original toise-etalon was of
iron, and the standard temperature in France differed from that in
England.1 In his opinion the French should have sent over an
iron half toise in exchange for the English brass yard ; but this
criticism loses much of its force when it is remembered that in 1742
neither England nor France had fixed upon a temperature at which
their standards were to be regarded as of the true length. On the
return of the rod from Paris Mr. Graham caused Jonathan Sisson
to divide the English yard and the French half toise each into three
equal parts, after which the rod was deposited in the archives of
the Royal Society, where it still remains.2 Objection having been
made that the original and legal standard yard of England was
not the one at the Tower, but the Elizabethian standard at the Ex-
chequer, the Royal Society requested Mr. Graham to compare his
newly-made scale with the latter standard, and on Friday, April
22, 1743, he did so in the presence of a committee of seven mem-
bers of the Royal Society. In the following week the same gentle-
men compared the Royal Society's scale with the standards at
Guildhall and the Tower, and also with the standard of the Clock-
makers' Company. These comparisons having shown that the copy
of the Tower yard upon the Royal Society's scale was about 0'0075
of an inch longer than the standard at the Exchequer, Mr. Graham
inscribed upon the Royal Society's scale a copy of the latter stand-
ard also, marking it with the letters Exch., to distinguish it from
the former, which was marked E. (English), and from the half toise
which was marked F. (French).3
In the year 1758 the House of Commons appointed a committee
to inquire into the original standards of weights and measures of
England; and, under instructions from that committee, the cele-
brated instrument maker, John Bird, prepared two brass rods,
respecting which the committee speak as follows in their report
:
"And having those rods, together with that of the Royal Society
laid in the same place, at the receipt of the Exchequer, all night
with the standards of length kept there, to prevent the variation
which the difference of air might make upon them, they the next
morning compared them all, and, by the means of beam compasses
brought by Mr. Bird, found them to agree as near as it was possible." *
One of these rods was arranged as a matrix for testing end meas-
^4, p. 37. 2 6, pp. 185-8. 3 7, pp. 541-556. *11, p. 434.
XLVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
ures, and the other was a line measure which the committee recom-
mended should be made the legal standard of Eifgland, and which
has since been known as Bird's standard of 1758. Respecting the
statement that after lying together all night the rods were all found
to agree as near as it was possible, Baily says : " This is somewhat
remarkable, and requires further explanation, which unfortunately
cannot now be accurately obtained. For it is notorious that the meas-
ure of the yard of the Royal Society's scale differs very considerably
from the standard yard at the Exchequer : * * * Owing to
this singular confusion of the lengths of the measures, which does
not appear to have been unraveled by any subsequent Committee,
it has happened that the Imperial standard yard * * * has
been assumed nearly 1 — 140 of an inch longer than the ancient
measure of the kingdom." 1 There is little difficulty in surmising
what Bird did. The Exchequer standard consisted of a rod and its
matrix. The Royal Society's committee assumed the rod to be the
true standard of 36 inches, and upon that assumption Graham's
measurements gave for the length of the matrix 36 -0102 inches, and
for the length of the Royal Society's yard 36 -0075 inches. The
Parliamentary committee of 1758 probably assumed the standard
to consist of the rod and matrix together, which seems the better
view ; and by laying the rod in its matrix and measuring to the
joint between them, Bird would have got a length of about 36*0051
inches. The mean between that and 36*0075 would be 36"0063,
which differs very little from the length of Bird's standard result-
ing from Sir George Shuckburgh's measurements. Thus the com-
mittee's statement is justified, and there has been no falsification of
the ancient standards.
On December 1, 1758, Parliament created another committee on
weights and measures which in April, 1759, repeated the recommen-
dation that Bird's standard of 1758 should be legalized, and further
recommended that a copy of it should be made and deposited in
some public office, to be used only on special occasions.2 The copy
was made by Bird in 1760, but owing to circumstances entirely un-
connected with the subject, no legislation followed for sixty-four
years.
The Royal Commission appointed during the reign of George III,
to consider the subject of weights and measures, made its first report
»34, p. 43. 2 12, p. 463.
ANNUAL ADDRESS OF THE PRESIDENT. XLVII
on June 24, 1819, and therein recommended the adoption of the
standard of length which had been used by General Roy in measur-
ing the base on Hounslow Heath
;
l but in a second report made
July 13, 1820, they wrote, " We * * * have examined, since
our last report, the relation of the best authenticated standards of
length at present in existence, to the instruments employed for
measuring the base on Hounslow Heath, and in the late trigonome-
trical operations—But we have very unexpectedly discovered, that
an error has been committed in the construction of some of these
instruments :2 We are therefore obliged to recur to the originals which
they were intended to represent, and we have found reason to prefer
the Parliamentary standard executed by Bird in 1760, which we
had not before received, both as being laid down in the most ac-
curate manner, and as the best agreeing with the most extensive
comparisons, which have been hitherto executed by various observers,
and circulated through Europe ; and in particular with the scale
employed by the late Sir George Shuckburgh." 3
Accordingly, when in 1824 Parliament at length took action,
Bird's standard of 1760 was adopted instead of that of 1758. The
former being a copy of a copy, its selection as a national standard
of length seems so singular that the circumstances which brought
about that result should scarcely be passed over in silence. Bird
had a very accurate brass scale 90 inches long, which he used in
all his dividing operations, whether upon circles or straight lines,
and which Dr. Maskelyne said was 0*001 of an inch shorter on
three feet than Graham's Royal Society yard E.* In the year 1792,
or 1793, the celebrated Edward Troughton made for himself a five
foot scale, which conformed to Bird's, and which he afterwards used
in laying down the divisions of the various instruments that passed
through his hands. This was the original of all the standard scales
he ever made, and at the beginning of the present century he be-
lieved these copies, which were made by the aid of micrometer
microscopes, to be so exact that no variations could possibly be de-
tected in them, either from the original or from each other. Among
the earliest of the scales so made by Troughton was the one used by
Sir George Shuckburgh in 1796-8 in his important scientific opera-
tions for the improvement of the standards. Subsequently, the
length of the meter was determined by comparison with this scale
^3, p. 4. 2 27, p. 92. 3 24, p. 3; also, 25 and 26. *13, p. 326.
XLVIII PHILOSOPHICAL SOCIETY OP WASHINGTON.
and with the supposed fac-simile of it made by Troughton for Pro-
fessor Pictet, of Geneva, and thus it happened 'that on the conti-
nent of Europe all measures were converted into English units by
a reference to Sir George Shuckburgh's scale. The Royal Commis-
sion of 1819, believed Bird's standard of 1760 to be identical with
Shuckburgh's scale, and they legalized it rather than the standard of
1758, in order to avoid disturbing the value of the English yard
which was then generally accepted for scientific purposes.
There are yet four other scales of importance in the history
of English standards—namely, the brass five-foot scale made for
Sir George Shuckburgh by Troughton in 1796 ; two iron standard
yards, marked 1A and 2A, made for the English Ordnance Survey
department by Messrs. Troughton and Simms in 1826-'7, and the
Royal Society's standard yard constructed by Mr. George Dollond,
under the direction of Captain Henry Kater, in 1831.
Bearing in mind the preceding history, the genesis of the present
English standard yard may be thus summarized : In 1742 Graham
transferred to a bar made for the Royal Society a length which he
intended should be that of the Tower yard, but which was really inter-
mediate between the Exchequer standard yard of Elizabeth and its
matrix. That length he marked with the letter E, and, although
destitute of legal authority, it was immediately accepted as the
scientific standard and was copied by the famous instrument makers
of the time with all the accuracy then attainable. Thus it is in
fact the prototype to which all the accurate scales made in Eng-
land between 1742 and 1850 can be traced. Bird's standard of
1758 was compared with the Exchequer standard and with the
Royal Society's yard E, and was of a length between the two.
Bird's standard of 1760, legalized as the Imperial standard in June,
1824, was copied from his standard of 1758. After becoming the Im-
perial standard, Bird's standard of 1760 was compared with Sir
George Shuckburgh's scale by Captain Kater in 1830 and by Mr.
Francis Baily in 1834; with the Ordnance yards 1A and 2A in
1834 by Lieutenant Murphy, R. E., Lieutenant Johnson, R. 1ST.,
and Messrs. F. Baily and Donkin ; and with Kater's Royal Society
yard by Captain Kater in 1831. On October 16th, 1834, the Im-
perial standard (Bird's standard of 1760) was destroyed by the
burning of the Houses of Parliament, in which it was lodged, and
very soon thereafter the Lords of the Treasury took measures to
ANNUAL ADDRESS OF THE PRESIDENT. XLIX
recover its length. Preliminary inquiries were begun on May 11,
1838, and on June 20, 1843, they resulted in the appointment of a
Commission to superintend the construction of new Parliamentary
standards of length and weight, among whose members the Astron-
omer Royal (now Sir George B. Airy), Messrs. F. Baily, R. Sheep-
shanks, and Prof. W. H. Miller, were prominent. The laborious
investigations and experiments carried out by that Commission can-
not be described here, but it will suffice to say that for determining
the true length of the new standard Mr. Sheepshanks employed a
provisional yard, marked upon a new brass bar designated " Brass
2," which he compared as accurately as possible with Sir George
Shuckburgh's scale, the two Ordnance yards, and Kater's Royal
Society yard. The results in terms of the lost Imperial standard
were as follows
:
Brass bar 2 = 36-000084 from comparison with Shuckburgh's scale, 0-36 in.
36-000280 " " " " 10-46 in.
36-000303 from comparison with the Ordnance yard, 1A.
36-000275 " " » " " 2A.
36-000229 from Capt. Kater's Royal Society yard.
Mean = 36-000234
Respecting this mean Mr. Sheepshanks wrote: "This should be
pretty near the truth ; but I prefer 36"0002o, if in such a matter
such a difference be worth notice. I propose, therefore, in con-
structing the new standard to assume that
—
Brass bar 2 = 36-00025 inches of lost Imperial standard at 62° Fab.."
And upon that basis the standard now in use was constructed.1
Turning now to the French standards of length, it is known that
the ancient toise de macons of Paris was probably the toise of
Charlemagne (A. D. 742 to 814), or at least of some Emperor
Charles, and that its etalon was situated in the court yard of the
old Chatelet, on the outside of one of the pillars of the building.
It still existed in 1714, but entirely falsified by the bending of the
upper part of the pillar. In 1668 the ancient toise of the masons
was reformed by shortening it five lines ; but whether this reforma-
tion was an arbitrary change, or merely a change to remedy the
HI, p. 664.
L PHILOSOPHICAL SOCIETY OF WASHINGTON.
effects of long use and restore the etalon to conformity with some
more carefully preserved standard, is not quite clear.1 These old
etalons were iron bars having their two ends turned up at right
angles so as to form talons, and the standardizing of end measures
was effected by fitting them between the talons. Being placed on
the outside of some public building, they were exposed to wear from
constant use, to rust, and even to intentional injury by malicious
persons. Under such conditions every etalon would, sooner or later,
become too long and require shortening.
Respecting the ancient toise of the masons there are two contra-
dictory stories. On December 1, 1714, La Hire showed to the
French Academy what he characterized as " a very ancient instru-
ment of mathematics, which has been made by one of our most ac-
complished workmen with very great care, where the foot is marked,
and which has served to re-establish the toise of the Chatelet, as I
have been informed by our old mathematicians." 2 Forty-four years
later, on July 29, 1758, La Condamine stated to the Academy that
" We know only by tradition that to adjust the length of the new
standard, the width of the arcade or interior gate of the grand pa-
vilion, which served as an entrance to the old Louvre, on the side
of the rue Fromenteau was used. This opening, according to the
plan, should have been twelve feet wide. Half of it was taken to
fix the length of the new toise, which thus became five lines shorter
than the old one." 3 Of these two contradictory statements that of
La Hire seems altogether most trustworthy, and the ordinary rules
of evidence indicate that it should be accepted to the exclusion of
the other.
In 1668 the etalon of the new toise, since known as the toise-etalon
du Chatelet, was fixed against the wall at the foot of the staircase
of the grand Chatelet de Paris—by whom or at what season of the
year is not known. Strange as it now seems, this standard—very
roughly made, exposed in a public place for use or abuse by every-
body, liable to rust, and certain to be falsified by constant wear
—
was actually used for adjusting the toise of Picard, that of Cassini,
the toise of Peru and of the North, that of La Caille, that of Mairan
—in short, all the toises employed by the French in their geodetic
operations during the seventeenth and eighteenth centuries. The
lack of any other recognized standard made the use of this one im-
1
1, p. 536 and 2, p. 395. 2 2, p. 395. 3 14, p. 484.
ANNUAL ADDRESS OF THE PRESIDENT. LI
perative, but the French academicians were well aware of its defects
and took precautions to guard against them.
The first toise copied from the etalon of the Chatelet for scientific
purposes was that used by Picard in his measurement of a degree of
the meridian between Paris and Amiens. 1 It was made about the
year 1668, and would doubtless have become the scientific standard
of France had it not unfortunately disappeared before the degree
measurements of the eighteenth century were begun. The second
toise copied from the etalon of the Chatelet for scientific purposes was
that used by Messrs. Godin, Bouguer, and La Condamine for meas-
uring the base of their arc of the meridian in Peru. This toise,
since known as the toise du Perou, was made by the artist Langlois
under the immediate direction of Godin in 1735, and is still pre-
served at the Paris Observatory.2 It is a rectangular bar of polished
wrought iron, having a breadth of 1*58 English inches and a thick-
ness of 0"30 of an inch. All the other toises used by the Academy
in the eighteenth century were compared with it, and, ultimately, it
was made the legal standard of France by an order of Louis XV,
dated May 16, 1766. As the toise of Peru is the oldest authentic
copy of the toise of the Chatelet, the effect of this order was simply
to perpetuate the earliest known state of that ancient standard.
The metric system originated from a motion made by Talleyrand
in the National Assembly of France, in 1790, referring the question
of the formation of an improved system of weights and measures,
based upon a natural constant, to the French Academy of Sciences
;
and the preliminary work was entrusted to five of the most eminent
members of that Academy—namely, Lagrange, Laplace, Borda,
Monge, and Condorcet. On March 19, 1791, these gentlemen, to-
gether with Lalande, presented to the Academy a report contain-
ing the complete scheme of the metric system. In pursuance of the
recommendations in that report, the law of March 26, 1791, was
enacted for the construction of the new system, and the Academy
of Sciences was charged with the direction of the necessary opera-
tions. Those requisite for the construction of a standard of length
1. The determination of the difference of latitude between Dun-
kirk and Barcelona.
1 5, Art. 4, p. 15. 2 14, p. 487 and 46, p. C.2.
LII PHILOSOPHICAL SOCIETY OF WASHINGTON.
2. The remeasuremeut of the ancient bases which had served for
the measurement of a degree at the latitude of Paris, and for mak-
ing the map of France.
3. The verification by new observations of the series of triangles
employed for measuring the meridian, and the prolongation of them
as far as Barcelona.
This work was entrusted to Mechain and Delambre, who carried
it on during the seven years from 1791 to 1798, notwithstanding
many great difficulties and dangers. The unit of length adopted
in their operations was the toise of Peru, and from the arc of 9° 40'
45" actually measured, they inferred the length of an arc of the meri-
dian extending from the equator to the pole to be 5,130,740 toises.
As the meter was to be one ten millionth of that distance, its length
was made 0*5130740 of a toise, or, in the language of the committee,
443*296 lines of the toise of Peru at a temperature of 13° Reaumur
(16*° C. or 6H° F.).1
Before attempting to estimate how accurately the standards we
have been considering were intercompared it will be well to describe
briefly the methods by Avhich the comparisons were effected. In
1742 Graham used the only instruments then known for the pur-
pose—namely, very exact beam compasses of various kinds, one
having parallel jaws for taking the lengths of the standard rods,
another with rounded ends for taking the lengths of the hollow beds,
and still another having fine points in the usual manner. The
jaws, or points, of all these instruments were movable by micro-
meter screws having heads divided to show the eight hundredth
part of an inch directly, and the tenth of that quantity by estima-
tion ; but Mr. Graham did not consider that the measurements
could be depended upon to a greater accuracy than one 1600th of
an inch.2
Troughton is generally regarded as the author of the application
of micrometer microscopes to the comparison of standards of length,
but the earliest record of their use for that purpose is by Sir George
Shuckburgh in his work for the improvement of the standards of
weight and measure in 1796-8.3 Since then their use has been
general ; first, because they are more accurate than beam compasses,
1 19, pp. 432, 433 and 642. *'7, pp. 545-6. 3 18, p. 137.
ANNUAL ADDRESS OF THE PRESIDENT. LILT
and, second, because they avoid the injury to standard scales which
necessarily results from placing the points of beam compasses upon
their graduations. As the objective of the microscope forms a mag-
nified image of the standard, upon which the micrometer wires are
set by the aid of the eye piece, it is evident that in order to reduce
the effect of imperfections in the micrometer, the objective should
have the largest practicable magnifying power. To show the pro-
gress in that direction the optical constants of the microscopes, by
means of which some of the most important standards have been
compared, are given in the accompanying table.
1797
1817
1834
1834
1850
1864
1880
1883
Observer.
Sir Geo. Shuckburgh
Capt. Henry Kater
Francis Baily
Lieut. Murphy. E. E.
R. Sheepshanks
Gen. A. R. Clarke, R. E
Prof. W. A. Rogers, 1 in. obj.
" " £ in. obj.
" " \ in. obj.
International Bureau
14
18
27
60
90
o <u
si
btio
1.7
(2.3)
(2.0)
(2.0)
(2.8)
4.
(12.7)
(28.6)
(52.7)
7.5
Inches.
1.50
0.67
0.83
CD "-*= S
p a p
s o S
Inches.
0-01000
•00428
•00500
•00500
•00358
•00287
•00079
•00035
•00019
0-00394
Note.—The magnifying power of Sir Geo. Shuckburgh's microscope
seems to be referred to a distance of twelve inches for distinct vision. The
powers inclosed in parentheses are estimated upon the assumption that the
respective micrometer screws had one hundred threads per inch.
In the memoirs of the French Academy nothing is said respect-
ing the method adopted by the Academicians for comparing their
various toises ; but in his astronomy, Lalande states that the com-
parisons were effected partly by beam compasses, and partly by
superposing the toises upon each other and examining their ends,
both by touch and with magnifying glasses ; they being all end
standards.1 For the definitive adjustment of the length of their
l i6, p. 8.
LIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
meters, which were also end standards, the French Metric Commis-
sion used a lever comparator hy Lenoir.
In 1742 Graham used beam compasses, which he considered trust-
worthy to 0'00062 of an inch, in comparing standards of length
;
but at that time the French Academicians made their comparisons
of toises only to one twentieth, or one thirtieth of a line, say O'OOSOO
of an inch, and it was not until 1758 that La Condamine declared
they should be compared to 0*01 of a line, or 0'00089 of an English
inch " if our senses aided by the most perfect instruments can attain
to that." x Half a century later, ten times that accuracy was attained
by the lever comparator of Lenoir, which was regarded as trust-
worthy to 0-000077 of an inch.2
The heads of micrometer microscopes are usually divided into
one hundred equal parts, and if we regard one of these parts as the
least reading of a microscope, then in 1797, Sir George Shuckburgh's
microscopes read to one ten thousandth of an inch ; and the least
reading of microscopes made since that date has varied from one
twenty thousandth to one thirty-five thousandth of an inch. A few
investigators, among whom may be mentioned Professor "W. A.
Rogers, of Colby University, have made the least reading of their
microscopes as small as one 90,000 of an inch, but it is doubtful if
there is any advantage in so doing. At the present day the errors
committed in comparing standards arise, not from lack of power in
the microscopes, but from the difficulty of determining sufficiently
exactly the temperature of the standard bars, and the effect of flexure
upon the position of their graduations. In order to ascertain the
length of a three foot standard with an error not exceeding 0"000020
of an inch, its temperature must be known to 0"06° F. if it is of brass,
or to 0'09° F. if it is of iron. To get thermometers that will indicate
their own temperature to that degree of accuracy is by no means
easy, but to determine the temperature of a bar from their readings
is far more difficult. Again, we imagine the length of our standards'
to follow their temperature rigorously, but what proof is there that
such is the case? If we determine the freezing point of an old ther-
mometer, then raise it to the temperature of boiling water, and im-
mediately thereafter again determine its freezing point, we in-
variably find that the freezing point has fallen a little ; and we ex-
plain this by saying that the glass has taken a set, from which it
1 U, p. 483. 'Base du Systeme Metrique. T. 3, pp. 447-462.
ANNUAL ADDRESS OF THE PRESIDENT. LV
requires time to recover. Is it not probable that an effect similar
in kind, although less in degree, occurs iu all solids when their
temparature is varying? When we look at the highly polished
terminols of an end standard, we are apt to regard them as mathe-
matical surfaces, separated by an interval which is perfectly definite,
and which could be measured with infinite precision if we only had
the necessary instrumental appliances ; but is that a correct view?
The atomic theory answers emphatically, No. According to it, all
matter consists of atoms, or molecules, of a perfectly definite size,
and with definite intervals between them ; but even if that is denied,
the evidence is now overwhelming that matter is not homogeneous,
but possesses a grain of some kind, regularly repeated at intervals
which cannot be greater than one 2,000,000th nor less than one 400,-
000,000th ofan inch. Accordingly, we must picture our standard bar
as a conglomeration of grains of some kind or other, having magni-
tudes of the order specified, and all in ceaseless motion, the ampli-
tude of which depends upon the temperature of the bar. To our
mental vision the polished terminals are therefore like the surface
of a pot of boiling water, and we recognize that there must be a
limit to the accuracy with which the interval between them can be
measured. As a basis for estimating how near this limit we have
approached, it will suffice to say that for fifty years past it has been
customary to state comparisons of standards of length to one 1,000,-
000th of an inch. Nevertheless, most authorities agree that although
one 100,000th of an inch can be distinguished in the comparators,
one 25,000th of an inch is about the limit of accuracy attainable
in comparing standards. Possibly such a limit may be reached
under the most favorable circumstances, but in the case of the yard
and the meter, which are standard at different temperatures, the
following values of the meter by observers of the highest repute
render it doubtful if any thing like that accuracy has yet been at-
tained.
1818. Capt. Henry Kater .... 39'37079 inches.
1866. Gen. A. R. Clarke 39-37043 "
1883. Prof. Wm. A. Rogers .... 39*37027 "
1885. Gen. C. B. Comstock .... 39*36985 "
The earliest standard of English weight of which we have any
very definite knowledge is the mint pound of the Tower of London.
It weighed 5,400 troy grains, and the coinage was regulated by it
45
LVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
up to the year 1527, when it was abolished in favor of the troy
pound of 5,760 grains. Contemporaneously with^ the tower pound
there was also the merchant's pound, whose exact weight is now in-
volved in so much doubt that it is impossible to decide whether it
consisted of 6,750 or of 7,200 grains. The tower pound and the
troy pound were used for weighing only gold, silver, and drugs,
while all other commodities were weighed by the merchant's pound
until the thirteenth or fourteenth century, and after that by the
avoirdupois pound. It is not certainly known when the troy and
avoirdupois pounds were introduced into England, and there is no
evidence of any relation between them when they first became
standards. The present avoirdupois pound can be clearly proved
to be of similar weight to the standard avoirdupois pound of Ed-
ward III (A. D. 1327-1377), and there is good reason for believing
that no substantial change has occurred either in its weight or in that
of the troy pound since their respective establishment as standards
in England.
The oldest standard weights now existing in the English archives
date from the reign of Queen Elizabeth, and consist of a set of bell-
shaped avoirdupois weights of 56, 28, and 14 pounds, made in 1582
and 7, 4, 2, and 1 pounds made in 1588 ; a set of flat circular
avoirdupois weights of 8, 4, 2, and 1 pounds, and 8, 4, 2, 1, £, i, i,
and tV ounces, made in 1588 ; and a set of cup-shaped troy weights,
fitting one within the other, of 256, 128, 64, 32, 16, 8, 4, 2, 1, i, i, i
(hollow), and & (solid) ounces, also made in 1588. 1 All these stand-
ards were constructed by order of Queen Elizabeth, under the di-
rection of a jury composed of eighteen merchants and eleven gold-
smiths of London ; the avoirdupois weights being adjusted according
to an ancient standard of 56 pounds, remaining in the Exchequer
from the time of Edward III ; and the troy weights being adjusted
according to the ancient standard in Goldsmiths' Hall.2
In view of the fact that the weight mentioned in all the old acts
of Parliament, from the time of Edward I (A. D. 1274-1307) is
universally admitted to be troy weight, the Parliamentary Com-
mittee of 1758, appointed to inquire into the original standards of
weights and measures in England, recommended that the troy pound
should be made the unit or standard by which the avoirdupois and
other weights should be regulated ; and by their order three several
1 11, p. 430. 2 11, pp. 435 and 443-448.
ANNUAL ADDRESS OF THE PRESIDENT. LVII
troy pounds of soft gun-metal were very carefully adjusted under
the direction of Mr. Joseph Harris, who was then assay master of
the Mint. To ascertain the proper mass for these pounds the com-
mittee caused Messrs. Harris and Gregory, of the Mint, to perform
the following operations in their presence: 1
First.—In the before-mentioned set of troy weights, made in 1588,
which were then the Exchequer standard, each weight, from that
of 4 ounces up to that of 256 ounces, was compared successively
with the sum of all the smaller weights ; and by a process for which
no valid reason can be assigned,2 it was concluded from these weigh-
ings that the troy pound composed of the 8 and 4 ounce weights
was 1} grains too light.
Second.—The aforesaid 8 and 4 ounce weights of the Exchequer
were compared with five other authoritative troy pounds, four of
which belonged to the Mint and one to Mr. Freeman, who, like his
father before him, was scale maker to the mint, and from the mean
of these weighings it appeared that the sum of the Exchequer 8 and
4 ounce weights was one grain too light.
The Committee adopted the mean between the latter result and
that which they had deduced from the Exchequer weights alone,2
and accordingly Mr. Harris made each of his three troy pounds 1£
grains heavier than the sum of the Exchequer 8 and 4 ounce weights
;
but sixty-six years were destined to elapse before Parliament took
action respecting them.
The Commissioners appointed in 1818 to establish a more uniform
system of weights and measures, repeated the recommendations of
the committee of 1758,3 and as the avoirdupois pound which had
long been used, although not legalized by any act of the legis-
lature, was very nearly 7,000 troy grains, they recommended that
7,000 such troy grains be declared to constitute a pound avoirdu-
pois.4 These recommendations were embodied in the act of Parlia-
ment of June 17, 1824, and thus one of the troy pounds made in
1758 became the Imperial standard. That standard, like Bird's
standard yard, was deposited in the Houses of Parliament and was
burned up with them in October, 1834.
The present English standard pound was made in 1844-46 by
Prof. W. H. Miller, who Avas one of the members of the Commission
appointed in 1843 to superintend the construction of the new par-
1 11, p. 437. JSee Note B, below. s See 23, 24, and 25. *28, pp. 4-5.
LVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
liamentary standards of length and weight destined to replace those
destroyed in 1834. A number of weights had beea very accurately
compared with the lost standard ; namely, in 1824 or 1825, by
Capt. Kater, five troy pounds of gun-metal, destined respectively
for the use of the Exchequer, the Royal Mint, and the cities of
London, Edinburgh, and Dublin ; and in 1829, by Capt. v. Nehus,
two troy pounds of brass and one of platinum, all in the custody
of Prof. Schumacher, and a platinum troy pound belonging to the
Royal Society. The first step for recovering the mass of the lost
standard was manifestly to compare these weights among themselves,
and upon so doing it was found that for the brass and gun-metal
weights the discrepancies between the weighings made in 1824 and
1844 amounted to 0"022G 1 of a grain, while for the two platinum
weights the discrepancies between the weighings made in 1829 and
1845 was only 0"00019 2 of a grain. With a single exception, all
the new brass or gun-metal weights had become heavier since their
first comparison with the lost standard, the change being probably
due to oxydation of their surfaces, and on that account the new
standard was made to depend solely upon the two platinum weights.
For convenience of reference these weights were designated respec-
tively Sp (Schumacher's platinum), and RS (Royal Society). A
provisional platinum troy pound, T, intermediate in mass between
Sp and RS was next prepared, and from 286 comparisons made in
January, February, July, and August, 1845, it was found that in a
vacuum 3 %
T = Sp+ 0-00105 grain,
while from 122 comparisons made in January, July, and August*
1845,
T = RS — 0-00429 grain.
By combining these values with the results of the weighings
made in 1824-29, namely,
Sp = U — 0-52956 grain,
RS = U - 0*52441 grain,
where U designates the lost standard—the comparisons with Sp
gave
T = U - 0-52851 grain,
while those with RS gave
T = U — 0-52870 grain.
HO, p. 772. 2 40, p. 941. s 40, pp. 819-20.
ANNUAL ADDRESS OF TIIE PRESIDENT. LIX
To the first of these expressions double weight was assigned, be-
cause the comparisons of T and U with Sp were about twice as
numerous as those with RS. The resulting mean was therefore
T = U — 0-52857 grains = 5759*47143 grains,
and from that value of T the new standard avoirdupois pound of
7000 grains was constructed.
From some time in the fifteenth century until the adoption of the
metric system in August, 1793, the system of weights employed in
France was the poids de marc, having for its ultimate standard the
pile de Charlemagne, which was then kept in the Mint, and is now
deposited in the Conservatoire des Arts et Metiers. The table of
this weight was
72 grains = 1 gros = 72 grains.
8 gros = 1 once = 576 "
8 onces = 1 marc= 4608
2 marcs = 1 livre = 9216
The origin of the pile de Charlemagne is not certainly known,
but it is thought to have been made by direction of King John (A.
D. 1350-1364). It consists of a set of brass cup-weights, fitting
one within the other, and the whole weighing fifty marcs. The
nominal and actual weights of the several pieces are as follows: 1
LX PHILOSOPHICAL SOCIETY OF WASHINGTON.
The metric standard of weight, called a kilogram, was constructed
under the direction of the French Academy of Sciences simulta-
neously with the meter ; the work being done principally by Lefevre-
Gineau and Borda. It was intended that the kilogram should have
the same mass as a cubic decimeter of pure water at maximum
density, and the experimental determination of that mass was made
by finding the difference of weight in air and in water of a hollow
brass cylinder whose exterior dimensions at a temperature of 17'6°
C. were, height = 2"437672 decimeters, diameter = 2'428368 deci-
meters, volume = 11'2900054 cubic decimeters. The difference of
weight in question was first measured in terms of certain brass
weights, by the aid of which the platinum kilogram of the archives
was subsequently constructed, special care being taken to apply the
corrections necessary to reduce all the weighings to what they
would have been if made in a vacuum.1
The best results hitherto obtained for the weight of a cubic deci-
meter of water, expressed in terms of the kilogram of the archives,
are as follows
:
2
;
Date.
ANNUAL ADDRESS OF THE PRESIDENT. LXI
These results show the extreme difficulty of determining the exact
mass of a given volume of water. The discordance between the
different observers amounts to more than one part in a thousand,
while good weighings are exact to one part in eight or ten millions.
Without doubt two weights can be compared at least a thousand
times more accurately than either of them can be reproduced by
weighing a specified volume of water, and for that reason the kilo-
gram, like the English pound, can now be regarded only as an ar-
bitrary standard of which copies must be taken by direct compari-
son. As already stated, the kilogram is equivalent to 15432'34874
English troy grains, or about two pounds three ounces avoirdupois.
In consequence of the circumstance that the mass of a body is not
affected either by temperature or flexure, weighing is an easier pro-
cess than measuring ; but in order to obtain precise results many
precautions are necessary. Imagine a balance with a block of wood
tied to its right-hand pan and accurately counterpoised by lead
weights in its left-hand pan. If with things so arranged the bal-
ance were immersed in water the equilibrium would be instantly
destroyed and to restore it all the weights would have to be re-
moved from the left-hand pan, and some of them would have to be
placed in the right-hand pan to overcome the buoyancy of the wood.
The atmosphere behaves precisely as the water does, and although
its effect is minute enough to be neglected in ordinary business
affairs, it must be taken into account when scientific accuracy is
desired. To that end the weighing must either be made in a vacuum,
or the difference of the buoyant effect of the air upon the substances
in the two pans must be computed and allowed for. As very few
vacuum balances exist, the latter method is usually employed. The
data necessary for the computation are the latitude of the place
where the weighing is made and its altitude above the sea level
;
the weights, specific gravities, and coefficients of expansiou of each
of the substances in the two pans ; the temperature of the air, its
barometric pressure, and the pressure, both of the aqueous vapor,
and of the carbonic anhydride, contained in it.
Judging from the adjustment of the pile de Charlemagne, and
the Exchequer troy weights of Queen Elizabeth, the accuracy at-
tained in weighing gold and silver at the mints during the four-
teenth, fifteenth, and sixteenth centuries must have been about one
part in ten thousand. The balance which Mr. Harris of the Lon-
LXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
don mint used in 1743 indicated one-eighth of a grain on a troy
pound, or about one part in 50,000 ; while according to Sir George
Shuckburgh the balance used by Messrs. Harris and Bird in mak-
ing their observations upon the Exchequer weights, apparently in
1758 or 1759, turned with one 230,000th part of its load.
1 In 1798
Sir George Shuckburgh had a balance sensitive enough to indicate
0*01 of a grain when loaded with 16,000 grains, or about one part
in 1,600,000. The balance used by Fortin in 1799, in adjusting
the kilogram of the archives, was not quite so delicate, its sensi-
tiveness being only the 1,000,000th part of its load ; but in 1844,
for the adjustment of the present English standard pound, Professor
Miller employed a balance whose index moved about 0'01 of an
inch for a change of 0'002 of a grain in a load of 7,000 grains.
2 He
read the index with a microscope, and found the probable error of
a single comparison of two avoirdupois pounds to be one 12,000,000th
of either, or about 0'00058 of a grain. At the present time it is
claimed that two avoirdupois pounds can be compared with an
error not exceeding 0*0002 of a grain ; and two kilograms with an
error not exceeding 0'02 of a milligram.
The mean solar day is the natural unit of time for the human
race, and it is universally adopted among all civilized nations.
Our ultimate standard of time is therefore the rotation of the earth
upon its axis, and from that rotation we determine the errors of our
clocks and watches by astronomical observations. For many pur-
poses it suffices to make these observations upon the sun, but when
the utmost precision is desired it is better to make them on the
stars. Until the close of the seventeenth century quadrants were
employed for that purpose, and so late as 1680 Flamsteed, the first
English astronomer royal, thought himself fortunate when he suc-
ceeded in constructing one which enabled him to be sure of his ob-
served times within three seconds.
3 About 1690 Roemer invented
the transit instrument, which soon superseded the quadrant, and
still remains the best appliance for determining time Most of his
observations were destroyed by a fire in 1728, but the few which
have come down to us show that as early as 1706 he determined
time with an accuracy which has not yet been very greatly sur-
1 18, p. 148. 2 40, pp. 762 and 943.
3 Account of the Rev. John Flamsteed. By Francis Baily. pp. 4-">-0.
(London, 1835. 4to.)
ANNUAL ADDRESS OF THE PRESIDENT. LXII1
passed. Probably the corrections found in the least square adjust-
ment of extensive systems of longitude determinations afford the
best criterion for estimating the accuracy of first-class modern time
observations, and from them it appears that the error of such ob-
servations may rise as high as ± 0'05 of a second.
During the intervals between successive observations of the
heavenly bodies we necessarily depend upon clocks and chronom-
eters for our knowledge of the time, and very erroneous ideas are
frequently entertained respecting the accuracy of their ruiming.
The subject is one upon which it is difficult to obtain exact infor-
mation, but there are few time-pieces which will run for a week
without varying more than three-quarters of a second from their
predicted error. As the number of seconds in a week is 604,800,
this amounts to saying that the best time-pieces can be trusted to
measure a week within one part in 756,000. Nevertheless, clocks
and chronometers are but adjuncts to our chief time-piece, which is
the earth itself, and upon the constancy of its rotation depends the
preservation of our present unit of time. Early in this century
Laplace and Poisson were believed to have proved that the length
of the siderial day had not changed by so much as the one hun-
dredth part of a second during the last 2,500 years, but later inves-
tigations show that they were mistaken, and, so far as we can now
see, the friction produced by the tides in the ocean must be steadily
reducing the velocity with which the earth rotates about its axis.
The change is too slow to become sensible within the lifetime of a
human being, but its ultimate consequences will be most momentous.
Ages ago it was remarked that all things run in cycles, and there
is enough truth in the saying to make it as applicable now as on the
day it was uttered. The Babylonian or Chaldean system of weights
and measures seems to be the original from which the Egyptian
system was derived, and is probably the most ancient of which we
have any knowledge. Its unit of length was the cubit, of which
there were two varieties, the natural and the royal. The foot was
two-thirds of the natural cubit. Kespecting the earliest Chaldean
and Egyptian system of weights no very satisfactory information
exists, but the best authorities agree that the weight of water con-
tained in the measure of a cubic foot constituted the talent, or larger
unit of weight, and that the sixtieth or fiftieth parts of the talent
constituted, respectively, the Chaldean and Egyptian values of the
mina, or lesser unit of commercial weight. Doubtless these weights
LXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
varied considerably at different times and places, just as the modern
pound has varied, but the relations stated are belteved to have been
the original ones. The ancient Chaldeans used not only the decimal
system of notation, which is evidently the primitive one, but also a
duodecimal system, as shown by the division of the year into twelve
months, the equinoctial day and night each into twelve hours, the
zodiac into twelve signs, etc., and a sexagesimal system by which
the hour was divided into sixty minutes, the signs of the zodiac into
thirty parts or degrees, and the circle into 360 degrees, with further
sexagesimal subdivisions. The duodecimal and sexagesimal systems-
seem to have originated with the Chaldean astronomers, who, for
some reason which is not now evident, preferred them to the decimal
system, and by the weight of their scientific authority impressed
them upon their system of weights and measures. Now observe how
closely the scientific thought of to-day repeats the scientific thought
of four thousand years ago. These old Chaldeans took from the
human body what they regarded as a suitable unit of length, and
for their unit of mass they adopted a cube of water bearing simple
relations to their unit of length. Four thousand years later, when
these simple relations had been forgotten and impaired, some of the
most eminent scientists of the last century again undertook the
task of constructing a system of weights and measures. With them
the duodecimal and sexagesimal systems were out of favor, while
the decimal system was highly fashionable, and for that reason they
subdivided their units decimally instead of duodecimally, sexagesi-
mal^, or by powers of two ; but they reverted to the old Chaldean
device for obtaining simple relations between their units of length
and mass, and to that fact alone the French metric system owes its sur-
vival. Every one now knows that the meter is not the ten millionth
part of a quadrant of the earth's meridian, and in mathematical
physics, where the numbers are all so complicated that they can
only be dealt Avith by the aid of logarithms, and the constant -, an
utterly irrational quantity, crops up in almost every integral, mere
decimal subdivision of the units counts for very little. But in
some departments of science, as, for example, chemistry, a simple
relation between the unit of length (which determines volume), the
unit of mass, and the unit of specific gravity, is of prime impor-
tance ; and wherever that is the case the metric system will be used.
To engineers such relations are of small moment, and consequently
among English-speaking engineers the metric system is making no
ANNUAL ADDRESS OF THE PRESIDENT. LXV
progress, while, on the other hand, the chemists have eagerly-
adopted it. As the English yard and pound are the direct descend-
ants of the Chaldean-Babylonian natural cubit and mina, it is not
surprising that the yard should be only 0*48 of an inch shorter
than the double cubit, and the avoirdupois pound only 665 grains
lighter than the Babylonian commercial mina ; but, considering the
origin of the metric system, it is rather curious that the meter is
only 1*97 inches shorter than the Chaldean double royal cubit, and
the kilogram only 102 grains heavier than the Babylonian royal
mina. Thus, without much exaggeration, we may regard the pres-
ent English and French fundamental units of length and mass as
representing respectively the commercial and royal units of length
and mass of the Chaldeans of four thousands years ago.
Science tells us that the energy of the solar system is being slowly
dissipated in the form of radiant heat ; that ultimately the sun will
grow dim ; life will die out on the planets ; one by one they will
tumble into the expiring sun ; and at last darkness and the bitter
cold of the absolute zero will reign over all. In that far-distant
future imagine some wandering human spirit to have penetrated to
a part of space immeasurably beyond the range of our most pow-
erful telescopes, and there, upon an orb where the mechanical arts
flourish as they do here, let him be asked to reproduce the standards
of length, mass, and time with which we are now familiar. In the
presence of such a demand the science of the seventeenth and eight-
eenth centuries would be powerless. The spin of the earth which
measures our days and nights would be irretrievably gone ; our yards,
our meters, our pounds, our kilograms would have tumbled with the
earth into the ruins of the sun, and become part of the debris of the
solar system. Could they be recovered from the dead past and live
again ? The science of all previous ages mournfully answers, No ;
but with the science of the nineteenth century it is otherwise. The
spectroscope has taught us that throughout the visible universe the
constitution of matter is the same. Everywhere the rythmic motions
of the atoms are absolutely identical, and to them, and the light
which they emit, our wandering spirit would turn for the recovery
of the long-lost standards. By means of a diffraction grating and
an accurate goniometer he could recover the yard from the wave
length of sodium light with an error not exceeding one or two thou-
sandths of an inch. Water is everywhere, and with his newly re-
LXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
covered yard he could measure a cubic foot of it, and thus recover
the standard of mass which we call a pound. Xhe recovery of our
standard of time would be more difficult ; but even that could be
accomplished with an error not exceeding half a minute in a day.
One way would be to perform Michelson's modification of Foucault's
experiment for determining the velocity of light. Another way
would be to make a Siemen's mercury unit of electrical resistance,
and then, either by the British Association method or by Lord
Rayleigh's modification of Lorenz's method, find the velocity which
measures its resistance in absolute units. Still another way would
he to find the ratio of the electro-static and electro-magnetic units
of electricity. Thus all the units now used in transacting the world's
business could be made to reappear, if not with scientific, at least
with commercial accuracy, on the other side of an abyss of time and
space before which the human mind shrinks back in dismay. The
science of the eighteenth century sought to render itself immortal
by basing its standard units upon the solid earth, but the science of
the nineteenth century soars far beyond the solar system and con-
nects its units with the ultimate atoms which constitute the universe
itself.
ANNUAL ADDRESS OP THE PRESIDENT. LXVII
NOTE A.
The appended table exhibits the principal comparisons hitherto
made of the more important early English standards of length.
The significations of the reference numbers, and the authorities for
the descriptions of the standards, are as follows:
No. 1. Standard yard of Henry VII (1490); an end measure
formed of an octagonal brass rod half an inch in diameter.
No. 2. Standard yard of Queen Elizabeth (1588) ; an end meas-
ure formed of a brass rod six-tenths of an inch square.
No. 3. Matrix to Queen Elizabeth's standard yard (1588) ; of
brass, li inches wide, 1 inch thick, and 49 inches long.
No. 4. StandUrd ell of Queen Elizabeth (1588); an end meas-
ure of brass, six-tenths of an inch square.
No. 5. Standard yard of the Clock-makers' Company (1671) ; a
matrix, formed by two pins in an octagonal brass rod half an inch
in diameter.
No. 6. Standard yard at the Tower ; a line measure, marked on
a brass bar seven-tenths of an inch square and 41 inches long.
No. 7. Graham's Royal Society scale (1742) ; a line measure,
on a brass bar half an inch wide, one-quarter of an inch thick, and
42 inches long. Line marked E. Mem. Roy. Ast. Soc, Vol. 9, p. 82.
No. 8. Ditto. Line marked Exch.
*
No. 9. Ditto. Paris half toise ; marked F.
Numbers 1 to 9 are described in the Philosophical Transactions,
1743, pp. 547-550.
No. 10. Bird's standard yard of 1758; a line measure, on a
brass bar l'Ol inches square, and 39'06 inches long. Mem. Roy.
Ast. Soc, Vol. 9, p. 80.
No. 11. Bird's standard yard of 1760; a line measure, on a
brass bar 1*05 inches square, and 39"73 inches long. Mem. Roy.
Ast. Soc, Vol. 9, pp. 80-82.
No. 12. General Roy's scale; a line measure, upon a brass bar
0'55 of an inch broad, about 0"22 of an inch thick, and 42 -8 inches
LXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
long ; divided by Bird. Phil. Trans., 1785, p. 401, and Measure-
ment of Lough Foyle Base, p. 73.
No. 13. Ramsden's bar, used in the trigonometrical survey of
Great Britain. Phil. Trans., 1821, p. 91; and Measurement of
Lough Foyle Base, pp. 73-4.
No. 14. Sir Geo. Shuckburgh's scale (1796) ; a line measure,
upon a brass bar 1*4 inches broad, 0*42 of an inch thick, and 67*7
inches long. Space compared, in to 36ia . Phil. Trans., 1798, p.
133, and Mem. Roy. Ast. Soc, Vol. 9, pp. 84-5.
No. 15. Ditto. Space compared, 10in to 46in .
No. 16. Ordnance yard 1A (1827) ; a line measure, upon an
iron bar 1*45 inches broad, 2*5 inches deep, and rather more than
3 feet long. Measurement of Lough Foyle Base, pp. 71, 82 and [28].
No. 17. Ordnance yard 2A (1827). Similar to 1A. Same
authorities.
No. 18. Captain Kater's Royal Society yard (1831); a line
measure, upon a brass plate 0"07 of an inch thick. Phil. Trans.,
1831, p. 345.
No. 19. The Royal Astronomical Society's standard scale (1834)
;
a line measure, upon a brass tube 1*12 inches exterior diameter,
0"74 of an inch interior diameter, and 63 inches long. The central
yard was the space compared. Mem. Roy. Ast. Soc, Vol. 9, p. 69.
No. 20. "Col. Lambton's standard;" a line measure, upon a
brass plate 0*92 of an inch broad, 0"21 of an inch thick, and 66
}
inches long ; strengthened by an edge bar of nearly the same breadth,
but only 0'08 of an inch thick. Phil. Trans., 1821, p. 88, and Mem.
Roy. Ast. Soc, Vol. 9, pp. 82-3.
The authorities for the comparisons given in the various columns
of the table are as follows:
Column A.—Comparisons by Mr. George Graham. Phil. Trans.,
1743, pp. 187, and 547-550.
Column B.—Comparisons by Sir Geo. Shuckburgh. Phil. Trans.,
1798, pp. 167-181.
Column C.—Comparisons by Capt. Kater. Phil. Trans., 1818,
p. 55, and 1821, p. 91.
ANNUAL ADDRESS OF THE PRESIDENT. LXIX
Column D.—Comparisons by Capt. Kater. Phil. Trans., 1830,
p. 377, and 1831, p. 347.
Column E.—Comparisons by Francis Baily, Esq. Mem. Roy.
Ast. Soc, Vol. 9, p. 145.
Column F.—Comparisons by Francis Baily, Esq. Mem. Roy.
Ast. Soc, Vol. 9, p. 120.
Column G.—Values adopted by R. Sheepshanks, Esq. Phil.
Trans., 1857, p. 661.
The values used by Mr. Sheepshanks in 1848 to determine the
length of the present Imperial standard yard were Nos. 14 D, 15 F,
16 and 17 G, and 18 D.
It will be observed that several different units are employed in
the various columns of the table, and care must be taken to allow
for that circumstance when comparing numbers not situated in the
same column.
Comparisons of the Fundamental English Standards of Length.
Ref.
No.
LXX PHILOSOPHICAL SOCIETY OF WASHINGTON.
NOTE B.
By direction of the Parliamentary Committee of 1758, and in
the presence both of that body and of Mr. Farley, deputy chamber-
lain, Messrs. Harris and Gregory of the Loudon Mint compared
the several standard troy weights of the Exchequer, with the fol-
lowing results :
4-oz. weight= All smaller weights — i grain.
8-oz. " = " +i "
16-oz. " = " +i "
32-oz. " = " +2 grains.
64-oz. " = " +3 "
128-oz. " = " +14 "
256-oz. " = " —21 "
The weighings which yielded these results were made at the Lon-
don Mint; the instruments employed being "a very curious and.
exact pair of scales, belonging to Mr. Harris, and the scales used
at the Mint for the weighing of gold." After recording the results
in their report,1 the Committee continued as follows
:
" Therefore beginning the difference from the sixteen-ounce weight, and
carrying it on to the greatest troy weight in the Exchequer, the total differ-
ence will be eight grains and one-half."
" The fourth part of which is two grains upon sixteen ounces, which is a.
grain and a half upon the twelve ounces or pound troy."
"Then the eight and four ounces troy of the Exchequer were compared
with the following weights : "
" First, with the pound troy used at the Mint in weighing of gold, which
was heavier than that at the Exchequer one grain."
" Secondly, with the eight and four ounces at the Mint of the 6th of
Queen Anne, 1707, which was heavier than that at the Exchequer half a
grain."
" The eight and four ounces of Queen Elizabeth 1588 at the Mint, was
heavier than that at the Exchequer three quarters of a grain ; another of
the same year of Queen Elizabeth at the Mint, stampt with a tower, a
thistle and crown, and EL and crown, was heavier than that at the Ex-
chequer one grain."
»11, p. 437.
ANNUAL ADDRESS OF THE PRESIDENT. LXXI
" Mr. Freeman produced a four and eight ounce of the 6th of Queen
Anne 1707 by which he makes weights for sale, which was heavier than
the same weights at the Exchequer one grain and three quarters : There-
fore, upon an average of all these weights, the pound troy should be one
grain heavier than the weights at the Exchequer, and that added to the
grain and a half, which, upon the former experiments, the weights at the
Exchequer are too light a medium taken from thence makes the proper
increase of the Exchequer pound troy to be one grain and one quarter."
"And it is to be observed, that the pound troy weight at the Mint, which
is now used for gold, and the eight and four ounces at the Mint, marked
with a tower, and in the time of Queen Elizabeth, are both one grain
heavier than the eight and four ounces of the Exchequer."
" And considering that the Exchequer weights have been used ever since
the 30th of Queen Elizabeth, 1588, one hundred and seventy years to size
other weights by, it is highly probable that the difference may have been
occasioned by the frequent use of the standard."
"Your Committee endeavored to compare the troy weights with the
original standard at Goldsmith's Hall, from whence it is said, in the afore-
said verdict of the 29th and 30th of Elizabeth, that the weights now at the
Exchequer were made, and for that purpose sent to Goldsmith's Hall for
the said weights ; but were informed that no such were to be found there,
the Goldsmith's having no weights older than those at the Exchequer ; "
The Committee's statement respecting the way in which the cor-
rection of 1J grains was deduced from the weighings of the Ex-
chequer weights is very obscure, and the result is not justified by
generally accepted principles. If we put x for the sum of all the
weights smaller than 4 ounces, then the results of the weighings
made by the Committee may be written in the form :
4-oz. divided = 1 x
4-oz. weight = 1 x — \ grain.
8-oz. weight = 2 x -{- I grain.
16-oz. weight = 4 x + 1 grain.
32-oz. weight = 8 x + 2i grains. (1)
64-oz. weight = 16 x + 5i grains.
128-oz. weight = 32 x + 22 grains.
256-oz. weight = 64 x -\- 9 grains.
Before proceeding further we must decide in what sense these
weights are to be regarded as standards, and perhaps the most
natural course will be to regard the entire set as a standard of 512
46
LXXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
troy ounces. la that case the summation of the several columns
gives
512 ounces = 128 x + 39 grains
whence
x = 4 ounces — 0*3047 grain (2)
and by substituting that value in the equations (1) we obtain the
corrections to the several weights given in the second column of
Table I.
Table I.
—
Corrections to the Exchequer Standard Troy Weights of 1588,
derived from the Weighings made by Messrs. Harris and Chiskolm.
Denomination
of
Weight.
ANNUAL ADDRESS OF THE PRESIDENT. LXXIII
and in adopting one and one-quarter grains the Committee seem to
have augmented the weight of the troy pound by about one-quarter
of a grain. The corrections which result to the Exchequer troy
weights upon the Committee's assumption that the sum of the eight
and four ounce weights was one^ and one-quarter grains too light
are given in the third column of Table I; while the fourth column
contains the corrections found by Mr. Chisholm in 1873,1 and the
fifth column shows the loss of weight which occurred between 1758
and 1873. In view of the fact that these weights were constantly
used for comparing local standards during a period of no less than
225 years, from 1588 to 1825, their excellent preservation is very
remarkable.
In the report of the Committee of 1758 there is another set of
comparisons of the Exchequer troy weights;2 said comparisons
having been made on April 14, 1758, in accordance with the di-
rections of the Committee, by Mr. Freeman and Mr. Keed, expert
scale makers, in the presence of Mr. Farley, deputy chamberlain.
They are as follows
:
i-oz. hollow = i-oz. solid
-f- h grain.
i-oz. we
£-oz.
1-oz.
2-oz.
4-oz.
8-oz.
16-oz.
32-oz.
64-oz.
128-oz.
256-oz.
ght = All smaller weights — £ grain.
«
LXXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
i-oz. weight = 2x.
£-oz. " = Ax.
1-oz. " = 8x.
2-oz. " = 16x.
4-oz. " = 32a; + J grain. (3)
.8-oz. " = 64a; + 1 "
16-oz. " = 128a; + 2 grains.
32-oz. " = 256.r+2 "
64-oz. " = 512a; + 6 "
128-oz. " = 1024a; +27 "
256-oz. " = 2048a; + 15 "
Summing the various columns
512 ounces = 4096a; -j- 54 grains
whence
x = i ounce — 001318 grains, (4)
and by substituting that value in the equations (3) we obtain the
corrections given for the several weights in the second column of
Table II. The third column contains the corrections which result
upon the Committee's assumption that the sum of the eight and four
ounce weights was one and one-quarter grains too light ; and the
fourth and fifth colums contain corrections given by Mr. Chisholm
in his seventh annual report.1 Mr. Chisholm does not explain how he
obtained the corrections quoted in the fourth column of the table, but
their close agreement with those in the third column renders it
almost certain that they were computed from the comparisons made
by Messrs. Freeman and Reed. As the Committee of 1758 used
Mr. Harris' weighings to the exclusion of those by Messrs. Freeman
and Reed, the adoption of the opposite course by Mr. Chisholm is
perhaps explained by the circumstance that in his report on the
Exchequer standards2 he has quoted the weighings by Messrs. Free-
man and Reed and has attributed them to Mr. Harris.
In addition to being less exact, the weighings by Mr. Freeman
differ from those by Mr. Harris principally in the sign of the cor-
rection to the 32-ounce weight ; the former stating that the 32-ounce
weight was lighter than the sum of all the smaller weights, and the
latter that it was heavier. To ascertain which was right we have
H3, p. 21. a 48,p. 11.
ANNUAL ADDRESS OF THE PRESIDENT. LXXV
only to compare the resulting systems of corrections with those fouud
by Mr. Chisholm in 1873. Table I shows that according to Mr.
Harris' weighings all the weights have grown lighter during the in-
terval from 1758 to 1873, while Table II shows that according to
Mr. Freeman's weighings some have grown lighter and others heavier,
and that by quantities which cannot be attributed to accidental
errors in the weighings. In view of these facts there cannot be a
doubt that the Committee of 1758 was right in using only Mr.
Harris' weighings, and it seems equally certain that the numbers in
Table I should be adopted to the exclusion of those in Table II.
Table II.
—
Corrections to the Exchequer Standard Troy Weights of 1588,
derived from the Weighings made by Messrs. Freeman and Chisholm.
Denomination
of
Weight.
LXXVI PHILOSOPHICAL SOCIETY OP WASHINGTON.
From comparisons of their troy pound with their avoirdupois
pound, and with the two-marc weight sent to them by the French
Academy in 1742, the Royal Society of London found1—
1. That the English avoirdupois pound weighed 7,004 troy grains;
2. That the French llvre, consisting of two marcs, weighed 7,560
troy grains
;
and for three-quarters of a century the latter value was universally
accepted. Further, when the metric system came into being, the
kilogram was declared to consist of 18,827*15 French grains, of
which the livre contained 9216 2 ; or, in other words, the kilogram
was declared equal to 2*04288 livres ; whence, with the Royal So-
ciety's value of the livre, the English equivalent of the kilogram was
computed to be 15,444 troy grains.
During some experiments at the London Mint in March, 1820,
it was found that the French livre belonging to that institution
weighed only 7555 troy grains. This discovery led to an examina-
tion of the Royal Society's standards of 1742, which had been care-
fully preserved, and it was found that their livre agreed with that
at the Mint, but their troy pound was nearly four grains lighter
than the Imperial standard of 1758, and their avoirdupois pound
weighed only 7000 troy grains instead of 7004. 3 Thus it was rendered
almost certain that the accepted English equivalent of the kilogram
was about ten grains too large, and to remove all possible doubt,
a direct comparison of the English and French standards of weight
was effected in 1821*, through the co-operation of the respective
governments, and then it was definitively ascertained that the weight
of the kilogram is only 15,433 troy grains.
The facts respecting the Royal Society's standards of 1742 are
as follows
:
1. The weighings recorded in the Philosophical Transactions,
1743, pages 553 and 556, give
J
6, p. 187. It is usual to designate 1742 as the date of the exchange of
standards, but the remark of Cassini de Thury (4, p. 135) shows that the
true date must have been prior to April, 1738. In his paper of November,
1742, Graham makes only the indefinite statement that the exchange was
" proposed some time since."
2 Base du Systeme Metrique, T. 3, p. 638.
3 See 36, Vol. 1, p. 140, and 28, p. 19. *28, pp. 19-22.
ANNUAL ADDRESS OF THE PRESIDENT. LXXVII
R. S. troy lb. = Exch. (8 oz. + 4 oz.) — } grain. (5)
R. S. troy lb. = Mint (8 oz. + 4 oz.) — 2| grains. (6)
whence
Exch. (8 oz. + 4 oz.) = Mint (8 oz. + 4 oz.) — If grains. (7)
2. The weighings by Mr. Harris, for the Parliamentary Com-
mittee of 1758, give 1
Exch. (8 oz. + 4 oz.) = Mint (8 oz. + 4 oz.) — J grain. (8)
whence, by (6),
R. S. troy lb. = Exch. (8 oz. + 4 oz.) — If grains. (9)
In equations (6) and (8) the weights at the Mint were those of
the sixth of Queen Anne, 1707.
3. In the Philosophical Transactions, 1742, page 187, it is stated
that the Paris two-marc weight weighs 7560 troy grains. As the
true weight of two marcs is 7554 -22 grains, this implies that the
Royal Society's troy pound was too light by 5'78 (5760 -f- 7560) =
4*40 grains.
In the Philosophical Transactions, 1742, page 187, it is stated
that the Royal Society's avoirdupois pound weighed 7004 troy
grains, while the comparisons made in 1820 show that its weight
was then only 7000 such grains. This implies that the Royal So-
ciety's troy pound was too light by 4 00 (5760 -=- 7000) = 3'29
grains.
Finally, the comparisons of 1820 showed that the Royal Society's
troy pound was " nearly four grains too light."
The mean of these three independent results shows that the Royal
Society's troy pound was 3'9 grains lighter than the Imperial
standard of 1758 ; whence
R. S. troy lb. + 3*9 grains = Standard of 1758 (10)
but
Standard of 1758 = Exch. (8 oz. + 4 oz.) + 11 grains (11)
and therefore
R. S. troy lb. = Exch. (8 oz. + 4 oz.) — 2f grains. (12)
Considering the indefiniteness of the data respecting the weigh-
1 11, p. 437.
LXXVIII PHILOSOPHICAL SOCIETY OF WASHINGTON.
ings made in 1820, equations (9) and (12) agree fairly well, but
equation (5) is very discordant, as are also equations (7) and (8).
All the evidence seems to point to an error of about one and one
half grains in equation (5) ; and if instead of (5) we write
E. S. Troy lb. = Exch. (8 oz. + 4 oz.) — 2 grains (5')
(7) will become
Exch. (8 oz. + 4 oz.) = Mint (8 oz. + 4 oz.) — f grain (7')
and then all the equations will be reasonably accordant.
ANNUAL ADDRESS OF THE PRESIDENT. LXXIX
LIST OF THE PRINCIPAL AUTHORITIES CONSULTED IN
THE PREPARATION OF THE FOREGOING- ADDRESS.
Note.—The abbreviation " E. P. P." is used to designate English Par-
liamentary Papers. Some of these papers are of folio size and others of oc-
tavo size, but in the official sets they are all bound up indiscriminately in
volumes of folio size, measuring 13 by 8^ inches.
Throughout the preceding pages authorities in this list are usually cited
by number and page. For example, "27, p. 91 " would indicate page 91
of Capt. Kater's account of his comparisons of various British standards of
linear measure, contained in the Philosophical Transactions for 1821.
1.
—
Picard; M. l'Abbe. De Mensuris. Divers ouvrages. Mem. de
l'Acad. Roy. des Sciences, 1666-1699, Tome 6, pp. 532-549. Paris, 1730.
2. Hire ; M. de la. Comparaison du pied antique Romain a celui du
Chatelet de Paris, avec quelques remarques sur d'autres mesures. Mem. de
l'Acad. Roy. des Sciences, 1714, pp. 394-400. Paris, 1717.
3. Matjperttjis. La figure de la terre, determined par les observations
de MM. de Maupertuis, Clairaut, Camus, le Monnier, * * * Outhier,
* * * Celsius, * * * faites par ordre du Roy au cercle polaire.
Paris, 1738. 16mo., pp. xxviii + 184.
4. Cassint de Thttrt. Sur la propagation du son. (On p. 135 has
statement respecting standards of length exchanged between the French
Academy and the English Royal Society.) Mem. de l'Acad. Roy. des Sci-
ences, 1738, pp. 128-146. Paris, 1740.
5.—Degre du meridien entre Paris et Amiens, determine par la mesure
de M. Picard et par les observations de MM. de Maupertuis, Clairaut,
Camus, le Monnier, * * * Paris, 1740, 16mo, pp. lvj
-f 116.
6. Graham ; George. An account of the proportions of the English
and French measures and weights, from the standards of the same, kept at
the Royal Society. Phil. Trans., 1742, pp. [185-188].
7. Graham ; George. An account of a comparison lately made by
some gentlemen of the Royal Society, of the standard of a yard, and the
several weights lately made for their use; with the original standards of
measures and weights in the Exchequer, and some others kept for public
use, at Guild-hall, Founders-hall, the Tower, etc. Phil. Trans., 1743, pp.
[541-556].
8. Cassini de Thxjry. La meridienne de l'observatoire royal de Paris,
verifiee dans toute l'etendue du royaume par de nouvelles observations :
Paris, 1744. 8vo, pp. 292
-f- ccxxxvj.
LXXX PHILOSOPHICAL SOCIETY OP WASHINGTON.
9.
—
Condamine; M. de la. Nouveau projet d'une mesure invariable,
propre a servir do mesure commune a toutes les nations. Mem. de l'Acad.
Koy. des. Sciences, 1747, pp. 489-514. Paris, 1752.
10.
—
Bouguer, Camus, Cassini de Thury & Pingre. Operations
faites par ordre de l'Academie pour mesurer l'intervalle entre les centres des
Pyramides de Villejuive & de Juvisy, &c. Mem. de l'Acad. Royale des
Sciences, 1754, pp. 172-186. Paris, 1759.
11.—1758. Report from the Committee appointed to inquire into the
original standards of weights and measures in this Kingdom, and to con-
sider the laws relating thereto. (Agreed to by the House June 2, 1758.)
Printed on pp. 411-451 of Reports from Committees of the House of Com-
mons, which have been printed by order of the House, and are not inserted
in the Journals. Reprinted by order of the House. Vol. 2. (June 10,
1737, to May 21, 1765). Folio, 16|" X 10£". pp. 468.
12.—1759. Report from the Committee appointed (upon the first day of
Dec, 1758) to inquire into the original standards of weights and measures
in this Kingdom, and to consider the laws relating thereto. (Agreed to by
the House April 12, 1759.) Printed on pp. 453-463 of Reports from Com-
mittees of the House of Commons, which have been printed by order of the
House, and are not inserted in the Journals. Reprinted by order of the
House. Vol. 2. (June 10, 1737, to May 21, 1765). .Folio, 16f" X 10f'.
pp. 468.
13. Maskelyne; Rev. Nevil (Ast. Royal). The length of a degree
of latitude in the province of Maryland and Pennsylvania, deduced from
the foregoing operations (by Messrs. Chas. Mason and Jeremiah Dixon);
by the Astronomer Royal. Phil. Trans., 1768, pp. 323-325.
14.— Condamine ; M. de la. Remarques sur la toise-etalon du Chate-
let, ct sur les diverse? toises employees aux mesures des degres terrestres &
a celle du pendule a secondes. Mem. de l'Acad. Roy. des Sciences, 1772,
2e partie. pp. 482-501. Paris, 1776.
15. Roy; Maj.-Gen. Wm. An account of a measurement of a base on
Hounslow Heath. (Four large folding plates.) Phil. Trans., 1785, pp.
385-480.
16. La Lande ; Jerome le Francais. De la grandeur et de la figure
de la terre. Astronomie, Tome 3, pp. 1-47. (3d edition ; Paris, 1792.)
17. Borda, Coulomb, Legendre, Laplace, Prony, et Brisson. Rap-
port sur la verification de l'etalon qui doit servir pour la fabrication des
poids republicans. Annales de Chiinie, Paris, 1797, Tome 20, pp. 269-273.
18. Shuckburgh Evelyn; Sir Geo. An account of some endeavors
to ascertain a standard of weight and measure. Phil. Trans., 1798, pp.
133-182.
ANNUAL ADDRESS OP THE PRESIDENT. LXXXI
19.
—
Van-Swinden, Tralles, Laplace, Legendre, Mechain, De-
LAMBRE, Ciscar. Rapport lur 1?, determination de la grandeur de Pare
du meridien compris entre les paralleles de Dunkerque et Barcelone, et sur
la longueur du metre qu'on en deduit. Base du Systeme Metrique Decimal,
Tome 3, pp. 415-433. Paris, 1810. 4to.
20. Kater; Capt. Henry. An account of experiments for determin-
ing the length of the pendulum vibrating seconds in the latitude of London.
Phil. Trans., 1818, pp. 33-102.
21. Kater; Capt. Henry. On the length of the French metre esti-
mated in parts of the English standard. Phil. Trans., 1818, pp. 103-109.
22.—Experiments relating to the pendulum vibrating seconds of time in
the latitude of London. 41 pp. (E. P. P.) Accounts and papers. Ses-
sion, 27 Jan.-lO June, 1818. Vol. 15. Folio, 13}" X W- This is a ver-
batim reprint of Capt. Kater's papers in the Phil. Trans., 1818, pp. 33 to 109.
23. Banks, Clerk, Gilbert, Wollaston, Young, and Kater. First
Report of the Commissioners appointed to consider the subject of weights
and .measures. (Dated 24 June, 1819) 17 pp. (E. P. P.) Report from
Commissioners. Session, 21 Jan.-13 July, 1819. Vol. 11. Folio, 13}"
X8J"-
24. Clerk, Gilbert, "Wollaston, Young & Kater. Second Report
of the Commissioners appointed hy His Majesty to consider the subject of
weights and measures. (Dated July 13, 1820) 40 pp. (E. P. P.) Reports
from Commissioners. Session, 21 April to 23 Nov. 1820. Vol. 7. Folio,
131" X 8J".
25. Clerk, Gilbert, Wollaston, Young & Kater. Third Report
of the Commissioners appointed by His Majesty to consider the subject of
weights and measures. (Dated Mar. 31, 1821) 6 pp. (E. P. P.) Reports
from Committees. Session, 23 Jan. to 11 July, 1821. Vol. 4. Folio,
13}" X 8}".
26.—Report from the Select Committee on weights and measures. (Dated
May 28, 1821) 7 pp. (E. P. P.) Reports from Committees. Session, 23
Jan. to 11 July, 1821. Vol. 4. Folio, 13}" X 8J".
27. Kater ; Capt. Henry. An account of the comparison of various
British standards of linear measure. Phil. Trans., 1821, pp. 75-94.
28.—Report from the Select Committee of the House of Lords * * *
(on petition from Glasgow relative to) * * * the bill entitled " An act
for ascertaining and establishing uniformity of weights and measures"
* * * together with the minutes of evidence taken before said Commit-
tee. (Dated 2 Mar., 1824) 35 pp. (E. P. P.) Reports from Committees.
Session, 3 Feb. to 25 June, 1824. Vol. 7. Folio, 13" X 8£".
29. Kater; Capt. Henry. An account of the construction and adjust-
LXXXII PHILOSOPHICAL SOCIETY OF WASHINGTON.
ment of the new standards of weights and measures of the United Kingdom
of Great Britain and Ireland. Phil. Trans., 1823, part 2, pp. 1-52.
30.
—
Kater ; Capt. Henry. On errors in standards of linear measure,
arising from the thickness of the bar on which they are traced. Phil.
Trans., 1830, pp. 359-381.
31. Kater, Capt. Henry. An account of the construction and verifica-
tion of a copy of the imperial standard yard made for the Royal Society.
Phil. Trans., 1831, pp. 345-347.
32.—Minutes of evidence taken before the Select Committee on bill to
amend and render more effectual two acts of the 5th and 6th years of the
reign of his late Majesty King George the 4th, relating to weights and
measures. 67 pp. (E. P. P.) Reports from Committees. 1834. Vol. 18,
part 1. Folio, 13" X 8\"
.
33.—Report from the Select Committee on the weights and measures act
;
together with the minutes of evidence. (Dated 17 June, 1835) 60 pp. (E.
P. P.) Reports from Committees. Session, 19 Feb.-lO Sep., 1835. Vol.
18. Folio, 13" X 8J".
34. Baily ; Francis. Report on the new Standard Scale of this (the
Royal Astronomical) Society. (Gives also a history of English standards
of length.) Mem. Roy. Ast. Soc, 1836. Vol. 9, pp. 35-184.
35. Airy, Baily, Bethune, Herschel. Lefevre, Lubbock, Pea-
cock, Sheepshanks. Report of the Commissioners appointed to consider
the steps to be taken for restoration of the standards of weight and measure.
(Dated 21 Dec, 1841) 106 pp.. (E. P. P.) Reports from Commissioners.
Session, 3 Feb.-12 Aug., 1842. Vol. 25. Folio.
36. Kelly ; Patrick. The universal cambist : being a full and accu-
rate treatise on the exchanges, coins, weights, and measures of all trading
nations and their colonies. By P. Kelly, LL.D. 2nd edition. London,
1835. 2 vols., 4to. Vol. 1, pp. xl + 422 ; Vol. 2, pp. xxiv + 380.
37. Yolland ; Capt. Wm. An account of the measurement of Lough
Foyle base in Ireland, with its verification and extension by triangulation ;
etc., etc. Pub. by order of the Hon. Board of Ordnance. London, 1847.
4to, pp. 154 + [117].
38. Airy, Rosse, Wrottesley, Lefevre, Lubbock, Peacock, Sheep-
shanks, Herschel, Miller. Report of the Commissioners appointed to
superintend the construction of new parliamentary standards of length and
weight. (Dated March 28, 1854) 23 pp. (E. P. P.) Reports from Com-
missioners. Session, 31 Jan.-12 Aug., 1854. Vol.19. Folio, 13" X 8J".
39.—Abstract of " Report of the Commissioners appointed to consider the
steps to be taken for restoration of the standards of weight and measure."
16 pp. (E. P. P.) Reports from Commissioners. Session, 12 Dec, 1854-
14 Aug., 1855. Vol. 15. Folio, 13" X 8J".
40. Miller; Prof. W. H. On the construction of the new imperial
ANNUAL ADDRESS OF THE PRESIDENT. LXXXIII
standard pound, and its copies of platinum ; and on the comparison of the
imperial standard pound with the Kilogramme des Archives. Phil. Trans.,
1856. pp. 753-946.
41 .
—
Airy ; Sir Geo. B. Account of the construction of the new national
standard of length, and of its principal copies. Phil. Trans., 1857. pp.
621-702.
42. Clarke ; Capt. A. K. Comparisons of the standards of length of
England, France, Belgium, Prussia, Russia, India. Australia, made at the
Ordnance Survey Office, Southampton. Published by order of the Secretary
of State for War. London, 1866. . 4to, pp. 287.
43. Chisholm ; Henry Williams. Seventh annual report of the
Warden of the Standards on the proceedings and business of the standard
weights and measures department of the Board of Trade. For 1872-3.
8vo, pp. 105. (Contains : Appendix IV.—Account of the standard weights
and measures of Queen Elizabeth, pp. 10-26 : Appendix V.—Account of
the standard weights and measures of Henry VII. pp. 27-34 : Appendix
VI.—New standard weights and measures constructed and legalised from
the reign of Queen Elizabeth to George IV. pp. 35-40.) (E. P. P.) Re-
ports from Commissioners. Session, 6 Feb.-5 Aug., 1873. Vol. 38.
44. Chisholm ; H. W. On the science of weighing and measuring,
and standards of measure and weight. By H. W. Chisholm, warden of the
standards. 16mo, pp, xvi -(- 192. London : Macmillan & Co. 1877.
45. Hilgard; Julius E. Report on the comparison of American and
British standard yards. Report of the Superintendent of the U. S. Coast
Survey, 1877. Appendix No. 12, pp. 148-181. 4to.
46. Wolf
; C. Recherches historiques sur les etalons de poids et mes-
ures de l'Observatoire, et les appareils qui ont servi a les construire. An-
nates de l'Observatoire do Paris. Memoirs, Tome 17, pp. C.1-C.78. (Pub-
lished in 1883.)
47. Wolf ; C. Resultats des comparaisons de la toise du Perou au me-
tre international, executees au Bureau international des Poids et Mesures
par M. Benoit. Comptes Rendus, 3 Avril, 1888. Tome 106. pp. 977-982.
48.—Copies "of a letter from the Comptroller General of the Exchequer
to the Treasury, dated 3 June, 1863, transmitting a report on the Exchequer
standards of weight and measure, dated 27 April, 1863, by Mr. Chisholm,
chief clerk in the office of the Comptroller General of the Exchequer ; to-
gether with a copy of his report: " and, of a memorandum by the Astron-
omer Royal, dated 24 April, 1862, containing notes for the Committee on
Weights and Measures, 1862. 51 pp. (Contains a complete descriptive list
of all the old Exchequer standards ; a discussion on the moneyer's pound
;
and a history of English legislation on weights and measures.) (E. V. P.)
Trade (Generally). Session, 4 Fel>.-29 July, 1864. Vol. 58. Folio.
49.—Annual reports of the Warden of the Standards on the proceedings
and business of the standard weights and measures department of the Board
LXXXIV PHILOSOPHICAL SOCIETY OF WASHINGTON.
of Trade. 8vo. (Printed as English Parliamentary Papers, and contained
in the volumes of "Reports from Commissioners.")
No. of
Report
ANNUAL ADDRESS OF THE PRESIDENT. LXXXV
51.
—
Airy; Sir Geo. B. Extracts of papers, printed and manuscript,
laid before the Commission appointed to consider the steps to be taken for
restoration of the standards of weight and measure, and the subjects con-
nected therewith. Arranged by G. B. Airy, Esq., Astronomer Royal.
Printed by order of the Lords Commissioners of the Treasury. London,
1840. 4to, 155 pp. (Consists of a vast number of brief extracts giving the
opinions of many experts upon various points connected with the construc-
tion and use of standards of weight and measure, and the advantages and
disadvantages of various systems of such standards.)
52. Clarke
;
Lt. Col. A. R. Results of the comparisons of the stand-
ards of length of England, Austria, Spain, United States, Cape of Good
Hope, and of a second Russian Standard, made at the Ordnance Survey
Office, Southampton. By Lieutenant-Colonel A. R, Clarke, C. B., R. E.,
F. R. S., &c., under the direction of Major-General Sir Henry James, R. E.,
F. R. S., &c, director-general of the Ordnance Survey. "With a preface
and notes on the Greek and Egyptian measures of length by Sir Henry
James. Phil. Trans., 1873, pp. 445-469.
53. Adams ; John Qtjincy. Report upon weights and measures, by
John Quincy Adams, Secretary of State of the United States. Prepared in
obedience to the resolution of the Senate of the 3d of March, 1817. Wash-
ington : printed by Gales & Seaton. 1821. 8vo, pp. 245. (Contains report
of F. R. Hassler on comparisons of English and French measures, pp. 153-
170.)
54. Alexander
; J. H. Report (made to the governor of Maryland) on
the standards of weight and measure for the State of Maryland
; and on the
construction of the yard-measures. Baltimore, Dec. 13, 1845. 8vo, pp.
iv + 213.
55. Hassler; Ferdinand Rodolph. Comparison of weights and meas-
ures of length and capacity. Reported to the Senate of the United States
by the Treasury Department in 1832, and made by Ferd. Rod. Hassler. 22d
Congress, 1st Session, Ho. of Reps., Doc. No. 299. Washington, 1832. 8vo,
122 pp., with 4 folding plates. (Contains a paper by Tralles giving impor-
tant details, not published elsewhere, respecting the original iron meters of
the Commission des Poids et Mesures of 1799.)
56. Hassler
; F. R. Report from the Secretary of the Treasury, trans-
mitting the report of F. R. Hassler, superintendent of the Coast Survey, and
of the fabrication of standard weights and measures. 25th Congress, 2d
Session, Senate, Doc. No. 79. Washington, 1837. 8vo, 16. pp. (Explains
method adopted for determining subdivisions of the troy pound.)
57. Hassler; F. R. Report upon the standards of the liquid capacity
measures of the system of uniform standards for the United States ; with
description of a new original barometer, and of the balance for adjusting
the half bushels by their weight of distilled water. By F. R. Hassler. 27th
LXXXVI PHILOSOPHICAL SOCIETY OF WASHINGTON.
Congress, 2d Session, Senate, Doc. No. 225. Washington, 1842. 8vo,
26 pp. and 3 folding plates.
58.
—
Bache, A. D., & McCulloh, R. S. Reports from the Secretary of
the Treasury, of scientific investigations in relation to sugar and hydrome-
ters, made, under the superintendence of Prof. A. D. Bache, by Prof. R. S.
McCulloh. 80th Congress, 1st Session, Senate, Ex. Doc. No. 50. Wash-
ington, 1848. 8vo, pp. 653.
59. Bache ; Prof. Alexander D. Report to the Treasury Department
on the progress of the work of constructing standards of weights and measures
for the custom-houses, and balances for the States, and in supplying stand-
ard hydrometers to the custom-houses, from 1 Jan., 1848, to 31 Dec, 1856.
34th Congress, 3d Session, Senate, Ex. Doc. No. 27. Washington, 1857.
8vo, 218 pp. with 6 folding plates. (Contains descriptions of yard dividing
engine, and various comparators.)
60. Rogers ; Prof. W. A. On the present state of the question of stand-
ards of length. (Contains a bibliography.) Proceed. Amer. Acad, of Arts
and Sciences, 1879-80. Vol. 15. pp. 273-312.
61. Rogers; Prof. W. A. On two forms of comparators for measures
of length. 8vo, 12 pp. American Quarterly Microscopical Journal, April,
1879.
62. Rogers; Prof. Wm. A. Studies in metrology. 5 Plates. (Con-
tains description of the Rogers-Bond universal comparator.) Proceed.
Amer. Acad, of Arts and Sciences, 1882-'3. Vol. 18, pp. 287-398. 8vo.
63. Rogers ; Prof. W. A. An examination of the standards of length
constructed by the Societe Genevoise. Proceed. Amer. Acad, of Arts and
Sciences, 1884-'5. Vol. 20, pp. 379-389. 8vo.
64. Rogers; Prof. W. A. A study of the centimeter marked "A,"
prepared by the U. S. Bureau of Weights and Measures for the Committee
on Micrometry. 8vo, 23 pp. Proc. Amer. Society of Microscopists. Vol.
32, p. 184.
65 —Rogers; Prof. Wm. A. On a practical solution of the perfect screw
problem. 8vo, 44 pp. Trans. Amer. Soc. of Mechanical Engineers. Vol.5.
66. Rogers ; Prof. W. A. A critical study of the action of a diamond
in ruling lines upon glass. 8vo, 17 pp. Proc. Amer. Society of Microscop-
ists. Vol. 32, p. 149.
67.—Travaux et memoires du Bureau International des Poids et Mesures,
publies sous l'autorite du Comite International, par le Directeur du Bureau.
Paris. 4to. Tome 1, 1881, 391 pp. ; T. 2, 1883, 413 pp. ; T. 3, 1884, 3*48
pp. ; T. 4, 1885, 421 pp. ; T. 5, 1886, 416 pp.
BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON.
GENERAL MEETINGS.
47 (i)

BULLETIN
OF THB
GENERAL MEETINGS
295th Meeting. January 15, 1887.
President Harkness in the Chair.
Fifty-one members present.
Announcement was made of the election to membership of Messrs.
Henry Laurens Whiting and Thomas William Symons.
The following report of the Auditing Committee was presented
by its chairman, Mr. Woodward, and was accepted
:
January 15, 1887.
The undersigned, a committee appointed at the annual meeting
of the Philosophical Society of Washington, December 18, 1886, for
the purpose of auditing the accounts of the Treasurer, beg leave to
report as follows
:
We have examined the statement of receipts, including annual
dues, sale of Bulletin, and interest on bonds, and find the same to
be correct.
We have examined the statement of disbursements and compared
the same with the vouchers, and find them to agree.
We have examined the returned checks and the bank account
with Riggs & Co., and find the balance, $485.52, to agree with the
statement of the Treasurer's report.
We have examined the United States and other bonds belonging
to the Society, and find them to be in amount and character as rep-
resented in the Treasurer's report, aggregating $3,100.
R. S. Woodward,
Swan M. Burnett,
J. H. Kidder,
Committee.
(3)
4 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Mr. G. K. Gilbert presented a communication entitled
GRAPHIC METHODS IN RESEARCH.
[Abstract.]
An algebraic equation between two variables is the equivalent of
a plane curve, or, more strictly, of a line lying in a plane. An
equation containing three variables is the equivalent of a surface.
If in such an equation one of the variables be assumed equal to 1, 2,
3, etc., successively, there result a series of equations involving the
other two variables. Each of these equations may be represented
by a line in a plane, and the system of lines thus produced is the
representative of the original equation between three variables. The
single curve may be called a nomogram, the system of curves an
isogram.
In the simplest use of the graphic method in research the simul-
taneous quantitative observations of two phenomena are represented
on cross-section paper by a dot, a series of observations are repre-
sented by a system of dots, and a line is drawn through or among
these dots. This line expresses the law of the relation between the
two phenomena and is a nomogram.
When simultaneous observations are made of three phenomena,
two of the observations are expressed by a dot on section paper and
the third by a number attached to the dot. All the observations
having been represented by such numbered dots, a system of lines
is drawn over the area occupied by the dots, each line representing
an integral value of one of the variable phenomena, and being
drawn so as to pass through the dots marked with the correspond-
ing number. An isogram is thus produced without recourse to the
algebraic equation.
In the compound nomogram, two or more curves are drawn on the
same sheet, and with one system of ordinates in common. Each of
these curves represents an equation with two variables, one vari-
able being common to all the equations. By this means two or
more variable phenomena are compared with each other through
the mediation of another phenomenon with which they are related.
In the compound isogram two or more isograms are drawn on the
same sheet. Each isogram is the equivalent of an equation between
three variables, two variables being common to all the isograms,
GENERAL MEETINGS. 5
and one peculiar to each. By this means, variable phenomena are
compared with each other with reference to two other phenomena.
There are also phases of the graphic method in which lines are
not drawn, the arrangement of the platted dots being such that they
cannot be replaced by lines, but nevertheless lead to legitimate in-
ferences.
The function of the graphic method in research is the classifica-
tion of observations and their generalization, or the discovery of
their laws of relation. The same function is performed by math-
ematical analysis, both processes being restricted to the discussion
of quantitative observations. As compared to the mathematical
method, the graphic is more rapid and less precise. In matters
difficult of comprehension it aids the imagination by introducing a
sensory impression, and in this manner it suggests inferences and
hypotheses which might readily be overlooked if mathematical
methods were employed alone.
Mr. H. A. Hazen remarked upon the importance of this method
in meteorology. He suggested some precautions to be taken in at-
tempting to trace a connection by maximum or mininum epochs
between elements which are not clearly related or caused by the
same force.
Mr. Marcus Baker thought that the graphic method had its
chief use in rough approximations, and drew attention to the great
strides which had been made in geometry by the introduction of
analytical methods, supplementing and in part supplanting graphic
methods.
Mr. Paul remarked that the graphic method might be useful in
a preliminary determination of the most promising of several meth-
ods of possible analysis.
Mr. C. D. Walcott read a paper entitled
THE GEOLOGIC AGE OF THE LOWEST FORMATION OF EMMONS'
TACONIC SYSTEM,
illustrated by maps, drawings, etc.
[This paper, in abstract, appeared in the American Journal of Science,
3d series, 8°, New Haven, 1887, February, vol. 33, pp. 153-154.]
6 philosophical society of washington.
296th Meeting. January 29, 1887.
The President in the Chair.
Thirty-six members present.
Announcement was made by the President of the death of Gen-
eral William B. Hazen, a member of the Society, which took
place at 8 p. m., January 16.
Mr. F. W. Clarke read a paper entitled
THE PRESENT STATUS OF MINERALOGY.
[This paper is expected to appear in the Popular Science Monthly.]
A paper by Mr. R. T. Hill, entitled
THE TOPOGRAPHY AND GEOLOGY OF THE CROSS TIMBERS OF TEXAS,
was then read by Mr. W J McGee, as Mr. Hill had been called
away from the city after his paper was placed upon the programme.
[This paper appeared in full in the American Journal of Science, 3d
series, 8°, New Haven, 1887, April, vol. 33, pp. 291-303.]
297th Meeting. February 12, 1887.
The President in the Chair.
Forty-one members and guests present.
The President announced that Mr. Frank Hall Knowlton
had been elected to and had accepted membership in the Society.
A letter was read from the secretary of the Anthropological
Society announcing that Mr. Alfred Russell Wallace would deliver
an address Tuesday evening, February 15, on " Social versus Polit-
ical Economy" before the Anthropological Society, and inviting
the members of the Philosophical Society and their friends to be
present on that occasion.
Mr. H. A. Hazen made a communication on
THE SKY GLOWS OF 1883.
This communication was discussed by Messrs. Paul, E. Far-
quhar, Winlock, and the author.
GENERAL MEETINGS. 7
Mr. Bailey Willis presented a paper on
THE TOPOGRAPHY AND STRUCTURE IN THE BAYS MOUNTAINS,
TENNESSEE.
[This paper appeared in the School of Mines Quarterly, Columbia Col-
lege, 8°, New York, 1887, April, vol. 8, No. 3, pp. 242-252.]
Mr. G. Brown Goode made a communication on
THE GEOGRAPHICAL DISTRIBUTION OF SCIENTIFIC MEN AND IN-
STITUTIONS IN THE UNITED STATES.
[An abstract of this communication appeared in The Epoch, 4°, New
York, 1887, June 24, vol. 1, pp. 467-468.]
298th Meeting. February 26, 1887.
The President in the Chair.
Thirty-nine members and guests present.
The President announced the election to and acceptance of mem-
bership of Mr. Franklin Austin Seely.
Mr. C. V. Riley read a paper upon
our city shade-trees, their foes and their future,
illustrated by drawings and specimens.
[This paper was afterwards elaborated and published as Bulletin No. 10
of the entomological division of the Department of Agriculture, published
May 7, 1887, with the following title :
U. S. Department of Agriculture. Division of Entomology. Bulletin
No 10. Our shade-trees and their insect defoliators. Being a consideration
of the four most injurious species which affect the trees of the capital ; with
means of destroying them. By C. V. Riley, entomologist. Washington :
Government Printing Office, 1887. 69 pp., 8°, illustrated.]
This communication was discussed by Messrs. Gilbert, Mer-
riam, and Elliott.
8 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Lester F. Ward made a communication entitled
THE FREQUENCY OF COINCIDENCES.
[Abstract.]
Every one is constantly meeting with coincidences in every-day
life, but few ever take the trouble to record them. Mr. Ward had
always been struck by their frequent occurrence and remarkable
character, but until witbin about fifteen years had been content,
as most people are, to allow them to pass with only a momentary
expression of surprise. Certain comments upon them, however,
which he had met with in the writings of Auguste Comte and Dr.
George M. Beard had led him to take a wider view of their signifi-
cance and to commence in the year 1875 the practice of jotting
down in his note-book some of the more interesting and striking of
them. In this way a large collection of instances had accumulated,
a few of which were selected for presentation to the Society. These
were read directly from his notes, without change of phraseology, in
order to preserve their literal accuracy. Most of them were of a
character which, according to the mathematical law of probabil-
ities, would not occur again within any finite limitation of the
events with which they were associated.
The only application which it was attempted to make of the facts
was to point out their bearing upon the investigations which had
been recently conducted by the British Society for Psychical Re-
search, from which, in Mr. Ward's opinion, unwarranted conclu-
sions had been drawn, and which, he believed, receive their true
explanation only when the frequency of coincidences is fully recog-
nized.
This communication was discussed by Messrs. Woodward and
Clarke.
299th Meeting. March 12, 1887.
The President in the Chair.
Thirty-four members and guests present.
The President announced the death on March 5th, at Pensacola,
GENERAL MEETINGS. 9
Florida, of Capt. Edward Phelps Lull, U. S. Nm a member of
this Society.
The President also announced that Mr. Herbert Couper Wil-
son had been elected to and had accepted membership in the Society.
Mr. G. E. Curtis read a paper on
THE THEORY OF THE WIND-VANE.
[This paper appeared in the American Journal of Science, 3d series, 8°,
New Haven, 1887, July, vol. 34, pp. 44-52. It has also been reprinted in
the American Meteorological Journal, 8°, Ann Arbor, Mich., 1887, Sep-
tember, vol. 4, No. 5, pp. 215-224.]
Mr. H. A. Hazen thought that Mr. Curtls's formuloe showed
that a single-tailed vane is more sensitive than a doubled-tailed one
and would define a sensitive vane as that one which most quickly
assumes the direction of the wind.
Mr. Bates regarded these formula?, presented by Mr. Curtis,
which had been deduced for inelastic fluids moving in right lines as
inapplicable to elastic fluids moving in curved lines and often
affected by vortices.
Further remarks were made by Messrs. Abbe, Woodward, and
Curtis.
Mr. C. F. Marvin made a communication on
the electrometer as used in observations of atmospheric
electricity,
exhibiting in connection with it a diagram and the instrument
itself.
Mr. Bailey Willis made a communication on the
development of a perspective map from a contour map,
illustrated by three sketches and diagrams.
Mr. W. D. Johnson exhibited and explained a new plane table,
presenting a number of improvements, especially as to increased
stability, compactness, levelling, and mode of attaching the paper
to the board.
10 philosophical society of washington.
300th Meeting. March 26, 1887.
The President in the Chair.
Seventy-one members and guests present.
This meeting was held in the Assembly Hall of the Cosmos Club,
southeast corner of H street and Madison Place, the Club having
offered the use of its hall as a meeting place for the Society. Pre-
ceding meetings during this year and during several former years,
were by the courtesy of the Surgeon General of the United States
Army, held in the library of the Surgeon General's Office on the
east side of 10th and between E and F streets N. W.
The President briefly alluded to this removal to more commodi-
ous quarters upon the 300th meeting of the Society as marking an
epoch in its history.
Announcement was made of the election to membership of Mr.
Samuel Pierpont Langley and Mr. Harry King.
Mr. H. A. Hazen read a paper upon the
RELATION BETWEEN WIND VELOCITY AND PRESSURE,
illustrated by an apparatus resembling that used by him in recent
experiments at the Smithsonian Institution.
[This paper appeared, in the American Journal of Science, 3d series, 8°,
New Haven, 1887, October, vol. 34, pp. 241-248.]
The paper was discussed by Messrs. Billings, Woodward,
Harkness, Paul, and the author.
Mr. Bailey Willis made a communication on
MT. RAINIER AND ITS GLACIERS,
illustrated by perspective drawings of Rainier and Shasta, derived
from contour maps by the method explained at the last meeting.
The facts brought out by the illusti-ations and remarks indicate that
Rainier was a point of intense volcanic activity long since extinct,
and Shasta one of long continued less violent eruption. Rainier is a
ruin, Shasta a complete cone.
GENERAL MEETINGS. 11
Mr. Diller followed with an account of Mt. Shasta, contrasting
it with Mt. Rainier.
These communications were discussed by Messrs. Button and
Willis.
Mr. Marcus Baker made a communication entitled
WHAT IS A TOPOGRAPHIC MAP?
[Abstract.]
Referring to the volume of testimony taken by a joint committee
of the two houses of Congress charged with the duty of investigating
the relations of certain scientific bureaus, Mr. Baker remarked that
the time seemed opportune to discuss dispassionately certain points
previously discussed controversially.
Great diversity of view and of usage as to what constitutes topog-
raphy, topographic survey, topographic map, etc., was brought out by
citations from various authors and witnesses.
According to some, the relief of a portion of country constitutes
its topography; according to others, relief, drainage, and culture
together make up topography ; still others find that the delineation
or representation of such features constitutes topography. Topog-
raphy is also defined as " description of places " and as " a branch
of surveying."
A rather large and mixed assortment of maps was exhibited.
These maps, made by different nations, on different scales, in differ-
ent styles and colors, with different conventions and symbols, and
differing as to accuracy and completeness, were offered as samples
of a very large assortment, which it was proposed to classify.
"Topographic maps" should form one of the various classes into
which it would be desirable or convenient to divide maps. To de-
termine what principles should be adopted as guides for including
or excluding from this class was the object of the enquiry.
It was suggested that a satisfactory definition of " topographic
map" must take account of four things, viz.:
(a) scale.
(b) purpose.
(c) features to be represented.
(d) accuracy.
12 PHILOSOPHICAL SOCIETY OF WASHINGTON.
(a) Maps on a very small scale may be called generalized maps,
and, though showing topographic features as firily and completely
as the scale will permit, are still not properly^topographic but gen-
eralized maps.
Maps on very large scales, on the other hand, though sometimes
containing curves of equal altitude or contours, are yet rather dia-
grams or plans than topographic maps.
The topographic map requires a scale somewhere between the
small scale generalized map and the very large scale plan.
(b) The class to which any given map must be referred further
depends upon its purpose. If the purpose is to exhibit the geologic
structure, it is a geologic map ; if designed for military purposes, a
military map; if for nautical purposes, a nautical map—or, as it is
called, a chart—and if for exhibiting the topography, a topographic
map. If a topographic map is colored to exhibit the geologic
structure of the region shown, it is no longer a topographic but a
geologic map, etc. Most of the maps of the Coast Survey, though
exhibiting more or less topography, would not be classed with topo-
graphic maps, but with charts, being designed for nautical pur-
poses.
(c) The features to be exhibited on a map, in order that it may
be classed as topographic, are (1) the relief, (2) the drainage, in-
cluding in this term the whole water system of ponds, lakes, swamps,
streams, etc., and (3) the culture, this term implying the works of
man of such size or importance as to warrant their being classed as
topographic features. What features are topographic depends upon
the scale of the map.
(d) With respect to accuracy we shall have topographic maps
and topographic sketches. A topographic sketch controlled by
locations is a topographic map; not so controlled, it remains a
sketch.
This communication was discussed by Messrs. G. Thompson, H.
Farquhar, R. D. Mussey, and the author.
general meetings. 13
301st Meeting. April 9, 1887.
The President in the Chair.
Seventy-three members and guests present.
Prof H. Carrington Bolton, of Hartford, Conn., read, by in-
vitation, a paper on the
COUNTING-OUT RHYMES OF CHILDREN, THEIR ANTIQUITY, ORIGIN
AND WIDE DISTRIBUTION.
[Published in a volume of same name by Elliot Stock, London. Also
read before the New York Academy of Sciences.]
This paper was discussed by Messrs. Eastman, Billings, Mus-
sey, Hazen, Ward, Mason, Edward Eggleston, Babcock, and
by the author. In the course of the discussion several new rhymes
were brought forward together with many interesting references to
particular customs and formulas of speech.
302d Meeting. April 23, 1887.
The President in the Chair.
Sixty members and guests present.
Mr. Harkness presented a communication
ON A DEVICE FOR VIEWING THE SUN BY LIGHT OF ANY DESIRED
WAVE LENGTH.
[Abstract.]
If two precisely similar prisms are placed in contact, with their
refracting angles facing in opposite directions, the outer surfaces of
the combination will be parellel to each other, and light falling
upon the first prism will emerge from the second parallel to its origi-
nal direction and without suffering any dispersion whatever. So
long as the two prisms remain in contact the combination is, in
effect, a piece of thick piano-parallel glass, and objects seen through
it present only their natural colors. If, however, the prisms are
separated by a considerable interval a different action occurs. A
14 PHILOSOPHICAL SOCIETY OF WASHINGTON.
small pencil of nearly parallel rays falling upon the first prism
then suffers so much dispersion before reaching* the second prism
that the latter can no longer reunite the rays of different wave-
lengths, but it will still render them parallel to the directions they
had before entering the fir3t prism. Thus all the conditions neces-
sary for affording distinct vision of the radiant to an eye situated
behind the second prism are fulfilled, and at the same time the
wave-length of the light received by the eye can be completely con-
trolled by the adjustment of the prisms.
In the experimental apparatus actually constructed two sixty-
degree prisms were employed, separated by an interval of thirty-
eight inches. These prisms were fixed relatively to each other, and
behind the second one a viewing telescope of 6.5 inches focal dis-
tance and 0.84 of an inch clear aperture was mounted in such a
way that it could be moved through an arc sufficient to bring rays
of any desired wave-length to the center of its field. Slits were
placed immediately behind the first prism and before the objective
of the viewing telescope. Thus arranged, the instrument gave
images of the whole sun composed of tolerably homogeneous light ;
but the image of the surrounding sky was not composed of homoge-
neous light, and to remedy that defect a somewhat different arrange-
ment of the slits will be tried.
This communication was followed by a symposium upon the ques-
tion,
WHAT IS TOPOGRAPHY?
participated in by Messrs. M. H. Doolittle, W. D. Johnson, H.
G. Ogden, and Gilbert Thompson.
Mr. Doolittle began by declaring his ignorance until recently
of the subject and his resulting fitness to investigate without preju-
dice. He then pointed out the origin and development of the terms
geography, chorography, and topography, referring to the death of
the term chorography at the ripe old age of 1,500 years or there-
abouts and the alteration with time of the meaning of the words
geography and topography. The early meaning of topography,
description of places, appears to be obsolete or obsolescent. The
existing confusion concerning the meaning of the word topography
was made strikingly manifest by quotations from dictionaries.
GENERAL MEETINGS. 15
Mr. W. D. Johnson followed with a written communication, in
which he took the ground that topography had within recent years
lost almost or quite completely its old significance of description of
places, and was now almost universally understood to refer to sur-
face forms, the ups and downs, the hills and valleys, etc., and to
nothing else. This position was defended by very diverse and
numerous citations.
Mr. H. G. Ogden followed with a written communication, in
which he argued that the topographical features which, taken to-
gether, constitute topography, comprise not only natural relief, but
artificial relief also, such as railway cuts and embankments, dams,
mounds, etc., and that generally hills and valleys, streams and ponds,
towns and roads, etc., should be, as they have been, regarded as
topographical features.
Mr. Gilbert Thompson held that permanent hill features alone
constitute topography, and set forth the general applicability of
this view by illustrative crayon drawings.
A general discussion followed, participated in by Messrs. W. D.
Johnson, G. Thompson, Doolittle, Winlock, Harkness, E.
Farquhar, and M. Baker.
303d Meeting. May 7, 1887.
The President in the Chair.
Forty-four members and guests present.
Announcement was made of the election to membership of Mr.
Harry Vanderbilt Wurdemann.
Mr. J. W. Chickering read a paper on
THE MUIR GLACIER, ALASKA,
illustrated by a map and diagram.
Mr. Marcus Baker commented on this communication and re-
marked that in a careful inspection of the shores of Lynn Canal in
1880 he was unable to discover more than a small proportion of the
glaciers reported by Mr. Muir.
16 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. C. Hart Merriam read a paper upon
THE ECONOMIC PHASE OF THE ENGLISH SPARROW QUESTION.
[This paper appeared in the Report of the Commissioner of Agriculture,
1886, 8°, "Washington, Government Printing Office, 1887, pp. 227-246; with
map.]
Respecting the law protecting sparrows Mr. Hazen drew atten-
tion to the fact that a colored boy had recently been fined two
dollars in the Police Court of Washington for throwing stones at
sparrows.
Mr. W J McGee made an oral communication entitled
THE QUATERNARY DEPOSITS AND THE GREAT DISPLACEMENT OF
THE MIDDLE ATLANTIC SLOPE,
embodying the results of investigations set forth in part in a memoir
on the geology of the head of Chesapeake Bay, contained in the
Seventh Annual Report of the U. S. Geological Survey, and in part
in an article entitled Three Formations of the Middle Atlantic
Slope, which is expected to appear in the American Journal of
Science for February and March, 1888.
304th Meeting. May 21, 1887.
The President in the Chair.
Forty-five members and guests present.
Mr. C. E. Dutton made a communication on
A RECENT VISIT TO THE SCENE OF THE CHARLESTON EARTH-
QUAKE AND RESULTING CONCLUSIONS.
Mr. W. H. Dall made a communication entitled
SOUTH FLORIDA NOTES.
Remarks on this communication were made by Messrs. Bou-
telle, Head, and Toner.
Adjourned to October 15.
GENERAL MEETINGS. 17
305th Meeting. October 15, 1887.
The President in the Chair.
Fifty-one members and guests present.
The President announced the death at Wood's Holl, Massachu-
setts, on August 19, 1887, of Prof. Spencer Fullerton Baird,
one of the original members of the Society.
Mr. C. E. Dutton made a communication
ON THE DEPTH OF EARTHQUAKE FOCI.
[Abstract.]
Mr. Dutton first referred to the various methods which had been
resorted to in order to ascertain the depths of earthquake foci. The
method suggested by Mallet and based on the assumption that the
lines of fracture in the walls of buildings tended to arrange them-
selves transversely to the direction of propagation, he believed to be
unavailable and not sustained by observation. The motions of
buildings 'and of the ground itself during an earthquake were
highly complex, and, moreover, the lines of fracture, he believed,
were influenced far more forcibly by the nature of the structure,
the openings in the walls, and the natural directions of vibration
than by the directions of the impulses themselves.
Seebach's method, by ascertaining the variation of the speed of
the wave along the surface of the ground in the vicinity of the epi-
centrum, was regarded as impracticable, though the mathematical
considerations upon which it was founded were doubtless correct.
The speed of propagation is so high and the difficulty of obtaining
time observations of sufficient precision is so great that this mode
of solution must fail for want of the requisite data. Seebach seems
to have been under the impression that this speed was not more
than a very few hundred metres per second. The Charleston earth-
quake was transmitted with a speed probably exceeding 5,000 metres
per second, and Mr. Dutton was of the opinion that all true earth-
quakes were propagated with a speed differing but little from that
;
but, even if the speed were no greater than Seebach supposed, it
48
18 PHILOSOPHICAL SOCIETY OF WASHINGTON.
would still be expecting too much of human fallibility to suppose
that data of sufficient accuracy could ever be obtained.
There is, however, a method which is dependent, not upon time
data, but upon observations of intensity, which seems to offer the
means of computing the desired quantity. It is well known that
the intensity or energy per unit area of wave front diminishes as
the wave moves outwards from the centrum. Like all radiant
energy, it must be subject to the law of variation inversely as the
square of the distance. If the elasticity of the medium were perfect
and its density uniform the law would be rigorous. As a matter of
fact, it is not so ; but, on the other hand, we are assured that the
elasticity cannot be very imperfect, since if it were so the propaga-
tion of impulses to very great distances would be impossible, and
the waves would soon be extinguished in work done upon the me-
dium itself. Nor is there reason to suppose that the variations of
density are extreme. Thus, while the law of inverse squares may
be in some measure impaired, it may still be assumed as an approxi-
mate expression of the reality.
If, then, we were able to form a just estimate of the rate of varia-
tion of the intensity along lines radiating from the epicentrum, we
should have the means of computing the depth of the focus. Thus,
if O be the focus and E the epicentrum and P any point at a dis-
tance from the epicentrum, the intensity at P would be inversely
proportional to the square of O P. Calling EP = «) OP= r, and
O E = q, and designating by a the intensity at unit distance and
by y the intensity at any other distance x, we have the equation
:
a
r ' q + x2
This equation corresponds to a curve whose figure is approxi-
GENERAL MEETINGS. 19
mately represented in the diagram, and the curve will have a point
of inflexion at which the decrease in the value of y as E P in-
creases will be a maximum. Differentiating the equation twice
and equating the value of the second differential coefficient to zero
will give us the co-ordinates of this point of inflexion. The value
of the abscissa of this point will be
l/"3
From this value the constant a has disappeared, showing that it
is independent of the intensity of the original shock and dependent
upon the depth alone. The application of this analysis to the
problem is as follows : As we recede from the epicentrum the inten-
sity diminishes, but it does not diminish at a uniform rate with the
distance. There is some critical distance from the epicentrum at
which the rate of decrease of intensity has a maximum value.
This critical distance depends upon the depth of the focus and
upon nothing else, and the magnitude of this distance is equal to
the depth divided by l/3, and, conversely, the depth of the focus
is equal to the critical distance multiplied by 1/8. If, then, we can
locate the epicentrum and the points where the intensity diminishes
with greatest rapidity, we have at once the means of determining
the depth of the focus. In the case of the Charleston earthquake
this location has been approximately made and a depth of about
twelve miles has been deduced for the focus of the principal shock.
After a description of Mallet's second method of investigation by
the observation of the overturning power of earthquakes, the sub-
ject was discussed by the President and by Messrs. H. Farquhar,
Gilbert, and Dutton.
Mr. F. W. Clarke made an oral communication on the
MANCHESTER MEETING OF THE BRITISH ASSOCIATION FOR THE
ADVANCEMENT OF SCIENCE, 1887.
Remarks upon this communication were made by Mr. Abbe.
20 philosophical society op washington.
306th Meeting. October 29, 1887.
The President in the Chair.
Forty-one members and guests present.
Announcement was made by the President of the election to and
acceptance of membership of Mr. Jesse Herman Holmes.
The President also referred to the loss sustained by the scientific
world in the death of Prof. Spencer F. Baird, and announced
that the General Committee had taken the preliminary steps for
arranging a memorial meeting in commemoration of his life and
scientific work.
Mr. Cleveland Abbe read the following paper entitled
THE SIGNAL SERVICE BIBLIOGRAPHY OF METEOROLOGY.
Mr. Abbe stated that in 1872 he began, at his own expense
and for personal use, a more systematic collection of the titles of
works bearing upon all subjects that he was interested in, especially
meteorology. After corresponding in 1874 with the committee
of the Royal Society as to the probability of the publication of
their proposed subject-index to their Catalogue of scientific papers^
and being officially informed that this work would not be under-
taken, he decided to complete his systematic examination of all
the titles in that great work and copy the appropriate ones for
his own use. In 1878, when this work was nearly completed, so far
as regards the first six volumes, he addressed a note to Prof. Hann,
of Vienna, stating what he had done and inquiring whether any
one in Europe was similarly engaged. Almost simultaneously with
this Prof. Hann received and published 1 a letter from Dr. Hell-
mann, of Berlin, dated January 10, 1879, urging the importance of
a general index to the literature of meteorology. This letter had
evidently been suggested by a circular issued in October, 1878, by
the permanent committee of the first meteorological congress at
Vienna, proposing a programme for the second congress about to
be held at Rome in the approaching month of April, 1879. In this
circular the committee asked that the delegates prepare catalogues
^tschr. Met., Wien, 1879, xiv, 9G.
GENERAL MEETINGS. 21
of the meteorological observations, published or unpublished, for
their respective countries.
At the Rome conference Dr. Hellmann's letter was presented on
April 21 and by the congress referred to the newly-appointed Inter-
national meteorological committee. The congress also adopted
resolutions2 asking the delegates to prepare lists of the observations
for their respective countries, and the directors of meteorological
libraries to add lists of the works not found in the published library
catalogues of the Meteorological society of London and the observ-
atory at Brussels, or in Mr. Abbe's cards.
After the meeting at Rome Mr. Abbe received a letter from Dr.
Hellmann, to which he replied August 22, 1879, offering to co-
operate in the preparation of a general bibliography and to transfer
his cards either to the International meteorological committee or to
Dr. Hellmann personally, on the repayment of his expenses.
At the same time a similar offer was made to General Myer,
Chief signal officer, under the impression that the latter would be
pleased to complete the work as an official matter.
At the first or Berne meeting of the International meteorological
committee in August, 1880, letters of Dr. Hellmann were read
dated January 20 and July 20, 1880, giving a detailed scheme for
combining the various works and for the preparation of a catalogue,
and embodying Mr. Abbe's proposal of August, 1879, as well as
a similar one from Mr. G. J. Symons of London3 . The committee,
however, resolved that each country be requested to furnish lists
of observations and that Messrs. Scott and Hellmann be a sub-
committee to consider the means of carrying out Dr. Hellmann's
scheme.4
In the fall of 1881, Mr. Abbe wrote to Mr. Symons for more de-
tails as to his work. Mr. Symons' reply and Mr. Abbe's renewal
of his previous offer were then laid before General Hazen, Chief
signal officer, who decided to purchase the catalogues of both these
gentlemen with a view to their combination and completion by the
Signal office in case the International committee did not do this.
In November, 1881, Mr. Symons was authorized to prepare at the
expense of the Signal office, a copy of all meteorological titles in his
2 Rep. pr. internat. meteoral. cong. Rome 1879, Lond., 1879, p. 21, 75.
3 Rep. pr. internat. meteoral. comm. Berne 1880, Lond., 1881, p. 38, 40.
4 Ibid., p. 8-9.
22 PHILOSOPHICAL SOCIETY OF WASHINGTON.
collection, and in December, 1881, M Abbe's cards were pur-
chased.
Mr. Synions' catalogue was received in October, 1883, and on
March 4, 1884, Mr. C. J. Sawyer, librarian of the Signal office,
was relieved from the care of the library, and, as bibliographer,
ordered to devote his whole time to the completion of this work,
which was then transferred from the library to the study room
division of the Signal office.
At the second meeting of the International meteorological com-
mittee, at Copenhagen, in August, 1882, Messrs. Scott and Hell-
mann reported that the Meteorological office could not print the
proposed catalogue and that subscriptions were not practicable.
They therefore recommended each meteorological service to publish
a national bibliography, for which Hellmann's Repertorium der
deidschen Meteorologie, prepared in accordance with the ideas of
the committee and now just about to be published, should serve as
a model. It need only be added that since 1882 the International
meteorological committee have, with other meteorologists, acqui-
esced in the arrangement by which the Signal service has under-
taken to complete and, if possible, publish for its own and for gen-
eral use a general index to the literature of meteorology.
The importance of this work is especially endorsed by General
Greely, who, in his current annual report, October, 1887, as Chief
signal officer, says
:
The practical value of such a bibliography has been fully shown
by its constant use in current office work, and, in addition to the
official demands, almost daily calls for information have been re-
ceived from parties not connected with the service. The result of
this work is the collection of special bibliographies, which ensures
those consulting it a complete index of what has been accomplished
in each special line of meteorology. As has been well said, the
progress of meteorology is retarded and labor therein wasted owing
to the impossibility of ascertaining what has been done in its various
branches—an experience which, as scientific men well know, is by
no means confined to this science. The cost of time and labor to
the Government for the preparation of this work cannot be less than
$12,000 to $15,000, and the result of these labors has been the com-
pletion of a work which is of great value, both practically and sci-
entifically, to the entire world. The catalogue in its present condi-
tion is valuable, and sufficient for the pressing needs of this service,
but to view it in this light would evince a narrow and selfish dispo-
sition not in keeping with the scientific spirit of the age. At a cost
GENERAL MEETINGS. 23
of probably $8,000 or $10,000 this work can be printed and dis-
tributed to the world as a monument and evidence of the growing
scientific tendency of this nation. If such action is taken by Con-
gress, the Chief Signal Officer has no doubt, from the willing spirit
and hearty co-operation shown by leading scientists of other coun-
tries, that future international co-operation will secure, by a system
of rotation, from the various European governments the publication
of a series of supplements which will keep the world abreast of the
steadily increasing volume of meteorological publications. A large
number of American and foreign meteorologists and librarians have
given largely of their time and energy in the compilation of this
bibliography, as is shown by the fact that over one-half of the mate-
rial has been contributed from foreign countries, so that the bibli-
ography represents not only a large expenditure on the part of the
United States, but also many years of additional gratuitous labor.
The material could not be duplicated, and it would seem but a re-
spectable reciprocity of exchange that the Government should print
the catalogue, so as to enable the voluntary contributors to avail
themselves of the complete work. This fulfilment of obligations to
contributors by a public catalogue is an act of justice ; but, in addi-
tion, it should be considered that this bibliography will be of great
practical value to the agricultural, commercial, engineering, and
medical interests not only of the United States, but of the world.
Mr. Abbe stated that he had asked Mr. Sawyer to present to the
Philosophical society some account of his Avork, now nearing com-
pletion, but, as he could not be present, Mr. Abbe read the following
memorandum prepared by Mr. Sawyer
:
MEMORANDUM ON THE SIGNAL SERVICE BIBLIOGRAPHY OF
METEOROLOGY AND TERRESTRIAL MAGNETISM.
The bibliographical work of the Signal office dates from 1881,
and officially originated in correspondence begun by Prof. Abbe
with Prof. G. J. Symons, of London, Dr. G. Hellmann, of Berlin,
and Dr. A. Lancaster, of Brussels, who all manifested the greatest
interest in the proposed catalogue and have been the most impor-
tant contributors to it.
The meteorological titles in the Catalogue of scientific papers.
Compiled by the Royal society of London, vols, i-vi (1800-1&63), had
already been selected and extracted by Prof. Abbe and were trans-
ferred to the Signal office in December, 1881, on the repayment of
the expenses incurred by him in the work. At the request of the
Signal office. Prof. Symons undertook to furnish copies of all titles
on meteorology and terrestrial magnetism contained in his extensive
24 PHILOSOPHICAL SOCIETY OF WASHINGTON.
collection of titles on astronomy, meteorology, and allied sciences,
the expense to the office to be only his actual outlay for clerical
assistance. Prof. Symons' catalogue already represented many
years of bibliographical research, and to it he now added many
titles, securing the co-operation of European meteorologists by per-
sonal visits and by correspondence, and including the more impor-
tant English libraries.
This catalogue was received late in 1883, about two years having
been spent in its compilation ; it consisted of about 18,000 titles
chiefly of separate works, and may be considered as the foundation
of the present bibliography. No further work was done until
March, 1884, when an effort to secure the services of Prof. Lancaster
having failed, the librarian of the Signal office was assigned to the
work of preparing the catalogue for publication.
The original intention had been to extend Prof. Symons' work
only by the combination of titles from the Royal Society catalogue
including those in vols, vii and viii (1864-1873), selected but
not yet copied by Prof. Abbe, the catalogue to be arranged by
authors and to form only a first contribution to the general meteoro-
logical bibliography desired.
But the large amount of material on hand, and the conviction
that some recent contributions to the subject, especially the Reper-
torium der deutsehen Meteorologie by Dr. Hellmann, should be in-
cluded, and that the periodical literature previous to 1800 and
subsequent to 1873 should be represented, led to the consideration
of an enlargement in the scope of the work. It was foreseen that
the necessary delay in securing an appropriation for publication
would afford opportunity for still further extension, and it was
decided March 15, 1884, to complete the compilation so far as
possible without postponing publication for this purpose and to
issue an approximately complete general bibliography, of such form
as to serve as a basis for supplementary volumes.
In pursuance of this plan, every effort has been made to secure
contributions, especially by indexing periodicals, by examination of
printed and manuscript catalogues and bibliographies, and by cor-
respondence with meteorologists and librarians.
The lacunse in periodical literature have been filled by indexing
all periodicals available previous \o 1800 and subsequent to 1873,
and by the examination of all indexes, bibliographies, &c, avail-
able, such as Reuss, Young, Poggendorff, Kerl, Fortschritte der
GENERAL MEETINGS. 25
Physik, and many others. It was found that the general indexing
of the Royal society for the period from 1800 to 1873, was not
full enough for this special bibliography, and all periodicals rich in
meteorological literature were reindexed.
The International meteorological committee had already consid-
ered the subject of meteorological bibliography, and, uuable to secure
at once the publication of a general bibliography, had recommended
that each country compile a list of its own observations and that
special national bibliographies be prepared wherever possible.
Some work had been done in accordance with this recommendation,
especially in Germany and Russia, and an attempt was made by
the Signal office to secure the extension of this work and to obtain
from foreign meteorologists and librarians, bibliographies for their
respective countries. The great interest in the work was shown by
the hearty co-operation from all sections.
Among the special bibliographies received the following may be
mentioned as among the most complete and valuable : Germany, by
Dr. Hellmann ; Japan, by Dr. Knipping ; Norway, by Prof. Mohn ;
Poland, by Prof. Karlinski ; Portugal, by J. C. de Brito-Capello
;
Roumania, by Dr. Hepites ; Russia, by Profs. Wild and Woeikof;
South Africa, by Dr. Gamble ; Sweden, by C. G. Fineman amd C.
Annerstedt ; Victoria, by R. L. J. Ellery.
All the meteorological libraries of the world are represented, in-
cluding, as worthy of special mention, those of the Meteorological
office and Royal Meteorological Society, of London ; the Societe
meteorologique de France, Paris ; the large manuscript collection
of Prof. Poey, the Ronald's, Poulkova, and Brussels catalogues, all
contained in the catalogue of Prof. Symons ; the Deutsche Seewarte,
Hamburg (including the library of the late Prof. Dove), and the
k. k. Central-Anstalt, of Vienna (with that of Prof. Hann\ added
by the Signal office. The number of scientific and general libraries
represented is very large.
Letters, requesting lists of their works, were sent to about 400
writers (exclusive of those in Germany, where this method had been
employed by Dr. Hellmann), and the replies received have been of
the greatest value in the representation of living authors.
The desirability of securing as great completeness as possible, the
expectation of an early publication, and the fact that the Symons
and Hellmann catalogues ceased with 1881, led to the adoption of
this date as the close of the bibliography, and the following state-
26 PHILOSOPHICAL SOCIETY OP WASHINGTON.
ment of the titles on hand includes only those of works published
before January 1, 1882. A large amount of material for subsequent
years has been collected but has not been submitted to classification.
It may be included in supplementary volumes, or incorporated with
the bibliography if publication be delayed.
The chief sources of material and approximate number of titles
added to the bibliography, after the rejection of duplicates, are as
follows
:
Prof. Symons' catalogue ...... 18,000
Royal Society catalogue, i-viii ..... 11,000
Hellmann, Repertorium ...... 5,000
Printed catalogues and bibliographies, including Eeuss, Poggendorff,
&c. (400 vols.) ....... 4,000
Manuscript catalogues and bibliographies .... 3,000
Periodicals indexed (6,400 vols.) ..... 12,000
Total number before final revision .
Number of independent titles after final
. 53,000
revision, about 50,000
The duplication of titles by double classification will increase the
number of entries to about 55,000.
The form adopted for the work is that of a classed subject cata-
logue, with full author index. The general plan of the subject
catalogue is similar to that of the Poulkova catalogue and that
adopted by Drs. Houzeau and Lancaster for their Bibliographie
generate de I'astronomie, the arrangement being chronological under
each subject. The classification is based upon a scheme submitted
by Dr. Lancaster, at the request of the Signal office, some minor
modifications having been made after careful study and consulta-
tion with other meteorologists and bibliographers.
The general divisions of the classification are shown by the fol-
lowing outlines
:
I. General meteorology.
A. History and bibliography.
B. General and collected works.
C. Organization and methods.
D. Instruments.
II. Theoretical me-
teorology.
fl. Temperature.
T>1 . j. ., , 2. Moisture,
f A. Physics of the at- ! g Pres8Ure>
mosphere. j 4 Qptical phenomena
15-
"
LO.
Mechanics of the
atmosphere.
Cosmic relations of meteorology.
Electrical phenomena.
1. General circulation.
!1.
2. Winds.
3. Storms.
IV. Terrestrial magnetism. -
GENERAL MEETINGS. 27
(A. Weather prediction.
B. Agricultural meteorology.
C. Medical meteorology. ^
D. Climatology.
A. General.
B. Observations, instruments, and
methods.
C. Variation.
D. Distribution. i
E. Connection with meteorology.
V. Observations (meteorological and magnetic) classed geographically.
These have been largely subdivided, the number of divisions em-
ployed in the preliminary classification being 169. This number
will be varied somewhat in revision, the final classification depend-
ing largely on the number and character of the titles in each class.
The following example will indicate the character of the subdi-
vision :
1. General.
2. Description.
3. Height.
II. A. 6. f. Aurora. -{ 4. Frequency.
5. Periodicity.
6. Connection with meteorological phenomena.
7. Connection with terrestrial magnetism.
The classification has been from originals, where possible, and all
resources of the libraries available have been used for this purpose.
Where access to the work or article was not possible, correspondence
was maintained for the explanation of doubtful titles. The assign-
ment of cards to their subjects has been completed, but they are not
yet arranged under their respective heads. Consequently, no state-
ment of the number of titles under each class can yet be made, but
a rough estimate shows that of the 50,000 titles about 5,000 will be
under observations and 3,000 under terrestrial magnetism, leaving
about 42,000 entries for meteorological discussions.
The author index is similar to that adopted by Drs. Houzeau and
Lancaster, giving under the full name of the author, and for each
title, an abbreviation of the subject under which it is classed, the
date of publication, and the reference. Tbe index, as completed,
contains about 12,500 authors, or an average of four independent
titles for each author. A biographical note may be included under
each author.
The bibliography will be completed early in 1888, the only work
now remaining being arrangement by subjects, revision, sub-class-
28 PHILOSOPHICAL SOCIETY OF WASHINGTON.
ification of observations, preparation of subject index and periodical
list. The technical preparation of copy will follow when the appro-
priation for publication is made.
This communication was discussed by Messrs. Mann, Fletcher,
Marcus Baker, Gilbert, and the author.
Mr. Lester F. "Ward made a communication
ON THE GEOGRAPHICAL DISTRIBUTION OF FOSSIL PLANTS,
illustrated by a map.
[This paper will appear in full in the Eighth Annual Report of the U. S.
Geological Survey, for the fiscal year 188G-'87.]
307th Meeting. November 12, 1887.
The President in the Chair.
Fifty-two members and guests present.
Announcement was made by the President of the election to and
acceptance of membership of William Henry Babcock.
Mr. C. E. Dutton presented a communication which had been
jointly prepared by himself and Mr. S. Newcomb on
THE SPEED OF PROPAGATION OF THE CHARLESTON EARTHQUAKE.
[This paper appeared in full in The American Journal of Science, 3d
series, 8°, New Haven, 1888, January, vol. 85, pp. 1-15.]
This paper was briefly discussed by Mr. Clark and Mr. Dutton.
Mr. Harkness read a paper
ON THE REPRESENTATION OF COMET ORBITS BY MODELS,
illustrated by card-board models.
[This paper appeared in The Sidereal Messenger; conducted by Wm. W.
Payne. 8°. Northfield, Minn., Carleton College observatory, 1887, Decem-
ber, vol. 6, No. 10, pp. 329-349.]
GENERAL MEETINGS. 29
308th Meeting. November 26, 1887.
The President in the Chair.
Fifty members and guests present.
A circular letter from the New York Academy of Sciences, re-
questing co-operation in erecting a monument to the memory of the
ornithologist Audubon, was laid before the Society by the Secretary.
Mr. G. K. Gilbert presented a communication entitled
STATISTICS OF THE PHILOSOPHICAL SOCIETY FROM ITS
FOUNDATION.
[Abstract.]
The following data, except when otherwise noted, are compiled
from the published records of the Society.*
The Society was organized March 13, 1871, with a membership
of 44, and this was increased during the same year by the election
of 17. In each succeeding year new members were elected, the
smallest number being 8,
:
in 1876, and the largest 35, in 1884.
Fi'om time to time members have been dropped from the list for
non-payment of dues, others have died, and others resigned. The
average annual number of new members has been 18. The total
number of resignations has been 24. The membership has always
been classified as i*esident and non-resident, or " active " and
" absent." From time to time a list of the members has been pub-
lished in the Bulletin, and since 1879 these lists have been annual.
The following table shows the number of active members at each of
the indicated dates. It also shows the gross annual accession to
membership, and likewise the average attendance at ordinary meet-
ings for each year, beginning with 1875, previous to which time the
attendance is not noted in the published minutes. The year 1882
had the minimum attendance, 34, and 1887 the maximum, 49. The
general average of attendance at meetings for the reading of papers
is 40; at meetings for the election of officers, 36.
*The paper, as read, did not include the statistics for 1887, which were
necessarily imperfect at that time. The abstract for printing was brought
down to December 21, 1887, the date of the annual meeting. Certain indi-
cated data on membership were brought only to December 1, 1887.
30 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Table I.
Membership and Attendance of the Philosophical Society, by Years.
GENERAL MEETINGS. 31
The Anthropological Society was organized February 17, 1879, and
has now a membership of 154. The Biological Society was organ-
ized December 3, 1880, and has a membership of 174. The Mathe-
matical Section of the Philosophical Society held its first meeting
March 29, 1883. The Chemical Society was organized January 31,
1884, and now numbers 44 members. During the two years fol-
lowing the institution of the Anthropological Society our Society
witnessed maxima in the accession to membership, in the total
membership, in the attendance, and in the ratio of attendance to
membership. During the two years following the foundation of
the Biological Society each of these quantities reached or passed a
minimum. The year of the organization of the Mathematical Sec-
tion was characterized by an increase of attendance, but not of
membership. In the four years elapsed since the beginning of the
Chemical Society our membership and attendance have steadily
increased, their ratio remaining constant. If the relation of our
record to the Biological Society only were considered, it would be
easy to infer that our Society suffered from the formation of another
scientific society, but a contrary inference would be drawn from a
comparison of our record with the histories of the Anthropological
and Chemical Societies, and in view of all the facts it appears proper
to conclude that our membership and attendance have not been
materially influenced by the organization of the other societies.
The data of attendance have been, classified by months likewise
and finally by half-months, with the result which appears in Table
II. The data cover a period of 12 years, but are somewhat imper-
fect. To diminish the error from imperfection of record, a general
correction for annual phase was applied to all the observations
—
that is to say, they were all reduced to consistency with a mean
attendance of 40. Only ordinary meetings for the reading of papers
were included, and the year 1887 was omitted because the attend-
ance appeared to be greatly affected by the change of quarters
(March 26) from the Army Medical Museum to the Assembly Hall
of the Cosmos Club.
32 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Table II.
Average Attendance at Ordinary Meetings for Bach Half-Month,
Compiled from Records for 11 Years, 1875-1886.
March, first half 40.0
second half 40.8
first half 48.0
second half 40.3
first half 37.5
second half 37.3
first half 33.7
second half 28.6
October,
GENERAL MEETINGS. 33
more of the selected classes have been entered in each, and such
duplicate entries have been treated as integers and not as fractions.
To an extent dependent on this treatment the deduced ratios are
inaccurate.
It should be observed that the selection of classes has depended
largely on the nature of the material to classify. As the statistics
grew out of the work of indexing the Bulletin, the selection was
affected by the needs of the indexer, and as it was desired to learn
the influence of the organization of other societies on the scope of our
proceedings, the selection was affected by the classification of sub-
jects among the other societies. The following is the classification
:
Group 1, Mathematics ; Group 2, Astronomy, including calendars
;
Group 3, Physics, including molecular physics, electricity, acous-
tics, optics, and microscopy, which last subject happens in the litera-
ture of the Society to be almost entirely optical ; Group 4, Chemis-
try and mineralogy ; Group 5, Meteorology and thermometry ; Group
6, Geology ; Group 7, Geography, including physical geography,
surveying, and travel and exploration ; Group 8, Biology, includ-
ing zoology, botany, and human anatomy and physiology ; Group
9, Anthropology, including ethnology, archaeology, psychology, an-
thropometry, political economy, and social science and statistics;
Group 10, Miscellaneous, chiefly technology, but including also
biography and general philosophy. It will be seen that chemistry,
biology, and anthropology are defined so as to include the scopes of
the Chemical, Biological, and Anthropological Societies.
For convenience of discussion, the period of 17 years covered by
the statistics has been divided into five unequal parts, such that three
of the lines of separation correspond with the epochs of commence-
ment of the three sister societies. The time divisions begin on the
years 1871, 1875, 1879, 1881, and 1884, and contain, respectively, 4,
4, 2, 3, and 4 years. At the end of the second the Anthropological
Society was established, at the end of the third the Biological, at the
end of the fourth the Chemical. The Mathematical Section was
organized one year before the Chemical Society. For each time
division the number of papers of each class was ascertained, and
from these numbers were computed the percentages which appear in
Table III.
49
34 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Table III.
Percentages of Papers on Different Subjectsfor Different Periods.
Subjects.
1. Mathematics
2. Astronomy
3. Physics
4. Chemistry
5. Meteorology
6. Geology
7.' Geography
8. Biology
9. Anthropology
10. Miscellaneous
Periods.
1871-
1874.
1875-
1878.
6
23
10
4
9
6
15
9
6
12
100
5
18
14
2
5
8
13
9
15
11
100
1879-
1880.
2
18
12
6
4
9
7
10
19
13
100
1881-
1883.
9
7
12
1
13
14
7
9
11
17
100
1884-
1887.
2
6
9
4
11
27
10
6
13
12
100
1871
to
1887.
5
16
11
3
8
13
11
8
12
13
100
It appears from this table that in the two periods previous to the
organization of the Anthropological Society the subject of anthro-
pology furnished first 6 and then 15 per cent, of our material, and
in the following periods it furnished 19, 11, and 13 per cents. Biol-
ogy furnished in the first three periods 9, 9, and 10 per cents., and
after the beginning of the Biological Society 9 per cent, and 6 per
cent. The percentages of chemistry for the first four periods are 4, 2,
6, and 1, and for the single period of four years since the organization
of the Chemical Society, 4. These figures show that the organiza-
tion of scientific societies devoting themselves to the cultivation of
special scientific fields has not materially affected the interest of our
Society in the same sciences, so far as that interest may be judged
by the number of communications presented.
The table is not arranged to exhibit the effect upon our general
meeting of the institution of the Mathematical Section, but an inde-
pendent computation has been made with the following result : In
12 years previous to the Mathematical Section the Society listened
to 28 mathematical papers, an average of 2.3 per year. In the five
years following the general meeting listened to six mathematical
papers, an average of 1.2 per year. While the amount of mathe-
GENERAL MEETINGS. 35
matics before the Society in general meeting has been greatly dimin-
ished, the subject has not been entirely eliminated.
The general fact appears to be that the Philosophical Society,
being composed partly of men with a wide interest in scientific
matters and partly of specialists in many scientific branches, affords
a fitting arena for the discussion of subjects of general scientific
interest, but is not equally adapted to the presentation of highly
specialized researches. By a process of natural and unconscious
selection it has discountenanced those papers which from their
nature can interest only the devotees of a single science, and it,
therefore, has not fully met the needs of the scientific community of
Washington. The natural and proper result has been the institu-
tion, without and within the Society, of organizations undertaking
the cultivation of narrower fields, and these have found material of
their own without detraction of material which natually came to us.
In anthropology, in biology, in chemistry, and in mathematics we
still receive the communications which have a broad interest, and,
as such papers are largely written from a philosophic point of view,
it may well be that we are gainers by the multiplication of organi-
zations.
But while the modifications which have occurred in the ratios
in which various subjects have been represented on the floor of the
Society do not indicate an important yielding of our program to
outside influence, they do indicate progressive tendencies in other
directions. Astronomy, which during the first period was the lead-
ing theme, with a j)ercentage of 23, has fallen, through 18, 18, and
7, to 6 per cent.; geography, with 15 per cent, and 13 per cent, for
the first two periods, has 7, 7, and 10 for the last three. Geology, on
the other hand, with 6 per cent, at first, has increased steadily,
through 8, 9, and 14, to 27 per cent., and anthropology and meteor-
ology, while exhibiting fluctuations, have on the whole increased
their percentages. During the first period astronomy and geography
together gave 5 times as many papers as geology ; during the last
period their combined volume is only two-thirds that of geology.
The general explanation is not far to seek. Geology has gained in
importance on the floor of the Society because of the rapid growth
of the Geological Survey, which has brought to the city and to the
Society a large number of geologists. The increased attention oi
the Society to meteorology is traceable to the establishment of the
Study Room of the Weather Bureau, and the increase in anthro-
3G PHILOSOPHICAL SOCIETY OF WASHINGTON.
pology is correlated with the growth of the Bureau of Ethnology.
The great modification in the relative attention given to different
subjects is due to the large amount of new blood acquired by the
Society.
The statistics of the Mathematical Section are exhibited in the
following table
:
Table IV.
Statistics of the Mathematical Section from its Establishment to 1887.
Year 1883. 1884. 1885. 1886. 1887
Number of meetings
Number of communications
Average attendance
Number of members .
9
18
15
6
11
15
38
6
14
15
41
16
40
12
20
17
44
The whole number of papers presented to the Society, including
those addressed to ordinary and special meetings and to the Mathe-
matical Section, has been 786, and they have been communicated
by 184 persons. Fifty-seven guests and correspondents of the So-
ciety have furnished 67 papers, and 127 members have furnished
719. The total number of persons who have at various times been
elected to the Society is 312, and two-fifths of these have contributed
something more than remarks to the proceedings.
The following numerical data concerning the membership and
common membership of the Philosophical and three other scientific
societies were derived from what is known as the " Consolidated List
of the Philosophical Society," a list containing the names of the
active members of the four societies and the resident members of
the Cosmos Club. The list had been corrected to December 1, 1887.
In Table V the Anthropological, Biological, Chemical, and Philo-
sophical Societies are indicated by the initial letters of their names.
GENERAL MEETINGS.
Table V.
Common Membership of Four Societies.
37
Members of
one only.
A. ._.
B
C. ...
P. ._.
79
101
22
91
293
Members of
two only.
A.,B.„ 12
A.,C— 1
A., P.- 28
B., C— 2
B., P._. 25
0., P.- 10
78
Members
38 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. M. H. Doolittle read a paper
on newton's vis,
and was followed by-
Mr. B : Pickman Mann, who read a paper
ON REFERENCE INDEXING.
[Abstract.]
The author described in part the systems of indexing the litera-
ture of science which he had practised for many years, with illus-
trative examples and an argument to show their general applica-
bility and value.
He commented upon the extent and variety of the literature
of science as a whole, and the impossibility of obtaining a knowl-
edge of the literature relating to special departments of research
without the aid of indices prepared for the purpose. He then
dwelt upon the multitude of separate, partial indices now in ex-
istence, upon the difficulties experienced in making use of these
indices, and the waste of labor expended in disconnected attempts
to obviate these difficulties. He adverted to the advantages which
would accrue to all students through co-operative effort to obviate
the difficulties described, and remarked upon the necessity, in case
such co-operation were to take place, of determining upon a system
of carrying it out. He considered the advantages which would be
gained for temporary purposes by the combination of existing in-
dices into one index to be the property of the co-operators and
accessible either directly or mediately to all persons interested. He
then passed to a consideration of systems by which indices have
been constructed hitherto, and those which should obtain in the
formation of such an index as was contemplated here.
309th Meeting. December 10, 1887.
By courtesy of the trustees of the Columbian University the
meeting was held in the law lecture-room of the University building.
Invitations to "yourself and friends" to attend the meeting had
been mailed to all members of the Anthropological, Biological, and
GENERAL MEETINGS. 39
Chemical Societies, and of the Cosmos Club. About one hundred
persons were present.
Vice-President Mallery presided.
President Harkness then presented his annual address, the sub-
ject being
THE PROGRESS OF SCIENCE AS EXEMPLIFIED IN THE ART OF
WEIGHING AND MEASURING.
[Printed in full on page xxxvn of this volume.]
A vote of thanks for the address was passed by the audience.
310th Meeting. December 21, 1887.
the seventeenth annual meeting.
The President in the Chair.
Thirty-eight members present.
The minutes of the 294th, 308th, and 309th meetings were read
and approved.
The President announced the election to and acceptance of mem-
bership of Mr. Joseph William Spencer.
The annual report of the Secretaries was read and accepted.
[Printed in full on pp. xxxn, xxxiii of this volume.]
The annual report of the Treasurer was read and referred to an
auditing committee consisting of Messrs. J. S. Billings, J. C. Well-
ing, and C. O. Boutelle.
[Treasurer's report printed in full on pp. xxxiv, xxxv of this volume.]
The Treasurer read the list of members entitled, under Standing
Rule 14, to vote at the annual meeting.
The constitutional amendment proposed by Mr. Dall at the
last annual meeting was adopted by a vote of 26 for to 3 against it.
Election of officers was then held.
[The result is printed on page xv of this volume.]
The rough minutes of the meeting were then read and the Society
adjourned.



PROCEEDI NGS
AT A MEETING COMMEMORATIVE OF
THE LIFE AND SCIENTIFIC WORK
OF
SPENCER FULLERTON BAIRD,
HELD JANUARY 11, 1888,
UNDER THE JOINT AUSPICES OF THE
ANTHROPOLOGICAL, BIOLOGICAL, AND PHILOSOPHICAL SOCIETIES
OF WASHINGTON.
(41)

INTRODUCTION.
On August 19, 1887, Spencer Fullerton Baird. Secretary of
the Smithsonian Institution, Director of the U. S. National Museum,
and U. S. Commissioner of Fish and Fisheries, died at Wood's Holl,
Massachusetts, his post of duty in the last named office. His death
at once excited throughout the world feelings and expressions of
profound regret. At that time nearly all of his Washington asso-
ciates in scientific pursuits were absent from the city, on field duty
or in vacation, and were thus unable to jointly testify to the affec-
tion and respect in which he was held by them.
And especially the scientific societies of Washington, none of
which meet during the summer months, were unable to immediately
take any action in the matter or to give organized expression to the
sentiments of their members.
With the resumption of meetings, however, it was determined
that such expression should be given with all ceremonial complete-
ness, and as the senior of the Washington scientific societies, and
the one with which Professor Baird had been most closely con-
nected, the Philosophical Society took the initial steps in arranging
a joint meeting with the Anthropological and Biological Societies,
a meeting which might enable the members and their friends to
testify not only their profound respect for this foremost scientific
leader, but also their affectionate regard for the man.
The appended invitation and programme, which was mailed to
all members of the Philosophical, Anthropological, Biological, and
Chemical Societies, and of the Cosmos Club, sets forth the form
taken in those arrangements :
(43)
44 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Washington, January 4, 1888.
Sir:
The Philosophical Society in conjunction with the other scientific
societies of the city will hold a meeting on Wednesday evening,
January the eleventh, in commemoration of the life and services
to science of the late Spencer Fullerton Baird, Secretary of
the Smithsonian Institution, Director of the National Museum, and
United States Commissioner of Fish and Fisheries.
Memhers of the societies, and ladies and gentlemen whom they
may desire to invite, will assemble in the lecture-room of the Colum-
bian University, on the southeast corner of H and Fifteenth streets,
at a quarter past eight o'clock.
Your presence on this occasion is earnestly desired.
C. E. Dutton,
Eobert Fletcher,
J. H. Kidder,
Committee of Management.
Opening of the meeting, by the President of the Philosophical
Society.
Professor Baird as Administrator, Mr. W. B. Taylor, of the
Smithsonian Institution.
Professor Baird in Science, Mr. W. H. Dall, President of the Bio-
logical Society.
The Personal Characteristics of Professor Baird, Mr. J. W.
Powell, President of the Anthropological Society.
Mr. Garrick Mallery, President of the Philosophical Society,
called the meeting to order at the time and place above named.
RELATIONS BETWEEN PROFESSOR BAIRD AND
PARTICIPATING SOCIETIES.
By Mr. Garrick Mallert, President of the Philosophical Society.
Ladies and Gentlemen :
During several winters before 1871, a club, with commingled
social and scientific purposes, used to meet in this city at the houses
or* its members. A single paper on some scientific subject was read,
usually by the host of the evening, following which was a discussion.
Supper was always provided. The title of the club only related
to the night of meeting, Saturday, and the organization was so
loose that several of the survivors among the regular participants
at the meetings do not now remember whether they were actual
members, or indeed that there was a definite membership. As the
city of Washington emerged from the condition of a Southern vil-
lage, and the benign policy of the Government increased the num-
ber and force of the scientific institutions at the Capital, the need of
an organization which should bring scientific men together on an
equal footing and give more time to papers and their discussion
became manifest. To meet this want the attendants of the Saturday-
Night Club, on March loth, 1871, formed the Philosophical Society
of Washington, its object, in the words of the call, being "the free
exchange of views on scientific subjects and the promotion of scien-
tific inquiry among its members."
The term "Philosophical," as the first president of the Society,
Joseph Henry, stated in his first address, was chosen after consider-
able deliberation, "not to denote, as it generally does in the present
day, the unbounded field of speculative thought, which embraces
the possible as well as the actual of existence, but to be used in its
restricted sense to indicate those branches of knowledge that relate
to the positive facts and laws of the physical and moral universe."
Of the forty-three gentlemen who signed the call twenty-one are
now dead. Professor Baird was prominent among the founders,
and served continuously as a member of the General Committee from
the organization to November 10th, 1877, and from that date until
(45)
46 PHILOSOPHICAL SOCIETY OF WASHINGTON.
his death, on August 19th last, he was a member of the Committee on
Publications.
The first communication of a scientific paper to the Society was
made by him on March 18th, 1871. The most important and extended
original papers communicated by him were "On the decrease of
fish on the southern coast of New England," presented March 23d,
1872, and " On the artificial propagation of the cod, describing the
measures and process adopted at Gloucester, Mass., and the success
thus far obtained," presented March 1st, 1879.
The last-mentioned occasion is memorable to me, and some account
of it will be interesting to the younger members of the Society, few
of whom ever heard Professor Baird's voice raised in its hall. I
happened to join him on his way to the meeting, and during the walk
he spoke of the struggle at that moment between the sense of duty
requiring him to take his part in the proceedings of the Society and
his repugnance to making any formal address. This modesty
—
indeed, timidity—in an eminent writer and thinker, whose lightest
words were sure of eager attention in a society composed mainly of
his personal friends and wholly of his admirers, was the more remark-
able because his address, presented a few minutes later, was most
pleasing in its delivery as well as instructive in its substance. He
spoke without notes, and, though his style was conversational and
in no degree oratorical, his appropriate words in their rapid flow ex-
pressed his thoughts clearly, completely, and in orderly sequence.
During the same walk, Professor Baird mentioned with earnest
commendation the usage of the Society by which the perfect equality
of members is recognized through the omission of all official and
professional titles. This was not a merely unwritten custom but was
founded on a binding resolution, appearing in the minutes of June
6th, 1874. The Society is probably the only non-esoteric body in the
United States in which the titles ofJudge and General, Professor and
Doctor, Governor, Senator, and even Honorable Member are for-
bidden ; the simple and dignified Mr., the modern form of Magister,
being the only address allowed. Perhaps the plethora of titles and
the burdensome hierarchical gradations in Washington compelled
this measure of relief.
The Anthropological Society was founded February 17th, 1879, its
defined object being " to encourage the study of the natural history
of man, especially with reference to America." Professor Baird
warmly approved of the organization of this Society, took constant
\
GENERAL MEETINGS. 47
interest in it, and, at the time of his death, was the only honorary
member residing in the United States on its rolls.
The Biological Society was organized December 3d, 1880, "to en-
courage the study of the biological sciences," and Professor Baird was
the only honorary member ever elected by it. He did not take an
active part in the proceedings of either of the last-mentioned socie-
ties but gave them material assistance. Both of them met at first
in the Regents' Room of the Smithsonian Institution, placed by him
at their disposal, and he provided for the stereotyping and circula-
tion of their volumes of Transactions, a benefaction which the
Philosophical Society had earlier enjoyed.
President Henry, in his address before mentioned, stated that in
no other city in the United States was there, in proportion to the
number of its inhabitants, so many men actively engaged in pur-
suits connected with science as in Washington. In the seven fol-
lowing years the number of persons in the city engaged in scien-
tific work was nearly doubled, and most of them joined the Philo-
sophical Society, so that in the year 1878 it had become recognized
as the most efficient scientific body on this continent with a mem-
bership confined to a single locality. The criteria of this superiority
were not only the large membership and regular attendance of
members, but the number, quality, and variety of the papers pre-
sented and discussed. This abundance and, as was proved by the
later successful establishment of differentiated societies as an over-
flow, this superabundance of scientific papers occupied every mo-
ment of the meetings, so that the members, as such, had no oppor-
tunity to become acquainted with one another or to interchange
views, except in the formal discussions following the papers an-
nounced in the printed programs. There was no provision for
social introduction or intercourse. This appreciated want, the
converse of the inadequacy of the Saturday-Night Club, resulted
in the foundation of the Cosmos Club, on December 13th, 1878,
in the organization of which all the members of the Philosophical
Society were invited to join. It is needless to descant upon the
unique character of the Cosmos Club in its membership and objects,
its vital connection with science, literature, and art, and its imme-
diate but enduring success. The remark, however, is pertinent that,
in the winter of 1878, an unprecedented agitation, excited by im-
pending national legislation, perturbed the scientific circles of the
Capital, during which the proposition to form the Club was attacked
48 PHILOSOPHICAL SOCIETY OF WASHINGTON.
with virulence as a scheme in the selfish interest of a few individ-
uals, and one fraught with raachiavelian political designs ; but when
Professor Baird manifested his approval of the plan by accepting
the first presidency of the Club after its formal organization, con-
fidence in him was so dominant that suspicion was allayed and
opposition disappeared. To him profound thanks are due for the
timely establishment of the most important institution in the con-
joint social and scientific life of Washington.
But by his work in the organization of these several societies and
of the Cosmos Club, Professor Baird was, as in his other fields of
labor, a benefactor and not a participant in the benefits secured to
others. He was imbued with the cardinal principle of the Smith-
sonian Institution not only to establish and assist all useful agencies
for the promotion of the well-being of man, but afterwards, when
they had attained to successful operation, to leave them to them-
selves and explore new fields of beneficence. It was also his own
character, apart from any formulated maxim of the Institution,
that he could not rest in the personal enjoyment of accomplished
results. He was one of the ceaseless workers, born
until
" To scorn delights, and live laborious days,"
" Comes the blind Fury with th' abhorred shears
And slits the thin-spun life. But not the praise ! "
It is for us now, repressing sorrow, to join in tributes of praise to
our benefactor.
PROFESSOR BAIRD AS ADMINISTRATOR.
By Mr. Wm. B. Taylor, of the Smithsonian Institution.
We are met this evening to express in a memorial service our
respect for an honored fellow-member of our several societies, lately-
deceased, and to indulge as well in an interchange of affectionate
reminiscence of a departed friend. •
Spencer Fullerton Baird was born at Reading, Pa., February 3,
1823. He was graduated at Dickinson College, in Carlisle, Pa., in
1840, at the age of seventeen, and with an original fondness for
natural history and the study of the out-door world he spent several
years in his favorite pursuits and in collecting animal specimens
for preservation. In 1845, at the youthful age of twenty-two, he
was elected Professor of Natural History in his alma mater—Dick-
inson College.
Three years later, in 1848, while still pursuing with ardor the
study of nature, he applied for and obtained from the Smithsonian
Institution (then recently established) its first modest grant for the
promotion of original research. This was to be applied to the ex-
ploration of bone caves, and to the development of the local natural
history of southeastern Pennsylvania. The transaction appears to
have been the occasion of first bringing the young professor to the
favorable notice of the Smithsonian Director, Professor Henry, and
of initiating between the two a mutual respect and friendship that
continued throughout their several lives.
The early history of the Smithsonian Institution was signalized
by a long struggle—both in the Board of its Regents and in the
Halls of Congress—between the votaries of literature and those of
science for the disposal of the Smithson fund. During this period,
in 1850, when it was seen that the income of this institution was
not to be absorbed in the building up of a great National Library,
Professor Henry asked of the Regents authority to appoint an As-
sistant Secretary in the department of natural history to take
charge of the Museum and to aid in the publications and other in-
terests of the establishment. A resolution authorizing such an
appointment being adopted, Henry selected Professor Baird, of
50 (49)
50 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Dickinson College, as the one well fitted for the place. The ap-
pointment was unanimously confirmed by the Board July 5, 1850,
and Professor Baird being notified at once accepted and entered
upon his new duties. He deposited in the Museum his own valu-
able collections, comprising an extensive series of the skins of
various mammals (European as well as American), a large number
of bird skins (unmounted), representing about 500 American species
and half as many European species, a rich variety of birds' nests
and birds' eggs, more than 500 glass jars, tin vessels, and kegs con-
taining alcoholic specimens of reptiles and fishes, and a number of
vertebrate skeletons and of fossil remains.
The new Assistant Secretary was truly in his element, and showed
himself pre-eminently "the right man in the right place." In
Henry's Fourth Annual Report (that for 1850), after recording the
appointment of his Assistant, he adds : " He entered on his duties
in July last and, besides being actively engaged in organizing the
department of natural history, he has rendered important service
in conducting our foreign exchanges and attending to the business
of the press."
The Smithsonian system of exchanges was instituted for the pur-
pose offacilitating the reciprocal transmission between the Old World
and the New of the memoirs of learned societies, and this system has
become an essential agency in the interchange and diffusion of
knowledge, and in the more rapid advancement of scientific dis-
covery, by a wider and prompter co-operation. Previous to this
inauguration such distant scientific information was so rarely and
inconveniently accessible, largely through the delays and harass-
ments of customs exactions, that important principles had not un-
frequently been re-discovered abroad or at home, and sometimes with
a considerable interval of time, to subsequently disturb and dispute
a coveted and settled priority.
By the urgent zeal of the Smithsonian Director, representing to
foreign powers that only gratuitous distribution of the literary and
scientific memoirs of societies or of individuals (not usually found
on sale) was undertaken by the Institution, and that no commercial
enterprise calculated in any way to interfere with the legitimate
operations of trade was attempted—one port after another was
opened to its packages, until, in the course of a few years, the an-
nouncement was made that the Smithsonian exchanges were allowed
GENERAL MEETINGS. 51
to pass through every custom-house on earth, unopened and un-
questioned.
Creditable as this special liberality is, it has not yet, unfortunately,
been applied to the customary channels of book lore, and the quest
for knowledge is still held by a majority of civilized nations as an
indulgence very proper to be taxed. Our own legislators have also
made our higher education a source of revenue; possibly with a
view to the "incidental protection" of American science by the
heavy tariff laid on the foreign and imported article.
The advantage to the cause of science from this Smithsonian sys-
tem of international exchange of intellectual products, free of duty,
and with the freight expenses assumed by the Institution, can scarcely
be too highly appreciated. In the early promotion of this benefi-
cent scheme, Professor Baird became an energetic agent and sympa-
thetic co-adjutor of the Smithsonian Secretary. The remarkable
development of this service may be sufficiently indicated by a glance
at the amount of material transmitted through this Institution, on
each tenth year for thirty years, showing something like a geometrical
ratio of increase. The total weight of books, pamphlets, and charts
distributed in 1855 was about six tons; in 1865, about nine tons; in
1875, about twenty tons ; and in 1885, about eighty-five tons. With
the rapid growth of the exchange operations, the active and compre-
hensive faculties of Professor Baird seemed but to find a better field
of exercise.
At the same time, the accumulating collections of the museum
—
increased in 1858 by the transfer from the Patent Office to the Smith-
sonian building of the interesting contributions from the earlier
national exploring expeditions—demanded a large share of attention
for their proper arrangement, exposition, and superintendence.* To
say that this important work of organization was zealously and
judiciously carried out, is to characterize but imperfectly the di-
rective skill and energy of the museum curator.
Of Professor Baird's work in original biologic research,—of his
contributions to various scientific journals and society proceedings,
of his English translation of the popular " Iconographic Encyclo-
*This accession of the Government deposit of ethnological and natural
history specimens was estimated by Professor Baird, in his report for 1858,
as comprising not more than a fourth of the material already in the Smith-
sonian Museum or a fifth of the aggregate amount.
52 PHILOSOPHICAL SOCIETY OF WASHINGTON.
psedia," of his editorship of the "Annual Record of Science and In-
dustry " for eight years,—and of his other publications,—it is not
proposed here to speak. This aspect of his intellectual life will be
discussed by one in every respect far more competent to a just and
discriminating presentation of the theme. The present remarks will
be confined to a cursory review of Professor Baird's varied admin-
istrative work.
For a number of years a notable decline in the productiveness of
our extended fisheries had been with anxiety observed, the annual
yield of this important element of our food supply having in many
cases fallen off one-half of its amount a quarter of a century earlier.
So serious a diminution and consequent enhancement of cost of sub-
sistence was becoming a menacing problem. Were our leading
food-fishes undergoing a process of slow but certain extinction?
Several of the States (especially those of New England) appointed
commissions of inquiry into the causes and remedies of the threaten-
ing evil, but with little result.
In the stern competitive struggle that from the dawn of terres-
trial palseontogeny has been ordained by nature as the feudal tenure
of all existence, and from which service man himself is not ex-
empted, the feebleness of early youth in the individuals of every
race would speedily terminate the biology of our planet were
not provisions made for bridging over these cross lines of weakness
to preserve the continuity of species. In the lower classes of being
we find the crude expedient of a fertility so enormous as to allow
of the wholesale destruction of the unprotected eggs or of their
brood, and yet leave a remnant to spare for the chances of reaching
adult age. In numerous other classes, a marvellous sagacity is dis-
played by the mother in depositing her eggs where they will be least
exposed to accident or voracious attack, and where the progeny (that
she shall never see) will meet with their appropriate sustenance.
In insects this peculiar instinct—so difficult of explanation as " in-
herited experience"—is perhaps most strikingly displayed. And
lastly, when we ascend to the higher classes of birds and mammals,
we find the parental sentiment developed to an untiring vigilance
for the protection ,and provident care for the nutrition, of the new
generation until it is able to take up for itself the battle of life.
As an illustration of the reckless prodigality of productiveness in
some of the lower families of the vertebrate branch it may be recalled
that a single salmon will lay five thousand eggs; a trout, fifteen thou-
GENERAL MEETINGS. 53
sand eggs ; a perch, a herring, or a shad, thirty thousand eggs ; a
pike, one hundred thousand eggs; a carp, four hundred thousand
eggs; a mackerel, five hundred thousand eggs; a flounder, one
million eggs; a haddock, one million and a half of eggs; a halibut,
two and a half millions of eggs ; a pollock, four million eggs ; a cod-
fish of medium size, five million eggs ; a large-sized cod, nine million
eggs, and a turbot, nine million eggs. Such numbers are simply-
astounding ; they cannot be realized. Aud how great the marvel
when we consider that each of these nine million units is a potential
fish, capable of development into all the perfected attributes and
functions of the parent form ! Among the lower invertebrates may
be simply instanced the oyster—capable of producing the incredible
number of twenty or thirty million eggs, and if of large size as many
as forty or fifty million eggs.
If with this amazing fertility the various kinds offish just named
are not rapidly increasing, but are stationary or even decreasing in
numbers, how overwhelming must be their early destruction. Even
after allowing for the many millions of adult fish taken by man it
is obvious that of many species not one in a thousand or in ten thou-
sand of eggs or of the newly hatched can survive to maturity. Pro-
fessor Mobius estimates that for every grown oyster upon the beds
of Schleswig-Holstein more than a million have died.
To avert, if possible, the menace of increasing scarcity of fish
supply the attention of Congress was directed, to the subject;—the
more properly since in our National Government resided the juris-
diction over our extended sea coasts. By a joint resolution, approved
February 9, 1871, the President was authorized and required to
appoint a person of proved scientific and practical acquaintance with
the fishes of the coast to be Commissioner of Fishes and Fisheries,
with the duty to prosecute investigations into the causes of diminu-
tion, if any, in numbers of the food-fishes of the coast and the lakes
of the United States, and to report whether any and what protective,
prohibitory, or precautionary measures should be adopted in the
premises.
No man more suitable for this important and responsible position
than Professor Baird could have been selected. He was at once
appointed by President Grant and confirmed by the Senate as the
Commissioner. In his first report he announced, as the result of a
most careful and thorough examination, that the decrease of the
shore fishes of the New England waters during the preceding twenty
54 PHILOSOPHICAL SOCIETY OF WASHINGTON.
years was fully substantiated, and that it had been much more rapid
since the year 1865.
In furtherance of his great work, the resources of the Smithsonian
Institution were freely placed at the disposal of the Commissioner;
and, in the same report, he gratefully acknowledges this hearty co-
operation by saying : " I am indebted to Professor Henry for per-
mission to use the extensive collection of apparatus belonging to the
Smithsonian Institution, in the way of nets, dredges, tanks, &c, and
thus saving the considerable outlay which would otherwise have been
necessary."
The new studies into the life-history of the principal shore
fishes,—into the character and range of their enemies, and into
their appropriate means of subsistence, requisite to an intelligent
consideration of the conditions most favorable to their propaga-
tion,—involved investigations embracing the entire marine fauna
of the coast, vertebrate and invertebrate. These extensive and
varied researches necessarily demanded the aid of skilled assist-
ants—of a corps of eminent specialists in marine biology, and a
corresponding division of labor.
The results of these investigations have been given to the world
in hundreds of memoirs, published in the Reports and Bulletins of
the Commission, and in the Proceedings and Bulletins of the National
Museum. And it is quite within bounds to say that in importance,
in variety, and in extent of original information thus communicated,
no such quantity of contribution to our knowledge of zoology has
ever emanated from any other organization within the same in-
terval of time. Many species of fishes entirely new to science have
been discovered and carefully described ; and the number of in-
vertebrate forms known to inhabit the waters explored, has prob-
ably been fully doubled.
It was found, from the abundance of the lower forms of life, that
the decline of the useful fishes had not resulted from any lack of
their accustomed food-supply; nor had it resulted apparently from
any less favorable conditions of environment, nor from the preva-
lence of any epidemic diseases. It was therefore a consequence of
excess in their destruction.
Among all the ravages of predaceous fishes it was found that the
"bluefish" was the most voracious and devastating pirate of the
coast. In the report it is stated: "Sometimes among a school of
herring or menhaden thousands of bluefish will be seen biting off
GENERAL MEETINGS. 55
the tail of one and then another, destroying ten times as many fish
as they really need for food, and leaving in their track the surface
of the water covered with the blood and fragments of the mangled
fish." Fortunately this fish is itself valuable for food, and it is ac-
cordingly taken in large numbers.*
But by far the most rapacious and destructive scourge of the
waters is man himself. By reckless extravagance in his methods of
capture he would soon consume the capital of his abundant patri-
mony were no restraints imposed upon the thoughtless improvidence
of his greed. With the growth of population and demand and the
improved facilities for rapid transportation, the stimulus to inventive
ingenuity occasioned the establishing of fish-traps and fish-pounds
on a large scale that gathered thousands in their confines, with little
regard to the probable supply of the future. As these traps and
pounds were placed directly in the way of the fish to their spawn-
ing beds, it resulted that a very large proportion of spawn fishes
were taken by them, thus greatly reducing the prospects of the suc-
ceeding generation.
Whatever protective measures might be deemed expedient to
check this spendthrift waste, it was seen that the most immediate
and' promising work of the Commissioner would be to promote the
rapid multiplication of fish ; and to this dominant interest the an-
nual appropriations by Congress have been more and more largely
directed.
Pisciculture is by no means a recent art, it having been exten-
sively practiced by the Chinese for a number of centuries; and even
the artificial fecundation of fish-spawn is nearly a century and a
third old, having been apparently first introduced by Jacobi, a
German, of Westphalia. Most of the European nations had already
given attention to the practical application of fish-culture, and in
different parts of our own country enterprising individuals had un-
dertaken the operation with gratifying results.
Under the organizing direction of Professor Baird a careful study
was made of existing methods, extended experiments on artificial
propagation were conducted, and successive improvements in the
various stages of incubation, hatching, and development intro-
*In his first report, Professor Baird says: "I am myself cognizant of the
capture of no less than 20,000 bluefish, representing a weight of at least one
hundred thousand pounds, in one weir in the course of a single night."
56 PHILOSOPHICAL SOCIETY OF WASHINGTON.
duced,—each detail receiving a scientific treatment,—until a scale
of success has been effected far more complete and "satisfactory than
ever before attained. While under natural conditions but a small
proportion of the spawn deposited is hatched (the greater mass
being eagerly devoured by various aquatic tribes), and of the por-
tion hatched but a small percentage escapes to reach maturity,
under the careful breeding of art fully ninety per cent, of all the
eggs secured are fertilized and successfully developed.
Of the practical results of this great national enterprise it is un-
necessary to speak. A dozen varieties of our best food-fishes have
been disseminated throughout the inland waters and the seaboard
of our country in increasing quantities ; transported in the form of
the young fry, or in that of fertilized eggs to other hatching stations
;
and while an accurate estimate is, perhaps, at present not easily
attainable, it will hardly be held an exaggeration to say that these
productions are to be numbered by thousands of millions. Of these,
many millions (by a most praiseworthy public courtesy) have been
distributed to foreign countries—to Australia, to Brazil, to Canada,
to England, to France, to Germany, to Mexico, to The Netherlands,
to Scotland, and to Switzerland.
In the great International Fisheries Exhibition at Berlin in 1880
our national commission was authorized by Congress to participate.
Professor Baird appointed as his deputy to personally superintend
this movement Professor Goode, the present Fish Commissioner,
under whose energetic direction, in a remarkably short space of
time, the marvellous American exhibit was organized, transported,
and installed, to the wonder and admiration of every visitor. The
head of the American Commission was hailed by the President of
the German Fisheries Association as the " chief fish-culturist in the
world," and to him was awarded for the most complete and impos-
ing display of all the details and accessories of his scientific art the
unique first-honor prize of the exhibition, the gift of the Emperor
of Germany.
But time fails to permit more than a passing glance at other fields
of activity no less important in which Professor Baird employed his
remarkable powers of executive management. The Smithsonian
Institution from its inception had given great encouragement to
explorations, and its director had zealously labored to enlist, as far
as practicable, the various expeditions undertaken by the Govern-
ment, in the extension of scientific research. These efforts were lib-
GENERAL MEETINGS. 57
erally responded to by the Executive Departments, and trained ex-
perimentalists and observers were given every facility for physical,
physiographical, and biological investigations at distant points.
The Institution thus became almost the Government superintendent
of scientific expeditions. In all that pertained to ethnology and
natural history Professor Baird became of course the leading spirit,
and the various circulars of direction and of inquiry issued by him
show with what range and thoroughness he supervised this wide
department, while the resulting memoirs and valuable museum
accessions attest as their fruits the practical wisdom of the measures
and methods adopted.
Congress having made provision for the representation by the
Government in the National Centennial Exhibition to be held at
Philadelphia, the President of the United States requested the Ex-
ecutive Departments, together with the Smithsonian Institution, to
co-operate in a collection illustrative of our progress and resources.
In his report for 1875, Professor Baird formulated (as requested by
Professor Henry) his plans for the different details of the projected
exhibit, and, these being adopted, were carried out to a result that
made the Smithsonian display the leading attraction of the exten-
sive Government building.
At the death of Professor Henry, in 1878, his faithful assistant
and coadjutor was elected by the Regents as his successor, and his
long familiarity with the different lines of active operations pursued
by the Institution made him from the start an efficient director.
Another grave responsibility was thus thrown entirely upon his
shoulders, and he proved himself equal to the occasion.
In 1879, Congress made an appropriation (since continued an-
nually) for the prosecution of North American ethnology, to be
expended under the direction of the Smithsonian Institution. For
the administration of this important trust, Professor Baird selected
one whom he knew to be peculiarly fitted by training, by zeal, and
by congenial tastes, to pursue successfully the anthropologic study
of our waning aborigines, and the new Bureau of Ethnology was
judiciously committed to the control of the distinguished director of
the Geological Survey, Major Powell.
In the same year (that following Henry's death) an appropria-
tion (for many years importunately besought of Congress) was made
for the erection of a national museum building. In 1882 the com-
pletion of this building rendered necessary the re-organization of the
58 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Museum, with a staff of expert, curators, on a scale commensurate
with its importance, and the abundance of its previously stored ma-
terial.
Professor Baird hail now become the manager of three great
establishments -the Fisheries Commission, the Smithsonian Insti-
tution, and the National iMiiseuin ; either one of which was a charge
siillieient to fully task the energies of a vigorous man. No wonder,
with the strain of unremitted though divided attention to these
exacting duties, thai, while unconscious himself of any unaccustomed
or undue exertions, he should find even his robust and stalwart,
Strength was slowly failing under his accumulated labors.
Informed by his medical adviser that an entire and continued
rest from nil intellectual exertion was necessary to restore his nervous
energies to their wonted tone, he reluctantly accepted the decision.
A year ago he asked from the Smithsonian Regents authority to a p-
point two official assistants to relieve him from the greater portion
of his responsibility, and in hearty compliance with his expressed
desire, the eminent astronomer and physicist, Professor Langley, was
appointed assistant in charge of the Smithsonian operations, and
his well-tried friend and collaborator, Professor Goode, was ap-
pointed assistant, in charge of the Museum aifairs.
Put the relaxation came too late. After a vigorous resistance of
his strong constitution to the encroachments of internal organic
derangements, he finally succumbed to the Destroyer, and quietly
breathed his last, on the 1 9th of August, 1887 ;—another example
(far more frequent, in the higher than in the lower fields of occupa-
tion) of sacrifice to over-work.
Prom even this hurried and imperfect sketch of Professor Hand's
diversified administrative work it is at once apparent that he pos-
sessed, in a pre-eminent degree, two great capacities,—the faculty for
successful organization, and the faculty for continuous labor. As
a, biologist he had made a study of the entire range of organic
nature—vegetable and animal ; and with the accuracy of the special-
ist, he combined the larger and fuller perception of the genera] zoolo-
gist, as to the functional and genetic inter-relations of animated being,
The tenor Of his mind was rather Synthetic than analytic. While
he ever displayed a marvellous memory for particulars and a com-
prehensive grasp of details, these were apprehended more as the
constituents of a general end or purpose, than as the residuals of a,
disjunctive Conception. Clear-sighted and determined, he prevised
GENERAL MEETINGS. 59
and compassed the result in the means. Simple and unostentatious,
he received with ready affability a visitor, even when most pre-occu-
pied. What young naturalist ever applied to him for the resolution
of a difficulty or uncertainty without receiving cordial attention and
satisfactory enlightenment ?
Great as were his undoubted services in the original discovery of
biologic truths, it may well be doubted whether his indirect influ-
ence in the advancement of science was not still greater, by the
assistance and encouragement given to others and by his numerous
official occasions of directing the efforts of the aspiring into channels
of novel exploration whenever the opportunities of land or naval
expeditions presented themselves.
Now that the first shock of bereavement at missing one who has
occupied a prominent place in the public eye, as well as in our
private regard, has somewhat subsided, we but the more clearly
realize that in the lamented death of Spencer F. Baird the scientific
world has lost an accomplished and illustrious naturalist, the insti-
tutions over which he presided an energetic and judicious admin-
istrator, and we, assembled here, an exalted associate, a faithful
counsellor, an ever open-hearted friend.

PROFESSOR BAIRD IN SCIENCE.
By Mr. Wm. H. Dall, President of the Biological Society.
In accepting the honor of addressing you this evening on the bio-
logical work of Prof. Spencer F. Baird it is hardly necessary to state
that I have felt keenly the inadequacy of my own equipment for
the task. Not only does it happen that my own work has been
almost entirely in departments of biology different from those which
he adorned, but my early efforts were fostered by his wisdom and
geniality, the period of my scientific studies has coincided with an
acquaintance which ripened into affection and admiration, they
have depended for their results upon opportunities largely due to
the intervention of Professor Baird, and I feel that the best and
truest of him is that which cannot be put in words. The sense of
personal loss, as with many of you, is still so keen as to accentuate
the difficulty of doing justice to the theme assigned me.
I should have almost despaired of myself on this occasion were it
not that others have aided me in my endeavor to set forth the debt
owed by the various departments of research to Professor Baird's
original investigations. To naturalists so distinguished in their
specialities as Ridgway, Stejneger, Goode, Coues, Allen, Merriam,
and Yarrow, I am indebted either for direct contributions toward
the substance of this address or for matter in their published works
Avhich has been similarly utilized.
Professor Baird's scientific activity was exhibited in three prin-
cipal directions: First, in original investigation of the zoology of
vertebrates; second, in the diffusion of scientific knowledge and
methods through official documents, reports, cyclopedias, and records
of progress; and lastly, in the organization and administration of
scientific agencies such as the National Museum or the Fish Com-
mission, which include in their scope not merely public education
or economic applications of science, but the promotion of research.
Behind all these and hardly less important for science was the per-
sonal influence of the man himself, which shone through all the
planes of his activity as coruscations light the facets of a gem.
(61)
62 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Although it is very difficult to separate the phases of his work,
one from another, so closely were they inter-related, my theme to-
night is restricted to the impress left upon zoological science by
Baird's original investigations. So great has been his reputation as
an organizer, so numerous have been the publications in which he
has garnered for the public the precious grain of the annual scien-
tific harvest, that the extent and importauce of his original work,
except by specialists, is in danger of being overlooked.
We owe an excellent bibliography of his publications to Professor
Goode. From this we learn that, up to the end of 1882, the list
comprises nearly eleven hundred titles, from which, after deduction
of all notices, reviews, official reports, and works edited for others,
some two hundred formal contributions to scientific literature re-
main, many of which are works of monographic character and ex-
tensive scope.
"With the exception of a single early botanical paper these relate
to the vertebrates of America and, in their several branches, cover
nearly the entire field. Although descriptions of species in them-
selves afford a poor criterion of the value of the work containing
them, it is interesting to note that, among the terrestrial vertebrates,
the proportion of the fauna first made known by Baird to the total
number recognized at the time as North American varied from
twenty-two per cent, of the whole to forty per cent, in different
groups.
His method of study of new material was as far removed as possi-
ble from bookishness. In the case of the collections from Hudson
Bay or the Pacific Railroad Surveys, when birds, mammals, or rep-
tiles sometimes came to hand by hundreds, each specimen having
the collector's data attached, the whole collection was thrown to-
gether, each form to be sorted out on its merits and studied in the
light of a multitude of specimens.
Professor Baird's early life had iucluded so much of exercise in
the shape of long pedestrian journeys with gun aud gamebag, so
much familiarity with the wood-life of his favorite birds aud mam-
mals, that it would have been in any case impossible to class him
with the closet-naturalist, while to this knowledge he added a genius
for thorough, patient, and exhaustive research into all which con-
cerned the subject of his study, and a wonderful inventiveness in
labor-saving devices for labelling, museum work, and registration.
GENERAL MEETINGS. 63
He had a wonderful capacity for work. He undertook and car-
ried out successfully tasks which it would seem nobody else would
have dared to attempt, or, attempting, would have been physically
unable to complete. In the case of the immense volume on the
mammals of the Pacific Railroad Surveys he says in the preface,
July 20, 1857
:
" The examination of the material was actually commenced early
in 1855 and many of the articles written in that year or 1856.
With the continual accession of additional specimens it became
finally necessary to rewrite, alter, or extend all that had been pre-
pared prior to the present year (1857). It is to this that the fre-
quent want of uniformity is due, the time allowed not being suffi-
cient in many cases to permit the reworking of the whole matter.
* * * It is, perhaps, unnecessary to state that the matter of the
present report is entirely original throughout. * * * It is
proper to state that, owing to various circumstances, the work was
necessarily passed through the press with a rapidity probably un-
exampled in the history of natural-history printing, allowing very
little opportunity for that critical and leisurely examination so
necessary in correcting a work of the kind. For most of the time
the proof has been furnished and read at the rate of twenty-four to
thirty-two pages per day, nearly 400 pages having been set up,
read, and printed during the first half of July alone. Owing to
the urgent necessity for the speedy completion of the volume, no
time was allowed for the revision of the manuscript as a complete
work, nor, indeed, of its separate portions, and, for much of the
time, the preparation of much of the manuscript was only a few
hours iu advance of its delivery to the compositor."
The volume above referred to contains over 800 quarto pages
and 42 plates. The manuscript was entirely prepared after six
o'clock of working days which had been spent in the active admin-
istrative and executive work of the Assistant Secretary of the
Smithsonian Institution, then unassisted by stenographer or other
clerical supplement. Fortunately for science Baird did not always
have to work under such circumstances, but the incident shows
what he was capable of doing when the occasion seemed to him to
warrant it. Probably no other work of equal importance, on any
subject, was ever carried out under such pressure.
Mammals.—Professor Baird's contributions to a knowledge of
North American Mammals, though less voluminous than those re-
lating to birds, are not less important. Previous to this time but
64 PHILOSOPHICAL SOCIETY OF WASHINGTON.
one general work on the subject had been published, that of Audu-
bon and Bachman on the Quadrupeds of North* America, which
was issued in three volumes, from 1846 to 1854* Immediately
after the completion of this great work collections began to pour
into the Smithsonian Institution from the various exploring parties
of the Pacific Railway Surveys. This material comprised so large
a number of new species, and cast so much light upon many pre-
viously doubtful points concerning the relations of species already
described, that a revision of the whole subject became necessary.
Hence Professor Baird at once set about the preparation of the book
commonly known as the Mammals of North America. I have already
alluded to the manner in which it was prepared. This great work
was rapidly pushed to completion and appeared in 1857, just three
years after the publication of the last volume of Audubon and
Bachman's Quadrupeds. It constitutes the eighth volume of the
Pacific Railroad Reports, and is a ponderous quarto of more than
800 pages, accompanied by numerous excellent plates.
Though published thirty years ago, this work still remains the
standard general treatise on North American mammals. It con-
tains no biographical matter, but consists wholly of technical de-
scriptions. It treats of all the mammals then known from the
continent of North America north of Mexico, except the bats and
the truly pelagic forms—whales, sea cows, and seals. The total
number of known species was increased nearly twenty-five per
cent.
In fullness of synonymy, and in the correct assignment of species
previously described, Professor Baird was much in advance of pre-
vious workers. The descriptions, which are models of painstaking
accuracy and precision, are taken from the specimens themselves,
and are accompanied by long tables of measurements, the value of
which more than justifies the enormous expenditure of time neces-
sary in their preparation. Much more attention was paid to crani-
ological characters than had been the custom with previous writers,
which fact contributes largely to the permanent value of the work.
Professor Baird's long training as a careful observer, his power
of concentrating his knowledge of matters under investigation, the
* The volume on Mammals of Richardson's Fauna Boreali Americana
does not fall under this head, because it treats only of the northern portion
of the continent.
GENERAL MEETINGS. 65
wide scope of his information on nearly all departments of natural
science, his clear perception of details, together with his excellent
judgment, which was as marked in matters of minor detail as in
those requiring great executive ability, enabled him to draw con-
clusions which subsequent accumulations of material have verified
in a surprising manner ; in fact, his pre-eminent superiority as a
systematic zoologist is everywhere apparent.
Birds.—When the great interest he took in birds is considered,
and the long period over which his studies extended, it is somewhat
surprising to find that the number of separate papers on ornithology
published by Professor Baird sums up only some seventy-nine titles.
It is less to their number that he owed his fame as an ornithologist
than to their quality, combined with the fact that several of these
publications covered practically the entire field of North American
ornithology, and were of the nature of monographs.
" His reputation was, indeed, established," says Ridgway, " by
the first of his separate works, usually known and quoted as the
" Birds of North America," though not published under this title
until two years after it had been printed by the Government as
Volume IX of the Pacific Railroad Reports. With the publication
of this great quarto volume, containing more than a thousand pages,
in 1868, began what has been fitly termed by Dr. Elliott Coues the
" Bairdian period " of American ornithology. This period, cover-
ing almost thirty years, was characterized by an activity in ornitho-
logical research and a rapidity of advancement without a parallel
in the history of the science.
Of the "Birds of North America" Coues states* that "it repre-
sents the most important single step ever taken in the progress of
American ornithology in all that relates to the technicalities." The
nomenclature was entirely remodeled from that previously in cur-
rent use, and for the first time was brought abreast of the systematic
acquirements of the time. The synonymy of the work, in which is
embodied the history of investigation relating to each species, is
more extensive, reliable, and elaborate than any before presented.
With few exceptions, citations were original, and when, as occasion-
ally happened, they were necessarily at second-hand the fact was
*Bibl. app. to the Birds of the Colorado Valley, p. 650.
51
66 PHILOSOPHICAL SOCIETY OF WASHINGTON.
always indicated. The text comprised not only diagnoses and de-
scriptions of each species, but extended and elaborate commentary,
comparisons and criticisms.
In this learned and sagacious work Professor Baird was aided by
Cassin and Lawrence, two of the leading ornithologists of America.
It exerted an influence perhaps stronger and more widely felt than
any of its predecessors, Audubon and Wilson not excepted, and
marked an epoch in the history of American ornithology. The
data original to and embodied in this work have been used again
and again by subsequent writers with various modifications. Such
a monument of original research is likely to remain for an indefinite
period a source of inspiration to other writers, while its authority
as a work of reference will always endure.
The publication of this work rendered possible the studies and
progress of a large number of persons, who without it would hardly
have been able to enter the domain of scientific ornithology, but
who, aided by the book as a standard of reference and by the genial
correspondence and pregnant suggestions of its author, have made
reputations of more or less distinction for valuable and permanent
original investigation. The number of those who profited by this
stimulation has been very large and in this way arose what has
been called* the Bairdian School of Ornithologists, a school char-
acterized by exactitude in matters of fact, conciseness in deductive
statement, and careful analysis of the subject in all its various
bearings. Its work is marked by a careful separation of the data
from the conclusions derived from them, so that conclusions or
arguments can be traced back to their sources and duly weighed,
while the writings of the older European school afford little basis
for analysis. In substance, according to Dr. Stejneger, the Euro-
pean method required an investigator to accept an author's state-
ments and conclusions on his personal responsibility alone, while
the method originated by Baird furnishes him with tangible facts
from which to make his deductions.
These distinctive features were still further developed by the
publication in 1864-'66 of the "Review of American Birds," a
work of unequalled merit, displaying in their perfection Professor
Baird's wonderful powers of analysis and synthesis, so strongly
combined in his treatment of difficult problems. Although never
* Stejneger, Proc. U. S. Nat. Mus., VII, 1884, p. 76.
GENERAL MEETINGS. 67
completed, this work has received unstinted praise from all compe-
tent to estimate it. It is said on excellent authority that no other
single work on American birds has made so profound an impression
on foreign ornithologists, notwithstanding the fact that circum-
stances prevented it from being made complete.
Although in his systematic work Professor Baird, like other
naturalists, built partly on the scientific foundations laid by his
predecessors and contemporaries, always with due acknowledge-
ment, the high value of his work in this direction was largely
due to an unerring instinct which enabled him to recognize and
confirm the best features of the work of others and by adding ma-
terial from his own lines of original research to combine the whole
into a fabric which was a distinct advance on anything previously
offered to the scientific world.
While the bent of his genius led him, in this as in other depart-
ments, to devote a main proportion of his work to the systematic
biology which was the need of the time, and which, with the explora-
tion and description upon which it is based, must always precede
and lay the track for the theoretical biology more in vogue to-day,
it must not be supposed that the work of Baird was confined to de-
scriptive and systematic work. With the latter in his publications
are combined a host of biographical data such as the field naturalist
revels in. One of the earliest and most pregnant papers bearing
on mutations of specific forms which have been contributed to the
literature of evolution by American biologists is to be found in his
article on the " Distribution and Migrations of North American
Birds" published in the American Journal of Science in 1866.*
In this paper, an abstract of a memoir presented to the National
Academy of Sciences in 1865, are to be found the germs of much
of the admirable work which has since been elaborated by other
biologists on the correlation of geographical distribution and the
peculiarities of the environment, with the modifications of color,
size, and structure in the forms of animal life, called species.
Unlike some of his contemporaries twenty years ago, the views of
Darwin excited in him no reaction of mind against the hypotheses
then novel and revolutionary. His friendly reception of the new
theories was so quiet and undisturbed that, to a novice seeking his
*Am. Jour. Sci. and Arts, 2nd Series, XII, pp. 78-90, 184-92, 337-47,
1866.
68 PHILOSOPHICAL SOCIETY OF WASHINGTON.
inal. How well this work was done is shown by the fact that, in
spite of the changes which are constant in zoological classification,
nearly all the species still retain the names he applied to them. The
descriptions were so carefully prepared that later students have never
beeu troubled in making their identifications.
Notwithstanding his multifarious duties in later years, Professor
Baird never lost his interest in these animals, and up to the last
afforded every aid and encouragement to those studying them.
Much of the work done in this country by such herpetologists as
Girard, Kennicott, Hallowell, Cope, and others, found in his ex-
ample and encouragement the stimulus which made it possible, was
built on the foundations which he laid, and owes its publication to
agencies which he promoted or controlled.
Fishes.—Professor Baird's contributions to ichthyological liter-
ature number some fourteen or fifteen papers, chiefly of a descriptive
character, embodying the results of original research into the ichthy-
ology of western and southwestern America and of the marine
fishes of New Jersey and New York. Most of these papers were
published jointly with Charles Girard.
Besides these, however, he added more than four hundred titles
to the list of reviews, notices, reports, translations, and official docu-
ments relating to economic ichthyology, fish culture, and the gen-
eral progress of the science. In this way he was instrumental
in bringing together for the use and benefit of the English-speaking
public the largest body of facts relating to fish and fisheries ever
prepared and digested for such purposes by any individual or
organization. Recognized by experts of foreign countries with one
accord, as the most eminent living authority on economic ichthy-
ology, America owes to his fostering care and unwearied labor the
existence of a whole generation of ichthyologists, breeders of fishes,
and inventors of appliances of all sorts for use in connection
with the taking, preservation, and increase of these animals. So
thoroughly is this understood by all who are in any way acquainted
with American fish and fisheries, that to them this statement will
appear a truism.
It does not enter into the purpose of this address to enumerate
the economic results of the Commission which grew into such stately
proportions under his skillful and progressive leadership, nor yet
to enumerate the multitudinous researches in pure as well as eco-
GENERAL MEETINGS. 69
advice and opinion amid the clatter of contending voices, it seemed
almost as if the main features of the scientific gospel of the new era
had existed in the mind of Baird from the very beginning. His
thorough apprenticeship in the study of details of structure and their
expression in systematic classification, as well as his cautious and
judicial habit of mind, prevented him, notwithstanding his hearty
recognition of evolutionary processes, from falling into those exuber-
ancies of utterance and hypothesis characteristic of narrowness and
immaturity which, within the memory of most of us, have enjoyed
a sort of vogue now happily on the decline.
Batrachians and Serpents.—Professor Baird's contributions to
herpetology began as early as 1849, his first paper being a revision
of the North American tailed batrachians which appeared in the
Journal of the Academy of Natural Sciences of Philadelphia. Ex-
cluding notices of the work of others in the Annual Record between
1849 and 1880, he published fourteen papers on this branch of science
beside nine of which he was the joint author with Charles Girard.
His activity in original work in this, as in some other directions,
came to an end with the assumption of the burden of administrative
work required by the organization and development of the Fish
Commission.
Many of his herpetological papers were elaborate studies. One
of the most important of the early memoirs was that on the reptiles
of Stansbury's expedition to the valley of the Great Salt Lake, and
another, that on those collected by the United States exploring ex-
pedition under Wilkes. The catalogue of North American Reptiles
in the collection of the Smithsonian Institution is a classical work,
serving to the present day as a text-book for students of herpetology.
In 1859 appeared his great study of the reptiles collected by the
parties engaged in the explorations for a Pacific railroad, a monu-
ment of patient research and discriminating analysis. After this
his contributions to the subject were mostly short papers or an»
nouncements of new or interesting facts.
At the time Professor Baird began his studies of the amphibia
little had been done for herpetology in America. The classical work
of Holbrook contained little more than descriptions of Southern
species aud the work of Dumeril and Bibron was equally meagre.
Immense collections were placed in Baird's hands from the Western
plains, and the work upon these was necessarily in great part orig-
70 PHILOSOPHICAL SOCIETY OF WASHINGTON.
nomic biology for which this organization has furnished material
and means. No more emphatic object-lesson of the vital relations
existing between research, as such, and the promotion of the ma-
terial interests of mankind has ever been furnished to the so-called
" practical man " than that afforded by the work of the United
States Fish Commission as directed by Professor Baird.
Whether germane to the subject of scientific research or not, the
most narrow specialist can hardly grudge an allusion to the grandeur
of the methods by which the food supply of a nation was provided,
hundreds of rivers stocked with fish, and the very depths of ocean
were repopulated. Typically American we may call them in their
audacity and their success. The Fishery boards of foreign countries,
first quietly indifferent, then loudly incredulous, iu due time became
interested iuquirers and enthusiastic folloAvers. In a few years we
may fairly expect to see the food supply of the entire civilized
world materially increased, with all the benefits which that implies,
and this result will in the main be owing to the unremunerated
and devoted exertions of Spencer F. Baird.
THE PERSONAL CHARACTERISTICS OF PROFESSOR
BAIRD.
By Mr. J. W. Powell, President of the Anthropological Society.
Baird was one of the learned men of the world, and, to a degree
perhaps unexampled in history, he was the discoverer of the knowl-
edge he possessed. He knew the birds of the air, from the ptarmi-
gan that lives among everlasting snows, to the humming-bird that
revels among the orchids of the tropics ; he knew the beasts of the
forests and the prairies, and the reptiles that crawl through desert
sands or slimy marshes ; he knew the fishes that scale mountain
torrents, that bask in quiet lakes, or that journey from zone to zone
through the deep waters of the sea. In all this realm of nature he
had a minute and comprehensive knowledge that no other man has
ever acquired. What others have recorded in this field of research
he knew, and to their discoveries he made a contribution of his own
so bounteous, so stupendous, that he is recognized as the master of
systematic zoologists.
All of Baird's scientific work is an illustration of modern induc-
tive or scientific reasoning. The inductions or general principles of
modern science are reached by the accumulation of vast stores of
facts. He knew how to accumulate facts ; how to reject the trivial
and select the significant. Modern science is almost buried under
the debris of observation, the record of facts without meaning,
the sands of fact that are ground from the rock of truth by the at-
trition of mind; but Baird could walk over the sands and see the
diamonds. Then he knew how to marshal significant facts into
systems, and to weld them into fundamental principles. In all his
works there can be discovered no taint of a priori reasoning or
syllogistic logic ; for in his mind there was no room for controversy,
and disputation fled before the light of his genius. Formal logic,
a disease of modern thought,—the contagion of Arktotleina,—never
(71)
72 PHILOSOPHICAL SOCIETY OF WASHINGTON.
ravaged his brain. With healthful directness, he sought the truth
guided by wise inference, and told the truth in its simplicity.
Baird was an organizer of the agencies of research. When a
bold explorer essayed to penetrate the seas of ice by the path of
peril and in quest of fame, Baird would ever so manage that a corps
of quiet scholars should be attached to the expedition to study the
climate of the Arctic zone, the geology of the Arctic rocks, the flora
of the Arctic lands, or the fauna of the Arctic fields ; and the best
knowledge we have of the igloo-dwellers, the Eskimo whose home
is on the ice of the North, has been brought to us by the quiet students
he succeeded in attaching to Arctic exploring expeditions : and so
the love of glory was made to serve the cause of truth.
When, in the interests of international commerce, expeditions
were sent to explore and survey routes of travel and transportation
across Central America from sea to sea, he managed to send with
them corps of scientific men whose function it was to bring from
the tropics all forms of its abundant life, vegetal and animal, and
the relics of the arts of the people of Central America as they are
exhibited in stone and clay and gold ; and the National Museum
has been enriched by the results of this labor, and the boundaries
of human knowledge extended thereby : and so the greed of gain
was made to serve the love of truth.
When our army was distributed on the frontiers of the land, he
everywhere enlisted our scholarly officers into the service of science
and he transformed the military post into a station of research, an
Indian campaign into a scientific expedition. Scott, Marcy, Mc-
Clellan, Thomas, and many other of the great generals of America,
were students of natural history and collectors for Baird. When
our navy cruised around our shores, its officers were inspired with
that love of nature which made every voyage of military duty a
voyage of discovery in the realms of natural science; when they
journeyed among the islands of the sea they brought back stores of
scientific materials, and when they sailed through the littoral waters
of other continents they made voyages of scientific investigation.
Many of these earlier naturalists of the Navy in subsequent times
became commodores and admirals.
But time would fail me to tell of the exploring expeditions and
the railroad surveys throughout America, and the travels through-
out the world, which he utilized in the interest of science, or of
which he was the immediate projector. Of the abundant material
GENERAL MEETINGS. 73
thus gathered from all parts of the world, some has gone to enrich
American institutions of learning, and some has been gathered into
the National Museum—the outgrowth of Baird's organizing genius
and a splendid monument to his memory.
The hills of the land stretch not so far as the billows of the sea
;
the heights of the mountains are not so great as the depths of the
ocean ; and so the world was unknown until this greater region was
explored. The treasures of the land did not satisfy the desires of
Baird ; he must also have the treasures of the sea, and so he organ-
ized a fish commission, with its great laboratories and vessels of
research.
" What hid'st thou in thy treasure-caves and cells,
Thou hollow-sounding and mysterious main ?
Pale, glistening pearls and rainbow-colored shells,
Bright things which gleam unreck'd of, and in vain.
Keep, keep thy riches, melancholy sea
!
We ask not such from thee."
What the scholar asked of the sea was all its forms of life, its
organisms minute and lowly, its crawling articulates, its pearl-
housed mollusks, its fishes that swim in armies, and its leviathans
that prowl among the waves—the life of the reedy shore, the life
of the ocean-current, and the life of the deep sea. So, with many
ingenious appliances, he and his lieutenants sailed away to explore
the ocean's mystery.
So the Fish Commission was an agency of research ; but it was
more ; he made it an agency by which science is applied to the
relief of the wants of mankind, by which a cheap, nutritious, health-
ful, and luxurious food is to be given to the millions of men. He
affirmed that for the production of food an acre of water is more
than equal to ten acres of land, thus giving to the gloomy doctrine
of Malthus its ultimate refutation, and tearing away the veil of
despair from the horizon of the poor ; for, when the sea shall serve
man with all the food that can be gathered from its broad expanse,
the land cannot contain the millions whom it is thus possible to
supply.
In the research thus organized the materials for the work of
other scientific men were gathered. When a great genius reads to
the world a chapter from the book of nature the story is so beau-
tiful that many are stimulated to search in the same field for new
chapters of the same story. Thus it was that the publication of
74 PHILOSOPHICAL SOCIETY OF "WASHINGTON.
Baird's great works on natural history developed in America a
great corps of naturalists, many of whom have become illustrious,
and the stimulus of his work was felt throughout Europe. In the
research which he organized the materials were furnished for this
corps of naturalists ; but his agency in the development of this body
of Avorkers was even more direct. He incited the men personally
to undertake and continuously prosecute their investigations. He
enlisted the men himself, he trained them himself, he himself fur-
nished them with the materials and instruments of research, and,
best of all, was their guide and great exemplar. Thus it was that
the three institutions ov%r which he presided—the Smithsonian In-
stitution, the National Museum, and the Fish Commission—were
woven into one great organization—an university of instruction in
the methods of scientific research, including in its scope the entire
field of biology and anthropology. Such is Baird the investigator,
Baird the organizer, and Baird the instructor in the length, breadth,
and thickness of his genius, the solidarity of a great man.
All that I have said is a part of the public record ; it is found in
the great libraries of the world ; but, however exalted the feeling
of admiration we may entertain for Baird as a scholar and admin-
istrator, it is to his attributes as a man, as disclosed in his personal
relations with friends, associates, and contemporary men of affairs,
that we most fondly turn. It is in these relations that he most
clearly exhibited those kindly and modest traits of character which
made him so universally beloved.
As a man of affairs, Professor Baird exhibited great sagacity.
His plans for the organization of scientific work were of great mag-
nitude, and had they been presented to the administrative officers
of the Government or to legislative bodies with exaggeration, or
even had they been presented with the glow of an enthusiastic
missionary of science, they might well have encountered opposition.
But Baird had a wonderful faculty of presenting his plans with
extreme modesty, and with a degree of understatement, but sugges-
tion of possibilities which speedily caused him to whom the appeal
was made himself to become an advocate of the Professor's measure.
He had traits of character in this respect which are hard to explain,
and which seem at first to be contradictory. In the advocacy of
measures his modesty amounted almost to timidity, and he avoided
alike argumentation and ostentation, and he presented his measures
with the directness of a child. Notwithstanding all this, there was
GENERAL MEETINGS. 75
such a poise of faculties—such dignity of mien—that he impressed
those with whom he came in contact as a venerable and wise patri-
arch. He seemed devoid of personal interest or feeling, and solici-
tous only for the welfare of those to whom he was in fact appealing,
and he conveyed the impression that he was giving benignant ad-
vice. Thus the shrinking, sensitive man, who could not even stand
before a public body, such as a committee of Congress or a scientific
society and advocate a cause, could, from his seat by the fireside or
at the desk, so illumine the subject with which he had to deal that
men stood round him to gather his words, that nothing should be
lost, for in the exposition of his subject he illumined everything
with clear statement, arising from an exhaustive knowledge and
full understanding of results.
As the director of the work of research in which other men were
engaged, Professor Baird had marvelous insight and skill. The
appliances of modern research, alike in the inorganic world and in
biology, have come to be multifarious and diverse, and there is this
peculiarity about their use : That once used, so that the secret of
nature which they were planned to unlock has been revealed, they
speedily ^become obsolete, and immediately new keys, new appa-
ratus, new devices are necessary. Thus to a large extent skill in
research is absorbed in the skill necessary for the development of
the agencies of research. A continuous line of research, prose-
cuted by a corps of men so that the boundaries of knowledge are
carried far forward, can result only from a continuous line of in-
ventions in the apparatus of research, and it was here that Baird
exhibited his skill. His own devices were many and constant, and
ever he was fertile in suggestions to his assistants. No wonder,
then, that so many of the secrets of nature were unlocked through
his agency. It was in the direction of this work of research that
the man Baird stood forth as a giant; it was where his vast knowl-
edge of details was most apparent ; it was where his marvellous
skill was most shown ; it was where his insight into human char-
acter was most exhibited. With clearness he formulated his inter-
rogatories ; with aptness he selected his course of procedure ; with
judgment he sought the aid of others, and with suggestiveness di-
rected their work. And, lo ! his questions were speedily answered.
It was in this manner that his own good hands were supplemented
by the hands of many, that his own great mind was re-enforced by
76 PHILOSOPHICAL SOCIEXY OF WASHINGTON.
the best mental activity of many assistants ; and thus the whole
body of men under his control worked together a? one organic in-
teger for the increase and diffusion of knowledge among men.
In his work with his assistants he scrupulously provided that
every one should receive the meed of honor due for successful re-
search and treated all with generosity. Many an investigation
begun by himself was turned over to assistants when he found that
valuable conclusions could be reached ; and these assistants, who
were his warm friends, his younger brothers, reaped the reward
;
and he had more joy over every young man's success than over the
triumphs and honors heaped upon himself from every quarter of
the globe. He was the sympathetic counsellor of many men ; into
his ears were poured the sorrows and joys of others, and he
mourned with the mourning and rejoiced with the rejoicing. To
those in need his hand was ready and his purse was open, and
many and many were the poor who called him " blessed." Though
a man of great force of character, a man of great learning, a man
upon whom had been showered the honors of the scientific world,
in character he was as simple as a child. He had a fund of
" folk-lore," and loved the books and papers written for children.
In his later years, weakened with disease and burdened with many
labors, he still read St. Nicholas from month to month, and kept
the run of every little story, and was glad to be " a child again."
His life at home was pure and sweet, and full of joys, for he gave
and received love and trust and tender care. But the history of
his home life is sacred. Its words and acts abide in the hearts of
the wife and the daughter.
For many long months he contemplated the day of parting.
Labor that knew no rest, responsibility that was never lifted from
his shoulders, too soon brought his life to an end. In the summer of
the past year he returned to his work by the seaside, that he might
die in its midst. There at Wood's Holl he had created the greatest
biologic laboratory of the world ; and in that laboratory, with the
best results of his life-work all about him, he calmly and philosoph-
ically waited for the time of times. Three days before he died he
asked to be placed in a chair provided with wheels. On this he
was moved around the pier, past the vessels which he had built for
research, and through the laboratory, where many men were at
work at their biologic investigations. For every one he had a word
of good cheer, though he knew it was the last. At the same time,
GENERAL MEETINGS. 77
along the pier and through the laboratory, a little child was
wheeled. " We are rivals," he said, " but I think that I am the
bigger baby." In this supreme hour he was playing with a child.
Then he was carried to his chamber, where he soon became in-
sensible, and remained so until he was no more.
" Blessed are the pure in heart, for they shall see God."

BULLETIN
PHILOSOPHICAL SOCIETY OF WASHINGTON,
MATHEMATICAL SECTION
(79)

STANDING RULES
MATHEMATICAL SECTION.
1. The object of this Section is the consideration and discussion
of papers relating to pure or applied mathematics.
2. The special officers of the Section shall be a Chairman and a
Secretary, who shall be elected at the first meeting of the Section
in each year, and discharge the duties usually attaching to those
offices.
3. To bring a paper regularly before the Section it must be sub-
mitted to the Standing Committee on Communications for the
stated meetings of the Society, with the statement that it is for the
Mathematical Section.
4. Meetings shall be called by the Standing Committee on Com-
munications whenever the extent or importance of the papers sub-
mitted and approved appear to justify it.
5. All members of the Philosophical Society who wish to do so
may take part in the meetings of this Section.
6. To every member who shall have notified the Secretary of the
General Committee of his desire to receive them, announcements of
the meetings of the Section shall be sent by mail.
7. The Section shall have power to adopt such rules of procedure
as it may find expedient.
52 (81)
LIST OF OFFICERS AND MEMBERS
MATHEMATICAL SECTION OF THE PHILOSOPHICAL
SOCIETY FOR THE YEAR 1887.
Chairman, Wm. B. Taylor. Secretary, R. S. Woodward.
Abbe, C.
Avery, R. S.
Baker, M.
Bates, H, H.
Billings, J. S.
Burgess, E. S.
Christie, A. S.
Coffin, J. H. C.
Curtis, G. E.
DeLand, T. L.
DOOLITTLE, M. H.
Dutton, C. E.
Eastman, J. R.
Eimbeck, W.
Elliott, E. B.
Farquhar, H.
Flint, A. S.
Gilbert, G. K.
Gore, J. H.
Green, B. R.
Hall, A.
Harkness, W.
Hazen, H. A.
Hill, G. W.
HODGKINS, H. L.
King, A. F. A.
Kummell, C. H.
Martin, A.
Marvin, C. F.
McAdie, A. G.
McGee, W J
Newcomb, S.
Paul, H. M.
Ritter, W. F. M'K.
Robinson, T.
Russell, T.
Smiley, C. W.
Stone, O.
Taylor, W. B.
Upton, W. W.
Wilson, H. C.
Winlock, W. C.
Woodward, R. S.
Ziwet, Alex.
(82)
BULLETIN
OF THE
MATHEMATICAL SECTION,
24th Meeting. February 16, 1887.
The Chairman, Mr. Wm. B. Taylor, presided.
Present, eighteen members and one guest.
The Section proceeded to the election of officers for 1887 by ap-
pointing a Nominating Committee consisting of Messrs. Farquhar,
Baker, and Hill.
The Committee nominated Mr. Wm. B. Taylor for Chairman
and Mr. R. S.Woodward for Secretary ; these nominees were elected
by acclamation.
Mr. M. H. Doolittle read a paper on
ASSOCIATION RATIOS.
[Abstract.]
The present communication is an effort in the direction of a
science of statistics. It includes the principles involved in my
communication* of December 3, 1884, but presents them in a more
general manner.
Suppose that there are s occasions on which the presence or ab-
sence of the phenomena A and B are determined by observation.
Suppose that there are a instances of the occurrence of A, and b
instances of the occurrence of B, each including c instances in which
A is associated with B. There remain s— a— b
-f- c instances in
which A and B are both absent. If a= b = c, the two phenomena
are always found associated, and the association may be regarded
as perfect. If either A or B is ever found alone, the association is
*The verification of predictions. See Bulletin of Phil. Soc. for 1884,
vol. 8, pp. 122-127.
(83)
84 PHILOSOPHICAL SOCIETY OF WASHINGTON.
imperfect. I assume that the extent of association is a quantity
capable of numerical expression, and further assume it = —r.
This is tantamount to the assumption that whenever either of the
c c
ratios or - is constant, the extent of association varies directly as
a f)
the other ratio, and = 1 when they each = 1.
Not-A and Not-B may also be regarded as phenomena whose
presence is equivalent to the absence of A and B and vice versa.
Not-A, therefore, occurs s — a times ; and Not-B s — 6 times. The
following table will hardly need further explanation:
Phenomena. Both occur. Neither occurs. Extent of association.
A and B c s— a — b-\-c —,
ra cyA and Not-B a— c b — c £=
a(s— o)
(h C )»
Not-A and B b — c a— c
Not-A and Not-B s— a— b + c
(s— a) b
(s— a—b + cy
(s— a) (s— b)
For illustration, let blindness and deafness be the phenomena
denoted respectively by A and B. Then the extent of association
c
2
between blindness and deafness = —r\ that between sight and
deafness = -, -r, &c.
(s — a) b
I call the above expressions for extent of association indiscrimi-
nate association ratios. It is important now to understand that the
magnitude of each is determined both by general and special causes.
In an ordinary community the indiscriminate association ratio be-
tween sight and hearing is very large, nearly =1, for the general
reason that most people can see whether they can hear or not, and
most people can hear whether they can see or not. If there is a
special reason why a larger proportion of men able to see than of
blind men shall be able to hear, this special reason will tend to in-
crease the indiscriminate association ratio, and a contrary special
reason will tend to diminish it.
I now seek to obtain a discriminate association ratio, whose
magnitude shall be affected by special causes only, and which may
MATHEMATICAL SECTION. 85
therefore serve as a measure of their efficiency. The general problem
may be stated as follows : Having given the number of instances
respectively in which things are both thus and so, in which they
are thus but not so, in which they are so but not thus, and in which
they are neither thus nor so, it is required to eliminate the general
quantitative relativity inhering in the mere thingness of the things,
and to determine the special quantitative relativity subsisting be-
tween the thusness and the soness of the things.
If no special causes are in operation, the number of instances in
ab
which both A and B occur should be= — according to the general
theory of probabilities. The operation of such causes is therefore
ab
indicated by a difference between the values of c and — Now,J
8
instead of the ratio -, which varies directly as c, let us form a
ratio which shall vary directly as c and which shall — 1
when c= a. These conditions give us the ratio
ab
c i
s cs— ab
a (s— b)
In like manner, instead of the ratio r we have — —. Now, as-
b b (s— a)
suming that whenever either of these derivative ratios is constant,
the required discriminate association ratio varies directly as the
other ratio varies, and that it equals unity when they each equal
(@a (ib*)*
unity, it is found equal to their product = —=—, r^ rr3 * t ab (s— a) (a— by
For the phenomena A and Not-B the number of concurrences
probable from general causes =— -j and subtracting this quan-
s
tity from a — c, from a, and from s— b, the indiscriminate
. . .
(a— c) 2 . (ab— cs) 2 ...
association ratio -^ ,^ becomes —=—: —. rr< which diners
a (s— b) ab {s— a) (s — b)
from the discriminate association ratio for A and B merely in the
algebraic sign of the quantity under the exponent. This is as it
should be. Sight is precisely as favorable or unfavorable to hear-
86 PHILOSOPHICAL SOCIETY OF WASHINGTON.
ing as it is unfavorable or favorable to deafness. In like manner
the same discriminate association ratio is obtained for the phenomena
Not-A and B, and for Not-A and Not-B. The logical relation be-
tween sight and hearing is just as close as that between sight and
deafness, as that between blindness and hearing, and as that be-
tween blindness and deafness. It is in fact the same relation stated
in different words.
The sum of the four indiscriminate association ratios is
c
2 (a— c)2 (b— cy (s— a— b-{-cy
==1 (cs
— ab?
ab a (s— b) (s— a) b (s— a) (s— b) ab (s— a) (s— b)
Hence the discriminate association ratio = the sum of the indis-
criminate association ratios — 1. Since every instance of A or of
Not-A is necessarily associated with an instance of B or of Not-B
and every instance of B or of Not-B is necessarily associated with
an instance of A or of Not-A, this alternative association is perfect,
and its extent = 1 whatever A and B may denote. The excess of
the sum of the indiscriminate association ratios above unity may,
therefore, be taken as a measure of that portion of the aggregate
which is peculiar to any special signification of A and B. Such
association as belongs necessarily to any two classes of phenomena
whatever having been eliminated, the discriminate association ratio
measures that residue which indicates special relations.
I call c the concurrence residual. If c is less than — , the
s s
concurrence residual is negative and indicates that special causes
prevent oftener than they produce positive association between A
and B. If e= and a = s — b, the negative association (or disso-
ciation) is perfect, and the discriminate association ratio =1. These
conditions signify that the two phenomena are never both present
and are never both absent.
Denoting the discriminate association ratio by y, the concurrence
residual by x, and the class residuals a and b respect-
ively by a and /?, we have the equation
x
2
and regarding x and y as variables and a and p as constants this
equation is represented in Cartesian co-ordinates by a parabola.
MATHEMATICAL SECTION. 87
The value of the discriminate association ratio is not affected by
interchange of a and b. It is assumed that association and recip-
rocal association are equal.
The concurrence residual is significant in proportion to its square;
and this is in accordance with the general comparative importance
of residuals in the theory of least squares.
When s is infinite, with a, b, and c each finite, the discriminate
c
2
association ratio reduces to the indiscriminate -y. In this case the
ab
chances are as infinity to one against fortuitous concurrence ; and the
extent of association must be regarded as based wholly on special
relations.
This paper was briefly discussed by Messrs. Gilbert, H. Far-
quhar, Baker, and the author.
25th Meeting. March 2, 1887.
The Chairman presided.
Present, twenty-one members and two guests.
A symposium was held on the following problem in probabilities:
one-third of the apples on a tree are rotten and one-
fourth are wormy, what is the probability that an apple
taken at random from the tree will be (1) rotten only;
(2) wormy only; (3) both rotten and wormy; and (4)
SOUND ?
The discussion was begun by Mr. M. Baker who gave an analyt-
ical statement of the conditions of the problem and concluded that
the problem was an indeterminate one until some assumptions were
introduced. Without introducing anything additional to that stated
he concluded that the four probabilities were respectively
_?_^ _?_^ _d ± _dPi- 4 s ;^2- 3 s ; Vz- s 12 ; Pi- s ;
where d = the number of sound apples and 8 the total number of
apples.
88 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Mr. Doolittle, proceeding on the hypothesis that the problem
is indeterminate, gave an infinite series of possible values for the
respective probabilities. But he thought the problem should be
understood as determinate, and assigned -A- as the proper value for
the third probability.
Mr. Hill expressed the opinion that the probability TY for a
rotten and wormy apple is the proper value, but gave a solution of
the problem by means of double integrals which brought out a dif-
ferent result.
Messrs. Curtis, Elliott, and Farquhar gave different solutions
leading to y
1
^- for the third probability.
Mr. Farquhar objected to the result i as involving the absurdity
that if one-fourth are wormy the probability of the combination is
exactly the same for all values of the rotten between £ and f ; and
also further objected to calling a probability " indeterminate " be-
cause it was not a certainty.
Mr. Martin gave a brief history of the problem, which appeared
originally in his Mathematical Visitor,* and of which he gave three
solutions leading to £ for the third probability. He stated that the
correctness of his solution depended on the correctness of the view
that all possible values of any one of the probabilities are equally
probable.
The subject was further discussed by Messrs. Gilbert, Christie,
and Woodward.
Mr. Hill also read a letter from Prof. A. Hall relating to the
problem.
The discussion was closed with some remarks by the Chairman
on the language of the problem and its proper interpretation.
* The Mathematical Visitor; edited and published by A. Martin. 4°.
Erie, Pa. 1881. Vol. 1, No. 4, January, 1880, p. 115, problem 180; solu-
tions pp. 180-181.
MATHEMATICAL SECTION. 89
26th Meeting. March 16, 1887.
The Chairman presided.
Present, sixteen members.
Mr. Christie read a paper on
A PROBLEM IN PROBABILITIES.
In this paper he reviewed the conditions of the question in prob-
abilities discussed at the previous meeting. He considered it a
question susceptible of a definite answer, dependent only on a logi-
cal and mandatory application of the elementary principles of prob-
ability. In his analysis he derived expressions for the possible
combinations of the several events and deduced therefrom a func-
tion representing the probability of the probability of the compound
event (rottenness and worminess), the variable in this function being
the probability sought. The value of the variable making the func-
tion a maximum was taken as the required probability, the result
being j\.
If n = total number of apples, r — number rotten, w = number
wormy, x= number both rotten and wormy, then
and the chance of a particular apple being both rotten and wormy
is -. When x1 and x" are integral the chance is either —or — , that
n n n'
a/+ x"
is
—
J—
• When n, r, w are all infinite, the case of continuous
rw
number, this chance is —=-.
n?
Mr. Stone took the ground that the problem is susceptible of but
one interpretation, and gave a geometric solution leading to TV for
the probability of the compound event. He also gave some in-
stances of allied questions in dependent probabilities.
An animated discussion, extending over the remaining time of
the meeting, then followed. Of those who participated in the dis-
cussion, Messrs. Christie, Curtis, Doolittle, Elliott, Hill,
Kummell, Stone aud Ziwet considered the problem determinate,
while Messrs. Baker, Harkness, and Woodward considered it
indeterminate.
90 PHILOSOPHICAL SOCIETY OF WASHINGTON.
27th Meeting. March 30, 1887.
The Chairman presided.
Present, twelve members and two guests.
Mr. R. S. Woodward read a paper on
THE FREE COOLING OF A HOMOGENEOUS SPHERE INITIALLY
HEATED TO A UNIFORM TEMPERATURE.
[This paper appeared in full in the Annals of Mathematics. 4°. Char-
lottesville, Va. 1887, June ; vol. 3, no. 3, pp. 75-88. Also separately-
printed.]
Remarks were made on this paper by Messrs. Kummell, Hill,
and the Chairman. ,
Mr. Kummell read a paper on
THE BRACHISTHODE ON THE HELICOID.
[Abstract.]
The characteristics of this class of curves and the methods of com-
puting their lengths in the several cases were explained and dis-
cussed. Accurately constructed stereoscopic diagrams of several of
these curves were exhibited.
[This paper is expected to appear in the Mathematical Visitor.]
28th Meeting. April 13, 1887
The Chairman presided.
Present, nineteen members and one guest.
Mr. G. W. Hill read a paper on
THE MOTION OF HYPERION.
Although designed to meet the special case presented by Hyperion,
Mr. Hill's paper treated the general problem of three bodies under
the restrictions that they are all nearly in the same plane and that
MATHEMATICAL SECTION. 91
the mass of the one whose motion is sought is negligible in compar-
ison with the masses of the other two. The potential function for
the disturbed body was put in a general form for the purpose of
ascertaining the most advantageous variables for its development,
and some of the particular forms were derived and discussed. Mr.
Hill also indicated the methods which might be most advantage-
ously followed in the application of his theory to Hyperion.
This paper was discussed by Mr. A. Hall, who alluded to the
unique character of the motion of Hyperion, and stated some of the
more interesting facts concerning the observations of this satellite
and the failure of the theories thus far advanced to represent its
motion.
Other remarks were made by the Chairman and Mr. Woodward.
[This paper appeared in full in the Annals of Mathematics. 4°. Char-
lottesville, Va. 1887, June ; vol. 3, no. 3, pp. 65-73. Also separately-
printed.]
Mr. A. Hall presented a paper* on
THE PARALLAX OF a TAURI.
He gave a historical account of the early attempts at the deter-
mination of stellar parallax together with some of the results at-
tained. He exhibited in tabular form the principal data on which
his value for the parallax of a Tauri depends. In contrasting his
result with the larger value for the same star determined by Struve
he stated that his values for parallax are generally smaller than those
of other observers.
The brief discussion which followed was participated in by Messrs.
Eastman, Paul, and others.
29th Meeting. April 27, 1887.
The Chairman presided.
Present, thirteen members.
Mr. A. S. Flint read a paper on
the most probable value of the latitude and its theoret-
ical WEIGHT FROM ENTANGLED OBSERVATIONS OCCURRING IN
THE USE OF TALCOTT's METHOD.
In this paper Mr. Flint showed first how to express the weighted
92 PHILOSOPHICAL SOCIETY OF WASHINGTON.
mean value of the latitude and its weight in the most general case
of entanglement in terms of the results from individual pairs of
stars and their symbolical weights. To find the numerical values
of these symbolical weights he made use of the principle that
the weights of the individual results must be such as to make the
probable error of the weighted mean a minimum. After treating
the most general case he considered some of the speciahcases occur-
ring most commonly, and deduced practical formulas for computing
the weights of individual results. In illustration of his methods he
gave the details of the numerical operations in one of the more com-
plex cases presented in actual work.
In the discussion which followed, Mr. Harkness derived, by a
different and less complex process, some of the formulas given by
Mr. Flint. Others participating in the discussion were Messrs.
Paul, Farquhar, Stone, and Woodward.
Mr. E. B. Elliott began the presentation of a paper on
THE MUTUAL ACTION OF ELEMENTS OF ELECTRIC CURRENTS.
30th Meeting. May 11, 1887.
The Chairman presided.
Present, ten members and two guests.
Mr. E. B. Elliott continued his paper on
THE MUTUAL ACTION OF ELEMENTS OF ELECTRIC CURRENTS.
He stated that Ampere's theory of such currents involves the
assumption that the action between the elements is limited in direc-
tion to the line joining them. In conformity with this assumption
the result reached by Ampere, and now usually given in text
books, is that the action is proportional to
§ cos cos 6'— sin sin 0' cos u>,
in which and 6' are respectively the angles between the directions
of the elements and the line joining them, and w is the angle be-
tween the two planes defined by the directions of the elements and
the line joining them.
MATHEMATICAL SECTION. 93
In his own investigation Mr. Elliott makes no assumption or
restriction with reference to the direction of the action of the ele-
ments and finds the action proportional to the following expression
:
(cos
-f- sin . i) (cos 0' -\- sin 0' cos w . i -}- sin 0' sin u> . j)=
cos cos 0' — sin sin tf cos <a
-+- (sin cos (f + cos sin & cos w) i
+ cos sin 0' sin to . j
4- sin sin 0' sin w .ij.
In this expression 0, 0' and a> have the same signification as stated
above, and i,j and ij (or its equivalent k) are quadrantal versors.
The first term of this formula represents action in the line joining
the elements ; the second term represents action in the plane of the
connecting line and one of the elements and perpendicular to the
connecting line ; the third term represents action in a direction at
right angles to the plane just mentioned ; and the fourth terra rep-
resents torsion in a plane perpendicular to the connecting line.
The actions resulting in some special cases, as when the elements
lie in one plane, etc., were explained and discussed.
[This paper was presented to the American Association for the Advance-
ment of Science at its New York meeting, August, 1887, and appeared in
the Electrical World; a weekly review, etc. fol. New York, 1887, Au-
gust 27 ; vol. 10, no. 9, p. 116. Also separately printed.]
Mr. Hill, following Maxwell, gave some of the principal steps
in the process which leads to Ampere's result, indicating that that
process differs from Mr. Elliott's in leaving out of account cer-
tain couples and in assuming a certain undetermined quantity to
be zero.
The paper was further discussed by Mr. Harkness, the Chair-
man, and others.
Mr. Doolittle began the presentation of a paper on
association ratios.
94 PHILOSOPHICAL SOCIETY OF WASHINGTON.
31 st Meeting. May 25, 1887.
The Chairman presided.
Present, sixteen members and one guest.
Mr. M. H. Doolittle continued his paper on
ASSOCIATION RATIOS,
which consisted chiefly in a review and criticism of an article* by-
Mr. G. K. Gilbert on Finley's Tornado Predictions. The follow-
ing is an abstract of Mr. Doolittle's paper
:
By Mr. Gilbert's notation
:
s = whole number of predictions.
p = number of positive predictions.
o = number of occurrences.
c= number of verifications of positive predictions.
p' = s — p = number of negative predictions.
o' = s — o — number of non-occcurrences.
o — c = " measure of the failure in inclusion."
p — c = " measure of the failure in exclusion."
We should also have for consistency
c = measure of success in inclusion.
c' = s — o — p + c= measure of success in exclusion.
He says, "If inclusion and exclusion are equally important their
measures bear the same weights." This is as true for success as for
failure, but Mr. Gilbert gives to the measure of success in exclusion
no weight whatever, and entirely disregards it.
He has
o -(- p — 2c = measure of the general failure of prediction.
We should also have
s — o — p-\-1c= measure of the general success in prediction.
The latter measure consists of the "favorable cases;" the former
* American Meteorological Journal. 8°. Detroit, Mich., 1884, Sep-
tember; vol. 1, no. 5, pp. 166-172.
MATHEMATICAL SECTION. 95
of the "unfavorable;" and the "ratio of verification (the favorable
cases divided by the sum of the favorable and unfavorable," becomes
s — o — p + 2c c-\-c
v = -
—
= —!
s s
And this is Mr. Finley's method of computation.
Mr. Gilbert then employs a process to which he gives no name,
but which may be called the elimination of hypothetical chance.
on
He estimates that — verifications of positive predictions might
have been expected if the same number of positive predictions had
been made at random, and sets these cases aside as proving neither
discrimination nor want of it. In effect, he subtracts — from each
s
of the quantities o, p, and c, and proceeds with the residuals. This
portion of his reasoning is regarded as sound, and the process may
be applied with great utility to properly formed ratios.
The ratio v is k
c-\- c' c + c'
s
~p-\rp'
op
To eliminate hypothetical chance, — should be subtracted from
o'p'
each of the quantities c and p, and — from c' and p'. Denoting
the result by
96 PHILOSOPHICAL SOCIETY OF WASHINGTON.
under others, and it is not maintained that it has any scientific
value.
Mr. Gilbert says that he hopes " to show that Mr. Finley's method
involves a serious fallacy. This fallacy consists in the assumption
that verifications of a rare event may be classed with verifications
of the predictions of frequent events without any system of weight-
ing." It is not perceived that Mr. Gilbert has furnished any such
system. The fallacy, perhaps, consists rather in the supposition
that any valuable result can be obtained by averaging the percent-
ages of verification of heterogeneous classes of predictions. Mr.
Finley correctly computed his indiscriminate percentage of verifi-
cation, and thereby furnished a striking and, perhaps, much-needed
illustration of the*worthlessness of such computations. The elimi-
nation of hypothetical chance from such mixed percentages merely
renders their worthlessness less apparent.
This paper was briefly discussed by Messrs. Curtis, Farquhar
Hill, Baker, and Woodward.
Mr. H. Farquhar presented a solution and generalization of a
problem, proposed in Science* requiring the division of a rectangle,
by a single step-cut, into two parts which when put together will
form a square.
Mr. Marcus Baker presented a communication on
A COLLECTION OF SOLUTIONS OF THE TRISECTION PROBLEM.
[Abstract.]
The communication consisted of an informal statement from notes
and memoranda of progress in the direction of an exhaustive col-
lection of real solutions of the problem to trisect an angle. It was
pointed out that, though the problem was a very old and very
famous one, energy is constantly wasted in its study by those igno-
rant of what has been done, and that this misdirected energy might,
in large part, be due to the want of any satisfactory digest of results
hitherto attained. The author had himself felt the need of such a
digest, and, finding none, had some years ago begun a collection of
* See Science. 4°. New York, 1887, May 20; vol. 9, no. 224, p. 488,
query 5.
MATHEMATICAL SECTION. 97
notes and memoranda, with a view to the preparation of a fairly
complete collection of solutions of the problem and the preparation
of a bibliography.
Progress in the work had been slow, and the results are still very
incomplete, especially the bibliographic part, which was deemed the
most important.
The present collection of notes contained about a dozen different
solutions of the problem and a suggested classification for a digest
of the subject as follows
:
1. Historical Introduction.
2. Trisection by the conic sections.
3. Trisection by special or higher curves.
4. Trisection by mechanical devices.
5. Trisection by approximation.
6. False trisections.
7. Bibliography.
Of the trisections by the conic sections five were enumerated,
viz
:
1. By parabola and circle.
2. By parabola and parabola.
3. By parabola and hyperbola.
4. By the equilateral hyperbola.
5. By the hyperbola, whose asymptotes form an angle of 120°.
Trisections by the following curves were also enumerated
:
1. Conchoid of Nicomedes.
2. Conchoid on circular base = trisectrix = planetary curve of
Ptolemy = special case of limacon of Pascal.
3. Cycloid.
4. Epicycloid or trochoid.
5. Quadratrix of Dinostratus or Hippias of Elis.
6. Quadratrix of Tschirnhausen.
7. Spiral of Archimedes.
Respecting the cissoid of Diodes, it was remarked that no solu-
tion of the trisection problem, by its aid, had been found. Also
respecting the cycloid, which Sir Isaac Newton is said to state may
be used to trisect an angle, no solution by means of it had been
found, but the author had himself made one recently.
53
98 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Of the various mechanical devices used for trisection the liukage
of Thomas of Ceva was given, others being referred* to only.
Of false trisections, the number was stated to be very large and of
unequal value, some giving close approximations and others failing
ignominiously. Finally, in the bibliography, now containing some
fifty references, and believed to be only the beginning of a reason-
ably full list, it was proposed to make an authors' catalogue of en-
tries, and to follow each reference with a very brief characterization
of the contents of the article.
The foregoing scheme had been laid out but latterly had made no
progress, and the opinion of the section was sought as to the desira-
bility or advisability of carrying the work on.
Mr. Curtis made the following remarks:
Six or eight years ago I began a similar collection of trisection
methods, in looking over which I find a number of solutions addi-
tional to those presented by Mr. Baker.
The following six belong to the class in which an angle is trisected
by means of curves :
(1) ^-\- x2y — axy -\-hx
2
= o
;
the ophiuride of Dietrich Uhlhorn (1764-1837).
(2a2
-f)\(2) x = 4a2— ?/2
the polyode of Dr. "Win. Hillhouse,* Prof. J. W. Nicholson,f J. Bruen
Miller.J
(3) Ax2 + 12?/ 2= (1/1^4. yy_ Sy i/T=tf+ 4.
Dr. Wm. Hillhouse.
(4) [Curve drawn, but equation not given.] Ibid.
*The Analyst; edited and published by J. E. Hendricks. 8°. Des
Moines, Iowa. 1882, November, vol. 9, no. 6, pp. 181- i 84. See also same.
1876, September, vol. 3, no. 5, p. 151.
f Same. 1883, March, vol. 10, no. 2, pp. 41-43. See also The Multisector
and Polyode. By Prof. J. W. Nicholson, M. A., Professor of Mathematics.
Louisiana State University. 8°. New Orleans
;
published at the Times-
Democrat. 14 pp.
% Van Nostrand's Engineering Magazine. 8°. New York, D. Van Nos-
trand, 1880, March, vol. 22, no. 135, pp. 206-209.
MATHEMATICAL SECTION. 99
t+ivr-^+q-y) V2 2 >m
(6) x
2
-\- (Sy— 4ff = r2 im
Dr. William Hillhouse, of New Haven, has not only shown that
the last five curves may be used for trisecting an angle, but has
devised instruments for describing them. This latter step, as I
view the problem of trisection, is a necessary part of any real solu-
tion by means of curves. The simple determination of the equations
that will satisfy the analytical conditions of trisection, without the
instrumental means for describing the curves, does not constitute a
solution of the problem. It is essentially something to be done, not
something merely to be proved, and its fame arises from the im-
possibility of making the trisection of an angle by means of a ruler
and pair of compasses. Any proposed solution, therefore, must in-
dicate a geometrical instrument for accomplishing it, and the nature
of the motion applied therein determines the character of the solu-
tion.
A class of solutions, regarded the most elegant of all, is that in
which link machines trisect the angle directly, without the aid of
interposed curves. Of this class I have found three instruments,
invented respectively by the Marquis de l'Hopital (1661-1704),
A. B. Kempe, and Professor Sylvester. That of l'H6pital is a com-
bination of link and sliding motion ; those of Kempe and Sylvester
are pure linkages. With respect to the two, latter, I wish to call
attention to the elementary character of the solution. Euclid's
postulates require us to be able to draw a straight line and a circle,
and it is frequently assumed that they imply the use of a straight-
edge and a pair of compasses. But, manifestly, any other instru-
ments that can describe the circle and the straight line satisfy
equally the requirements of the postulates. Moreover, the use of a
straight edge assumes as accomplished the very thing proposed to
be done ; whence the straight-edge is not an original instrument
for describing a straight line. Such an instrument is given by the
linkage of Peaucellier. More originally, therefore, than by the
straight-edge, the postulates of Euclid may be assumed to imply
the use of pure link motion. Wherefore, if pure link motion be
considered as postulated by Euclidian geometry, the trisection of
an angle becomes one of the simplest of geometrical problems.
100 PHILOSOPHICAL SOCIETY OF "WASHINGTON.
Mr. Kummell remarked that the supposed analogy between the
duplication of a cube and the trisection of an angle 'does not exist,
since the latter requires a cubic with three real roots, while the
former requires a cubic having one real and two imaginary roots.
The subject was further discussed briefly by the Chairman aud
Mr. Bates.
32d Meeting. October 19, 1887.
The Chairman presided.
Present, sixteen members and one guest.
Mr. G. W. Hill read a paper on
THE INTEGRATION OF DIFFERENTIAL EQUATIONS ADMITTING PE-
RIODIC INTEGRALS.
[Abstract.]
The independent variable being conceived as time, a system of
ordinary differential equations may be said to admit periodic inte-
grals when the values of the dependent variables, either exactly or
with an approximate tendency, after a certain lapse of time, repeat
their series of values. In the latter case the longer the lapse is
made the more nearly is the repetition brought about. Strange as
it may seem, this subject, except in the case of simply periodic inte-
grals, is, at present, not completely understood. The text-books on
differential equations are almost wholly engaged with the cases,
which, by certain artifices, can be integrated in finite terms or re-
duced to quadratures. In the treatment of physical problems,
however, we seldom meet with equations of this class. Far more
frequently it is found that methods of approximation must be re-
sorted to. Cauchy appears to be the author who has done the most
for the elucidation of this part of the subject. His memoirs are in
his later Exercises and in the volumes of the Comptes Rendus for
1856 and 1857.
In this paper the mode in which simply periodic integrals arise
was discussed, and the theory afterwards illustrated by treating the
following problem:
Find the conditions of motion of any number of material points mov-
MATHEMATICAL SECTION. 101
ing about a centre under the action of central forces whose potential is
a function of the sum of the squares of the radii vectores.
The differential equations of this problem, in the case where the
radii are supposed to describe no areas, were first integrated by
Binet* But the addition to the forces of the terms arising from cen-
trifugal action much enhances the interest of the problem.
The chief point of interest brought out by the solution was that
while the directions of the points, whether as seen from the centre
or from each other, all return to the same values after the lapse of
a certain time, as do also the ratios of the radii vectores, the absolute
values of the latter have all a factor whose period is generally dif-
ferent from the former. Thus the movement of the system may be
conceived as taking place under the operation of two distinct causes,
viz : the first producing a revolution of all the points about the
centre in closed curves in the same time, while the second, having a
different period, changes the scale of representation of the system in
space.
[This paper appeared in full in the Annals of Mathematics. 4°. Char-
lottesville, Va. 1887, October; vol. 3, no. 5, pp. 145-153.]
Mr. Hill's paper was briefly discussed by Mr. A. Hall and the
Chairman.
Mr. A. Hall read a paper on
EULER's THEOREM (GENERALLY CALLED LAMBERT'S).
[Abstract.]
This theorem is well known to astronomers and is very useful in
computing the orbits of comets. The time of the passage of the
comet from one point to another of its orbit is expressed by means
of the two radii vectores drawn to the points, and the chord joining
these points. For many years, and by irikny writers even of the
present time, this theorem is attributed to Lambert. Mr. Hall
stated that it was first given by Euler about 1743. He gives two
proofs for the parabola, and then extends the theorem to the
ellipse. For this case Euler gives first an expression for the peri-
helion distance in terms of the sum of the two radii vectores and
the chord. He then gives an approximate expression for the time
of describing the arc in terms of the perihelion distance, the radii
* Journal de mathematiques
;
par J. Liouville. 4°. Paris, 1837. 1st
series, vol. 2, p. 457.
102 PHILOSOPHICAL SOCIETY OF WASHINGTON.
vectores and the eccentricity of the ellipse, and directs us to sub-
stitute the value of the perihelion distance. Euler does not, there-
fore, give an explicit expression for the time in terms of the radii
vectores and the chord, although he points out how this may be
done. Considering the results that he obtained, Mr. Hall thinks
that this theorem, with respect to all the conic sections, should be
known by the name of Eider.
Remarks on this communication were made by Messrs. Hill,
Stone, and Winlock.
33d Meeting, November 2, 1887.
The Chairman presided.
Present, fifteen members and one guest.
Mr. E. B. Elliott gave a brief description of a new form of com-
puting machine, which prints and arranges in the usual form for
addition any series of numbers and then prints their sum, the work
of the operator being merely mechanical as in the use of the type-
writer. Although designed especially for performing aud printing
work in addition, the machine may also be used for multiplication
and division.
Mr. Wm. Harkness presented a paper on
THE CONSTANT P IN OBSERVATIONS OF TERRESTRIAL MAGNETISM.
It was explained that this paper arose from a correspondence in
Nature concerning the modes of computing the constant. In a letter
published in the number of that journal for August 18th, 1887, Mr.
Harkness referred to an expression for P given in Stewart and
Gee's Practical Physics, and suggested a more convenient form for
logarithmic computation. In the number for September 8th, Mr.
William Ellis gave another but somewhat less accurate expression
for the computation of P; and in the number for September 29th,
Prof. Arthur W. Rucker gave what he considered a more accurate
expression than either of the others.
Starting from the fundamental equations of Gauss, Mr. Hark-
ness derived a formula for P correct to terms of the second order
inclusive. He then showed that Riicker's formula, which pur-
MATHEMATICAL SECTION. 103
ported to give terms of the second order, was incorrect, and pointed
out that the error in Riicker's process consisted in expanding to
terms of the second order an expression which included only terms
of the first order.
This paper was briefly discussed by Messrs. Hall, Abbe, Kum-
mell, and Harkness.
This and other related papers appeared in Nature*
Mr. R. S. Woodward read a paper on
THE CONDITIONED COOLING OF A HOMOGENEOUS SPHERE.
The salient features only of this paper were presented. The funda-
mental assumptions and analytical conditions of the problem were
indicated, and especial attention was directed to the distinction be-
tween the case of " conditioned cooling" and that of "free cooling,"
which latter was discussed by the author, at the 27th meeting of
the section. It was shown that the solution for the more complex
case of " conditioned cooling " is derivable by a comparatively simple
process from the solution for "free cooling." The probable discrep-
ancy between the data presented by the earth as a cooling sphere
and those assumed in the solution of the problem, and the additional
data requisite for a more complete solution were pointed out.
The presentation of the paper was followed by an informal dis-
cussion participated in by nearly all present. This discussion re-
ferred chiefly to the physical features of the earth as a cooling sphere,
and served to disclose a diversity of opinion concerning the con-
ductive and convective properties of such large masses.
[This paper appeared in full in the Annals of Mathematics. 4°. Char-
lottesville, Va. 1887, October; vol. 3, no. 5, pp. 129-144.]
* Nature, a weekly illustrated journal of science. 4°. London, 1887-1888.
1887, Aug. 18, vol. 36, no. 929, p. 366. On the constant P; by Wm. Harkness.
Sept. 8, vol. 36, no. 932, p. 436. Same; by Wm. Ellis.
Sept. 29, vol. 36, no. 935, p. 508. Same ; by A. W. Riicker.
Dec. 8, vol. 37, no. 945, pp. 127-128. Same ; by Harkness and re-
joinder by Riicker.
1888, Jan. 19, vol. 37, no. 951, pp. 272-273. Same; by Harkness and re-
joinder by Riicker.
104 PHILOSOPHICAL SOCIETY OF WASHINGTON.
34th Meeting. November 16, 1887.
The Chairman presided.
Present, ten members.
Mr. Ormond Stone read a paper on
THE ORBIT OF HYPERION.
[Abstract.]
The principal difficulty in the integration ofthe equations of motion
in the case of the problem of three bodies arises in the integration of
terms involving the inverse powers of the distances between the dis-
turbed and disturbing bodies. When the ratio between the radius
vectors is not too near unity, the inverse powers referred to can be
developed in rapidly converging series in terms of cosines of multiples
of the elongation. When, however, these ratios do not differ greatly
from unity the convergence of the series mentioned is very slow. If,
in addition, the mean motions of the two bodies are nearly com-
mensurate, the ordinary methods of solving the problem become in-
applicable.
Such a case presents itself in the determination of the perturba-
tions of Hyperion produced by Titan. On the other hand the mutual
inclination of the orbits of these satellites is so small as to have eluded
detection ; the eccentricity of the orbit of Titan is less than 0.03, and
the position of the aposaturnium of Hyperion so nearly coincides,
at least at present, with the point of conjunction of the two satellites
as to give rise to a suspicion that the eccentricity of its orbit is, in
reality, small, and that the apparent eccentricity is principally due
to the perturbations produced by Titan.
In view of these circumstances, that part of the disturbance has
been investigated, which may be determined by neglecftng the mutual
inclination and the eccentricities of the orbits of both bodies, reserv-
ing a discussion of the remaining portion for another paper. It was
accordingly assumed that
r = a (1 + ar cos -f a2 cos 20 -f- ... ),
_ = n (1 + n r cos -f n2 cos 20 -J- . . . )
;
where r and w are the radius vector and longitude in orbit of Hype-
rion, is the mean angular distance between the radius vectors of
MATHEMATICAL SECTION. 105
Titan and Hyperion, a and n are the mean values of r and w, and
av nlt etc., are constants to be determined. In the differential equa-
tions of motion for r and w, those terms not containing explicitly the
mass of Titan were expanded by Taylor's theorem into series of
sums of terms containing cosines of multiples of affected with con-
stant coefficients ; while the terms containing the mass of Titan ex-
plicitly were expanded mechanically into a series of cosines of mul-
tiples of by means of assumed values of the coefficients. Equating
the coefficients of the cosines of equal multiples of 0, a number of
equations were obtained from which to derive a corresponding num-
ber of the quantities av nlf etc. With these new values were ob-
tained and the process repeated. Instead, however, of considering
in' (the mass of Titan) as known, a3 was assumed to be given and m'
was considered as one of the unknowns.
[This paper appeared in full in the Annals of Mathematics. 4°. Char-
lottesville, Va., 1887. Vol. 3, No. 6, p. 161.]
Brief remarks on Mr. Stone's communication were made by the
Chairman and by Messrs. Baker, Hill, and Kummell.
Mr. E. B. Elliott presented a paper on
the quotients of space-directed lines.
He wrote down some of the fundamental relations of this analy-
sis and explained the nature and properties of the special symbols
employed. He called attention to the lectures of Hamilton on
quaternions, and to his "letters" on the same subject, as they ap-
pear in Nichol's Cyclopaedia;* and commented on the transition
from Hamilton's primary conception of a quartemion as a quotient
of two directed right lines in space to his secondary conception of
a quaternion as the sum of a directed right line and a number.
The presentation of this paper was followed by a discussion, in
which Messrs. Baker, Hill, Stone, Woodward, and the Chair-
man participated.
* See A cyclopaedia of the physical sciences, etc., by J. P. Nichol. * *
8°. London and Glasgow, 1857. pp. 625-628.
106 PHILOSOPHICAL SOCIETY OF WASHINGTON.
35th Meeting. November 30, 1887.
The Chairman presided. «
Eleven members present.
Mr. E. B. Elliott continued his remarks, begun at the last
meeting, on
THE QUOTIENTS OF SPACE-DIRECTED LINES.
[Abstract.]
Mr. Elliott said that the quotient of two space-directed lines is
not a line, but is abstract. It is a quantity which applied as a mul-
tiplier to one of the space-directed lines will produce the other.
He then gave as an illustration of this principle its application to
the problem of the mutual action of the elements of electric currents.
Let [i and p! represent, respectively, in length, current strength,
and direction, two elements of electric currents.
P and p' represent, respectively, in length and direction, the
lines connecting the centers of the elements.
represent the angle made by the element p. with the line
connecting the elements p and // ; that is, with p.
4> represent the angle made by the element pf with its rectan-
gular projection in the primary plane ; that is, the plane
determined by the element p. and the connecting line p.
<p represent the angle made in the primary plane by the rec-
tangular projection of the element p! and the connecting
line p*.
The effect of the action of p on pr will be as the product of the
current strength, the length, and the direction of the elements, and
inversely as the square of the distance, and the direction of the ac-
tion will be expressed'by the following formula
:
TJ - X U— = cos cos <p cos <p — sin cos <J> sin <p
P P
-j- [cos cos <p sin <p
-f sin cos <j> cos <p] i
-j- cos 6 sin (p . j
-f- sin sin <p . ij;
in which the first line denotes action (transference) in the direction
of the line connecting the centers of the elements ; the second line
MATHEMATICAL SECTION. 107
denotes action (transference) in the primary plane, but perpendic-
ular to the direction of the connecting line ; the third line denotes
the actjpn (transference) perpendicular to the connecting line in a
plane perpendicular to the primary plane ; the fourth line denotes
action (torsion) in a plane perpendicular to the primary plane.
If instead of the angles <p and <p the angles 0' and <o are used, tf
denoting the angle made by pf, with the line connecting the centers
of the elements, that is, with p' ; and u> denoting the angle which the
plane of // and p' makes with the plane of p. and p, the direction
of the resulting action will be expressed by the following formula:
U-XU-? = cos cos (?— sin sin (f cos <o
P P
-\- [sin 6 cos d'-\- cos 6 sin 0' cos <u] i
+ cos sin 0' sin m .j
+ sin sin 6' sin w . ij.
The values of the four parts of this formula are identical, respect-
ively, with the corresponding parts of the former one.
The mutual action of the unit - right - quotients (or quadrantal
versors) i, j and ij are such that i2 = — 1 ; j2= — 1 ; and ij (or its
substitute k2) = — 1, from which it readily appears that ij= k=
— ji; jk=i= — Id; and ki =j= — ik.
Brief remarks on Mr. Elliott's paper were made by the Chair-
man and by Mr. Christie.
Mr. Artemas Martin presented a paper on
methods of finding nth-power numbers whose sum is an
nth-power; with examples.
[Abstract.]
First method:
Let l n + 2n + 3n + 4" + . . . . xn = Sx>n
and assume the auxiliary formula
(p + q)
n
-pn= a; ... (1)
also assume d such that
S„ „,— a = d,
x, n '
whence
&
x
,
n-d+Pn= (P + <iy. • • (2)
108 PHILOSOPHICAL SOCIETY OF WASHINGTON.
The solution now consists in determining by trial whether d can
be separated into ?i'*-power numbers, all different.
Second method: •
In equation (1) a may sometimes be separated by trial into
n'*-power numbers, all different.
Third method:
Assuming bn nearly equal to but less than S x n , and putting r for
the difference, we have
S,,*- *• = &"• ... (3)
In formula (1) p and q may be any numbers chosen at pleasure.
In formula (2) x should be chosen equal to or greater than the
number of powers sought, and p and q any numbers that will give
d positive, provided p be not less than x.
Iu formula (3) b must be greater than x.
Formulae (1) and (2) are taken from Dr. Hart* who has treated
the cases of squares and cubes at some length. Formula (3) is found
to be especially serviceable if a large number of powers is sought.
Examples.—The values of Sx n for n= 2, 3, 4, and 5, respectively,
are here set down for reference as follows
:
S
x. 3 =-K(z+1) 2 ;
S
*, 4
= inr * (6**+ 1W+ 10z2- 1)
;
I. w=2:
Ex. 1. Using formula (2) assume x = 5, p = 6, and q=l.
Then d = 42, which by trial is found equal to
l 2 + 42+ 52 , whence
22 + 32
-f 6
2 = 7 2 .
*See The Mathematical Magazine. Edited and published by Artemas
Martin. 4°. Erie, Pa. 1882-1884. Vol. 1, No. 1 [January, 1882], pp. 8-9,
and No. 11 [July, 1884], pp. 173-176.
MATHEMATICAL SECTION. 109
Ex. 2. Using formula (1) assume p = 8 and q = 3 ; whence
a = 57, which is by trial found equal to l 2 -j- 22 +
42+62 and
l 2+22+42 +6 2+8 2 =ll\
ifo. 3. Using formula (3) assume x= 50 and 6 = 206; then
r= 489, which by trial is found equal to
l 2 + 22 + 222 or 52 + 82+ 202, etc.
;
whence we have two sets of 47 numbers, the sum of
whose squares is a square.
Ex. 4. Using formula (3) assume x= 100 and 6 = 1750;
then r = 2850, which by trial is found to equal
42+52 +532 ; whence
l2+22+32+62+72+ ...
+ 522+54a+ +1002 =17502
II. n = Z:
Ex. 1. Using formula (2) assume x= 5, p= 5, q=l, whence
d = 134, which by trial is found equal to l 3+23+ 5s
,
whence
33+43+53=63 .
Ex. 2. Using formula (1) assume^)= 8, q= l, whence a=217,
which by trial is found to equal l 3-{- 63 ; hence
r+33+4s+5 3+83=93.
Ex. 3. Using formula (3) assume x = 100 and b — 294
;
whence r= 90 316, which by trial is found to equal
13+ 63+ 113+ 21 3+ 433 , whence
23+
. .
53+73+ . . 103+123+ . .
203 + 223+ . . 423 + 44s . . + 1003= 2943 .
Ex. 4. Using formula (3) assume x =1000 and 6 = 6303;
whence r= 5 869 873, which by trial is found to
equal l 3 + 23 + 103+ 163+ 323+ 1803 ; hence,
33 +..93+ ll3 + .. 153 +173+ ..
313+ 3334. . m i793+ i81 3 + . . 10003= 6303s .
III. w=4:
Ex. 1. Using formula (2) assume re= 10, j»= 14, and q= 1
whence d— 13 124, which by trial is found equal to
1*
_j_ 24+ 3* + 5 4 + T 4- 104 , whence
4*+ 64+ 84+ 9
4 +144 = 154.
110 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Ex. 2. Using formula (3) assume x = 100 and 6 = 212;
whence r = 30 370194, which by 'trial is found
equal to
1*
_]_ 24+ 34+ 44+ 84+ 10* + 14*+ 24*+ 424+724 ;
hence if all the natural numbers from 1 to 100, ex-
cept the ten above given, be raised to the fourth
power and added, their sum equals 212*.
IV. ?i=5:
Ex. 1. Using formula (2) assume x= 10, p = 11, and 5=1;
whence d= 133 044, which by trial is found to equal
l 5+ 25+ 35 + 85 + 105 , and therefore
45 + 55 + 6 5+ 75+ 95 + ll 5 =125 .
Ex. 2. Using formula (1) assume^?= 29 and q = l; whence
a = 3788 851, which by trial is found equal to
55_j_io3 + 11 5 4- 165+ 195 ; hence
55+ iq5+ n o + i65 -f 195 + 295= 305.
Ex. 3. Using formula (2) assume x = 18, p = 31, 5=1;
whence d=l 731 920, which by trial is found to
equal l 5+254-454-55+
9
5+125+175 , and therefore
35 + 65 + 75 + 85+ 105+ ll 5 +
135+ 145 + 155 + 165 _J_ 185+ 315= 325#
In finding these numbers, use has been made of Barlow's tables of
fourth and fifth powers. To further facilitate the work the values
of Sz, n for n= 4 and n= 5 were tabulated.
This paper was discussed briefly by the Chairman and by Messrs.
Doolittle, Hill, Baker, and Kummell.
NOTE.
The following members have assisted the Chairman and Secretary
in the examination of abstracts of communications to the Mathe-
matical Section
:
Title.
Association ratios.
A collection of solutions of the
trisection problem.
The orbit of Hyperion.
Methods of finding «th-power
numbers whose sum is an wth
power.
Author.
M. H. Doolittle.
Marcus Baker.
G. E. Curtis.
Ormond Stone.
Artemas Martin.
Third member.
G. K. Gilbert.
Asaph Hall.
Asaph Hall.
Marcus Baker.
(Ill)

NOTE ON THE PUBLICATIONS OF THE SOCIETY.
The ten volumes of the bulletin now issued cover the proceedings
of the Society from its organization in March, 1871, to the end of
December, 1887, a period of 17 years. Volumes 1 to 3 of the Bulletin
apply to irregular periods ; volume 4 gives the proceedings for a
Society's year, beginning in October of one calendar year and end-
ing in June of the next. In 1882, the Society's year was changed
to coincidence with the calendar year, and volume 5 contains the
minutes from October, 1881, to December, 1882, inclusive. Volumes
6 to 10 cover, respectively, the calendar years 1883-1887.
The pages of all the volumes have been stereotyped at the expense
of the Smithsonian Institution, and after the Society's edition, usually
of 500 copies, has been priuted, the plates have gone into the cus-
tody of the Institution, which has subsequently issued an edition of
its own, constituting a paper of its Miscellaneous Collections. In
the Smithsonian edition, volumes 1, 2, and 3 of the Bulletin consti-
tute volume 20 of the Miscellaneous Collections, and volumes 4 and
5 constitute part of volume 25 of the Miscellaneous Collections.
Volumes 6 to 8 have been reprinted by the Institution, but not yet
gathered into a Collections volume for binding. Their numbers in
the Smithsonian list are as follows:
Vol.6 No. 543
Vol.7 No. 592
Vol.8 No. 636
The Smithsonian edition is in the main typographically identical
with the Society's edition, but the following differences are to be
noted.
Volume 20 of the Smithsonian Collections contains, in addition,
the following title page and contents
:
Smithsonian Miscellaneous Collections. Vol. XX. (Vignette and
motto.) Washington: Published by the Smithsonian Institution.
1881.
Contents. Article I. Bulletin of the Philosophical Society of
Washington. Vol. I, March, 1871, to June, 1874. Pp. 218.
54 (113)
114 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Article II. Bulletin of the Philosophical Society of Washington.
Vol. II, October 10, 1874, to November 2, 1878. .Pp. 452.
Article III. Bulletin of the Philosophical Society of Washington.
Vol. Ill, November 9, 1878, to June 19, 1880. Pp. 169.
The plates for this volume were changed by way of correction in
a number of details, and the following list of differences may be re-
garded as corrigenda for volumes 1, 2, and 3 of the Society's edition.
Differences in Volume I of Bulletin.
''age.
MATHEMATICAL SECTION. 115
Page.
116 PHILOSOPHICAL SOCIETY OP WASHINGTON.
age.
INDEX TO VOLUMES I-X.
Volume, Roman pagination, Arabic pagination, and pagination of appendix are distinguished
thus: ix, xvi, 23, (17).
The pages of appendices are differently numbered at top and at bottom ; the index refers to
the pagination at bottom.
The titles of all papers read to the Society are entered (with some duplication) under tho
following words: Acoustics, Anatomy, Anthropology, Archaeology, Astronomy, Biography, Biology,
Botany, Calendars, Chemistry, Electricity, Geography, Geology, Mathematics, Meteorology, Mi-
croscopy, Mineralogy, Miscellaneous, Oceanography, Optics, Physics, Political Economy, Psychol-
ogy, Seismology, Social Science, Thermometry, Zoology.
Page.
Abbe, Cleveland, communication on the
aerial currents observed in balloon as-
censions. Abstract 1 38
the laws governing the movement of
storm centers. Abstract i 99
the position of the planes of certain ne-
bula). Abstract and reference i 109
report of the committee to collect in-
formation relative to the meteor of
December 24th, 1873. In full. 2
figures il 123, 139
the aurora. Abstract iv 21
determining the temperature of the air.
Abstract vi 24
methods of verifying weather predic-
tions. Abstract viii 8
Signal Service bibliography of meteor-
ology. In full x 20
remarks on auroras 1 45
Stone Mountain earthquake i 102
land and sea breezes ii 18
the mean terrestrial ellipsoid, the geoid,
and levelling ii 24
Dakota calendar il 93
polarization of light by a narrow slit...iii 124
Benjamin Peirce iv 25
anomalies of sound v 37
deflection of rivers vii 23
report as treasurer.^ 17G, 180, vi xxii, viixxiv
Abbe de l'Epee's instruction of the dumb..vi 03
Abbe, Prof. E., Apertometer of. ili 18
cited on microscopy iii 26
Abbey, Westminster S., letter on a fish found
on the Florida coast. Bead by C. Abbe.
No abstract ii 202
Abel's researches in elliptic integrals vii 106
,
Achromatic objective ™ iii 65
Page.
Achromatic objectives, Corrections of. iii 39
Acoustic investigations by Joseph Henry..il 344
Acoustics, List of papers on
:
on phenomena of sound and experiments
with tuning forks. J. Henry. Title
only J 22
on sound in relation to fog-signals, from
investigations under the direction of
the U. S. Light House Board. J. Henry
In full „ „ „...i C5, ii (45)
recent experimental researches in acous-
tics, by Prof. A. M. Mayer. J. E. Hil-
gard. Titleonly i 90
experiments on fog signals during the
past summer. J.Henry. Title only ...t 90
[letter on fog-signals.] J. Tyndall. Com-
municated by J. Henry. No abstract. ..I 91
on audition. J.Henry. Titleonly ii 22
on fog-signals and abnormal conditions of
sound. J. Henry. Reference Ii 37
sound in connection with fog signals. J.
Henry. Reference ii 57
acoustic refraction. W. B. Taylor. Ab-
stract ii 57
an account of researches on sound in its
application to fog-signals. Annual ad-
dress, 1875. J. Henry. Reference ii 60
exhibition of a telaphon. E. Gray. Ab-
stract ii 67
[fog-signals.] J. Henry. Abstract ii 85
the telephone. A. G. Bell. Abstract ii 103
comments on the telephone. E. B. Elliott.
Title only ii 111
[scientific method and its application to
acoustic researches in connection with
fog signals.] Annual address, 1877. J.
Henry. In full ii 16J
(117)
118 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Acoustics, List of papers on—Continued,
the telephote. E. B. Elliott. Abstract.. .11 192
musical intervals. E. B. Elliott. Ab-
stract H 199
binaural audition. A. G. Bell. AbstraH.ill 68, 69
the spectrophone. A. G. Bell. In full.
Plate * lv 142
upon a modification of Wheatstone's mi-
crophone and its applicability to radio-
phonic researches. A.G.Bell. In full.
Plate lv 183
recent investigations by the Light House
Board on the anomalies of sound from
fog-signals. A. B. Johnson. In full.
2 maps, 1 figure v 23
anomalies of sound signals. J. C. Welling.
In full v 39
the difficulty in determining the direction
ofsound. A.B.Johnson. Abstract..-vitill, 12
the mechanism of "clicks" and "clucks."
A.G.Bell. Title only vlll 18
Action at a distance v 156
Adams, Prof. Carl, cited on Malfatti's prob.
lem 11 118
idams, Prof. W. G., cited on electric resist-
ance lv 154
Address of chairman of Mathematical Sec-
tion vl 117
of President Henry, 1871 1 v, 34
Henry, 1875 11 60
Henry, 1877 11 162
Newcomb, 1879 HI 52
Newcomb, 1880 lv 40
Woodward, 1881 v 49
Taylor, 1882 v 126
Powell, 1883 vl xxvii, 110
Welling. 1884 vll xxix. 81
Hall, 1885 vlll xxxiii, 30
Billings, 1886 lx xxxv, 46
Harkness, 1887 x xxxvii, 39
of retiring president, Resolution concern-
ing lv 30
on the life and character of Joseph Henry,
11 203, 368, 370
Adhesion and cohesion v 136
Adirondack region, Proposed reservoirs in
the 11 67, 82
Adjustmen t of conditioned observations.vlll 41
of the calendar 11 59
Administration of scientific work lx xliii
Adulteration of food lv 39
Aerolite. See Meteor.
Agassiz, Louis, Announcement of death of..i 93
Resolutions on death of 1 95
Agricola, Georg, cited on mineralogy 1 77
Ague, Conservative function of vl 5
Page.
Air, Contamination of lv 37
Alaska, Discoveries in! lv 163
Glaciation in vl 33, x 15
Results of travels in 1 22
Value to the United States of 1 25
Alaska-Siberia boundary lv 123
Albertype process of photo-engraving 1 42
Aleutian Islands, Shell heaps of. 11 65
Alexander, Stephen, communcation on the
zodiacal light. Read by J. E. Hilgard.
In full, 9 figures 1 105, (19)
Algebra, Logical 1 88
Algorithm of the nrithmetico-geometric
mean vll 102
Alignment curves on any surface vl 123
Allard, M. E., cited on the light-house service
of the United States lv 138
Alluvial basin of the Mississippi 1 (10)
Alphabet, Phonetic lx 17
Altitude of the Caspian and Aral seas 11 34
Altitudes deduced from combination of rail-
road levellings 11 23
Alvord, Benjamin, cited on gravitation form-
ula vill 40
communication on the habitability of the
elevated plateaus of the west. Title
only 1 74
the recent earthquakes in North Caro-
lina. Abstract 1 101
the mortality among army officers. Ref-
erence 11 49
proposed governmental insurance. No
abstract 11 49
a trigonometrical formula. Title only.. .11 104
the intersection of circles and the inter-
section of spheres. Title only 11 198
new points respecting the intersections
of circles and the intersections of
spheres. Title only 11 201
life and work of Joseph Henry. In
full 11 370
a curious fallacy as to the theory of grav-
itation. Infull v 85
some of the properties of Steiner's power
circle. Title only v 89
the compass plant. Reference v 106
a special case in maxima and minima.
Abstract vl 149
Death of vll 72, 127
List of mathematical papers by... vll 128
Memorial to vll 127
remarks on Lake Bonneville 11 103
Benjamin Peirce lv 23, 24
Arkansas bonds . vl 105
agricultural colleges vl li)6
Amendment to constitution lx 47, x 39
INDEX TO VOLUMES I-X. 119
Page.
Amendment to standing rules....ili 149, lv
xi, 38, vlii x, xi
American Academy of Arts and Sci-
ences vlli xxxvi
American Association for the Advancement
of Science vtli xxxix
American Philosophical Society vlli xxxiv
American scientific societies -vlll xxxiii
Ampere, Law of v 139
Anal notch in Pleurotomaria lii 76
Analysis of meteorite vii 32
Anatomy and Physiology, List of
papers on
:
on the alleged hermaphrodite described
by Drs. Accly, Blackman, and Jackson.
J.J.Woodward. Abstract and reference* 24
on the fluctuations of the temperature of
the human body. B. F. Craig. Ref-
erence 1 31
on fractures of the inner table of the cra-
nium. G.A.Otis. Title only i 73
[letter on autopsy of Agassiz.] Dr. Jack-
son. Communicated by J. J. Woodward.
No abstract.- i 93
on the similarity between the red blood-
corpuscles of man and those of certain
other mammals, especially the dog;
considered in connection with the di-
agnosis of blood-stains in criminal
cases. J. J. Woodward. Abstract and
reference ii 20
explanatory note in regard to the diagnosis
of blood-stains. J. G. Richardson.
Communicated by J. J. Woodward. Ref-
erence 11 41
tho conservative element in disease. A.
F. A. King. Abstract 11 111
the conservative influence of disease as
illustrated in the phenomena of pul-
monary phthisis. A. F. A. King. Ab-
stract 11 124
the influence of the cardiac and respiratory
movements upon the motion of the
lymph. S. C. Busey. Abstract and ref-
erence 11 133
asymmetry in the form of the human cra-
nium. C.A.White. Title only 11 190
the physiology of civilization. H. Reed.
Title only Ill 20
color perception and color blindness. S.
M. Burnett. Abstract and reference...lv 64
on the influence of the constant use of
high-heeled shoes upon the health and
form of the female, and upon the rela-
tion of the pelvic organs. S. C. Busey.
Abstract ,. v 117
Page.
Anatomy and Physiology, List of
papers on—Continued,
modern ideas of brain mechanism. F.
Baker. Title only vill 17
Anaxagoras' philosophy vil xxxii
Andromeda, New star in ix 14
Animal population of the globe lv 27
Annual address. See Address.
Annual meeting. See Election of officers and
Address.
Anomalies of sound from fog-signals v 23, 39
Anthropological Society of Washington x 46
Invitation from vlil 5, ix 15, x 6
Anthropological work of the Smithsonian
Institution 11 299
Anthropology, List of papers on. (See,
also, Archceology.)
on the characteristics and zoological rela-
tions of man. T.Gill. Abstract 1 24
on the mythology of the Numas. J. W.
Powell. Reference 1 96
on the genesis and demonology of the
Numa tribe of Indians. J. W. Powell.
Reference 1 104
a calendar of the Dakota Indians. G. Mal-
lery. Abstract and reference Ii 90
the philosophy of the North American In-
dians. J. W. Powell. Title only.M 109, 110
some common errors respecting the North
American Indians. G. Mallery. Ab-
stract and reference 11 175
poisons among the North American In-
dians. J.W.Powell. Abstract ii 182
the use of poisoned arrows by North Amer-
ican Indians. E. Coues and W. J. Hoff-
man. Title only il 183
the evolution of language. J. W. Powell.
Title only ii 199
the progressive dispersion of mankind
over the surface of the earth. A. Win-
chell. Title only ill 32
the future of the human race regarded
from the standpoint of evolution. S.
Newcomb. Presidential address. Title
only ill 52
on the gentile system of the Omahas. J.
O. Dorsey. In full; Zfigures ill 128
comparison of written language, with that
which is spoken only. O. T. Mason.
Abstract lii 139
limitations to the use of some anthropo-
logic data. J. W. Powell. Refer-
ence .". iv 134
the three methods of evolution. J. W.
Powell. Presidential address. In full.
vt xxvii, 110
120 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Page.
Anthropology, List of papers on—Cont'd,
composite photography applied to crani-
ology. J. S. Billings. Abstract vii 25
natural naturalists. W. Matthews. Read
by J. S. Billings. Abstract vii 73
mythological dry paintings of the Navajos.
W. Matthews. Abstract viii 14
anthropometric and reaction-time appa-
ratus. J. S. Billings and W. Matthews.
Abstract viii 25
two examples ofsimilar inventions in areas
widely apart. O.T.Mason. Abslract.Xx. 12
customs of every-day life. G. Mallery.
Abstract lx 19
bowyers and fletchers. O. T. Mason. Ab-
stract lx 44
counting out rhymes of children ; their
antiquity, origin and wide distribu-
tion. H. C. Bolton. Reference x 13
Anticlinal and synclinal axes ii (22)
Antisell, Thomas, communication on dust
from Armenia. No abstract t 25
meteorology of Japan. Title only 1 70
visit to Japan. No abstract 11 84
terrestrial geogony. Title only..il 132, 133, 134
temperatures of the Pacific Ocean. Ab-
stract 11 192
chemical molecular changes. Title
only Ill 28
the building up of organic matter. Title
only v 97
remarks on waterspouts 11 104
fauna! accommodation It 181
poisoned arrows 11 183
vegetation and environment 11 183
Wasatch fault 11 196
ravages of teredo v 98
artesian water on the Plains v 101
thermometer exposure vi 47
dissociation vii 16
volcanic dust vll 20, 25, 26
cause of thunderstorms vlll 11
odor vlll 27
Antlers, Morphology of It 135
Apertometers Ill 18
Aphakia vi 5
Appalachian mountains lv 60
topography lx 22
Apparatus, Base-line Ill 35
for examination of the eye Ill 53
for exhibiting local time at all points of
the globe ill 107
for viewing the sun by light of any desired
wave length x 13
to facilitate "sweeping" ill 142
Apples, Problem of rotten and wormy x 87, 89
Page.
Applied science. Plea for vil 11
Approximate quadratures ii 48
Aral sea, Altitude of 11 34
Archaeology, List of papers on :
[exhibition of] archaeological specimens.
O.T.Mason. Title only ii 48
the classification of objects of archaeology.
O.T.Mason. Title only 11 50
remarks on the Papyrus Ebers. J. J.Wood-
ward. Abstract ii 64
the succession of the strata of the shell-
heaps of the Aleutian Islands. W. H.
Dall. Abstract ii 65
the international symbols for charts of pre-
historic archaeology. O. T. Mason.
Abstract 1171, 72
prehistoric copper. J. D. Butler. Title
only ii 185
the fresh-water shell-heaps of the interior
rivers of North America. C. A. White.
Title only ill 32
the decipherment of some Aztec monu-
ments lately discovered in Guatemala.
O.T.Mason. Title only Hi 37
Arctic exploration i 92, il 89, ix 8
Argentine coinage ii 65, ill 38
Aristotle cited on atoms vii xxxii
mineralogy i 77
Arithmetic, Binary vi 3, 38
Arizona, Physical features of. 1 54
Volcanic activity in i 99
Army and Navy officers as scientific admin-
istrators ix xlix
officers, Mortality among ii 49
Medical Museum ix 35
Medical Museum building x 10, 31
Arrow, Sir F., cited on phenomena of sound.
Ii (49), (50)
Arrows, Poisoned Ii 180, 182
Artesian well with geyser action 1 103
wells on the Great Plains v 101
Arts, Evolution of vi xlviii
Assembly Hall of Cosmos Club x 10, 31
Association ratios x 83, 94
Astigmatism vi 4
Focal lines in vi 45
Astronomy, List of paper? on. (See aUo
Calendars)
:
on the elements of the Comet I, 1871. A.
Hall. Communicated by B. F. Hands.
Abstract : i 23
on two immense meteorites at Conception
and San Gregorio, Mexico. H. B.
Butcher. Reference 1 24
on astronomical photography. A. Hall.
Abstract and reference. i 28
INDEX TO VOLUMES I-X. 121
Page.
Astronomy, List of papers on—Cont'd.
on the transits of Venus, past and future.
S. Newcomb. Title only i 29
on the heat of the sun. B. Peirce. .46-
stract 1 31
on the physical constitution of the co-
rona of the sun. W. Harkness. Refer-
ence 1 31
on the spectrum of Encke's comet and
the appearence of Tuttle's comet. W.
Harkness. Reference i 34
on the astronomical proof of the existence
of a resisting medium in space. A.
Hall. Reference 1 34
[on the spectrum of Eneke's comet.] W.
Harkness. Reference i 34
on the appearance of Encke's comet as
seen at Harvard College observatory.
C. S. Peirce. Reference t 35
on the density of the hypothetical resist-
ing medium in space. W. Harkness.
Reference i 39
on the possibility of a universal atmos-
phere. S. Newcomb. Title only i 52
on the discovery of new planets having
especial reference to the asteroids. J.
C. Watson. Title only 1 53
[letter on solar eclipse.] Capt. Tupman.
Communicated by W. Harkness. No ab-
stract 1 56
[letters on Cordoba Observatory.] B. A.
Gould. Communicated by J. H. C. Coffin
and J. J. Woodward. No abstract 1 57
on the determination of the errors of a
provisory catalogue of tundamental
stars. O.Stone. Title only t 62
on the progress of the construction of the
new telescope for the Naval Observa-
tory. S. Newcomb. Reference i 62, 63
on our present knowledge of the planet
Jupiter. W. B. Taylor. Title only i 62
maps prepared by G. W. Hill for use in
connection with tho transit of Venus
in December, 1874. J. H. C. Coffin.
Reference i 63
on stellar photometry. ('. S. Peirce. Ref-
erence i 63
the proceedings of the commission to
arrange for the observation of the next
transit of Venus. S. Newcomb. Title
only 1 65
a comparison of the thermometers used
to determine the correction for at-
mospheric refraction at the U. S.
Naval Observatory. J. R. Eastman.
Abstract i 68
Page.
Astronomy, List of papers on—Cont'd.
on the results of astronomical observa-
tions at Sherman Station, Wyoming
Terr. R. D. Cutts. Abstract and refer-
ence 1 70
on the theories of the nature of comets'
tails. B. Peirce. Reference I 74
on the general star catalogue prepared
from the observations at the Naval Ob-
servatory since 1845. M. Yarnall. Ref-
erence 1 74
on the power necessary to drive the pend-
ulum of an astronomical clock. W.
Harkness. Title only 1 74
on a proposed method of observing astron-
omical transits. E. Foote. Title only.A 75
the frequency of the occurrence of the
zero and the nine digits in the tenths
of seconds from the chronographic
record of transit observations. J. R.
Eastman. Abstract 1 85
[letter on the Cordoba Observatory.] B.
A. Gould. Communicated by J. J. Wood-
ward. No abstract 1 88
[letter on proposed observatory.] J. Lick.
Communicated by J. Henry. No ab-
stract 1 91
a detailed account of the construction of
the lenses and other interesting por-
tions of the largo telescope now estab-
lished at the Naval Observatory. A.
Clark. Title only i 92
on the determination of the personal er-
rors in the observation of astronomical
transits. J. E. Hili;ard. Title oniy....i 92
on comets and meteors. A. Hall. Refer-
ence i 94
[the meteor of December 24, 1873.] P.
Parker. No abstract i 94
[letter on the meteor of December 24, 1873.]
B. Hallowell. Communicated by J.
Henry. No abstract i 95
on the adopted value of the sun's appar-
ent diameter. E. S. Holden. In full,
i 95, (3)
~ on various hypotheses in reference to
space. C. S. Peirce. Title only i 97
on specimens of meteoric iron from Chi-
huahua, Mexico, and the structure of
meteorites in general. F. M. Endlich.
Title only i 98
on meteor trains, and the upper atmos-
pheric currents. J.Henry. Title only.X 98
on the apparatus to be used in the observa-
tions of tho approaching transit, of
Venus. W. Harkness. Title only i 102
122 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Astronomy, List of papers on—Cont'd.
ou the zodiacal light. S. Alexander. Com-
municated by J. E. Hilgard. In full ; 9
figures i 105, (19)
on Sir William Herschel's observations of
the satellites of Uranus. E. S. Holden.
In full i 106, (30)
a new apparatus for the investigation of
personal error in astronomical transit
observations. J. E. Hilgard. Title
only i 106
on the position of the planes of certain
nebula. 0. Abbe. Abstract and refer-
ence i 109
on the correction of a comet's orbit. O.
Stone. Reference ii 22
[letter on transit of Venus, 1874.] C. H. F.
Peters. Communicated by A. Hall. Ab-
stract ii 31
[letter on transit of Venus, 1874.] C. W.
Raymond. Communicated by A. Hall.
Abstract ii 31
[letters] on the operations of the several
parties sent from the United States to
observe the transit of Venus on the8th
ofDec'r, 1874. A.Hall. Abstract 1131,33
[letter on transit of Venus, 1874.] W. Hark-
ness. Communicated by A. Hall. Ab-
stract ii 32
[letter on transit of Venus, 1874.] G. David-
son. Communicated by A. Hall. Ab-
stract -.__-._..._. .__..-—.. 32
the expedition to Pekin for observing the
late transit of Venus [1874]. C. A.
Young. Abstract ii 33
on the transit of Venus [1874]. S. New-
comb. Title only ii 41
two drawings of nebulse, made with the
XXVI-inch telescope of the U.S. Naval
Observatory, by Mr. L. Trouvelot, of
Cambridge, Mass. E. S. Holden. Ab-
stract ii 51
the methods of measuring the inequalities
of the pivots of a transit instrument.
W. Harkness. Title only ii 68
the temperature of space. W. B. Taylor.
Abstract ii 73
[search for Vulcan.] E. S. Holden. Ab-
stract ii 85
the appearance of Saturn's rings. A. Hall.
Abstract 11 94
on reference catalogues of astronomical
papers and memoirs. E. S. Holden.
Abstract ii 95
the shadow of the ball of Saturn projected
on the rings. E. S. Holden. AbstracL.il 101
Page.
Astronomy, List of papers on—Cont'd.
a bright spot which [has] recently become
visible on the ball of Saturn. A. Hall.
Abstract 11 102
thecosmogony. S. Newcomb. Title only..U 113
reportof the committee to collect informa-
tion relative to the meteor of Decem-
ber 24th, 1873. Read by C. Abbe. In
full; 2 figures, 1 map 11 123, 139
the position of the centre of gravity of the
apparent disk of a planet. A. Hall.
Reference 11 181
the results of [a] search for satellites of
Mars. A. Hall. Abstract and refer-
ence ii 18G
the nebular hypothesis and 'he inner moon
of Mars. M. H. Doolittle. Abstract,
ii 188, 190
aerolithic disturbance of planetary mo-
tions. M. H. Doolittle. Abstract 11 190
the recent transit of Mercury [1878]. S.
Newcomb. Abstract ii 199
a new eye-piece for observing personal
equations. A. Schott. Title only ii 200
the velocity of light and determination of
the solar parallax. W. Harkness. Title
only 11 201
observations of the total solar eclipse, July
29,1878. S. Newcomb. Abstract 11 203
notes on the brightness and the stellar
magnitude of the third Saturnian sat-
ellite, Tethys. E. S. Holden. Read by
A. N. Skinner. Title only ill 18
on the supposed discovery ot a trans-Nep-
tunian planet at the U. S. Naval Ob-
servatory in 1850. A.Hall. Abstract.iii 20
a note on the precession of stars in right
ascension. A. N. Skinner. Title only,
ill 21
on the satellites of Saturn. A. Hall. Ab-
stract ill 26
a personal equation instrument. J. R.
Eastman. Abstract 11133,37
the recurrence of eclipses. 8. Newcomb.
Title only ill 33
notes on the orbits of Titan and Hyperion.
A. Hall. Abstract ill 40
some results from the discussion of the
observations of the transit of Mercury
of May 6, 1878. J. R. Eastman Ab-
stract ill 43
a recent visit to California to inspect a site
for the new Lick Observatory. S. New-
comb. Title only «, ill 45
solar parallax from the velocity of light.
D.P.Todd. Reference Hi "i
INDEX TO VOLUMES I-X. 123
Page.
Astronomy, List ol papers on—Cont'd.
a pile of balls. M. H. Doolittle. Abstract,
Hi 76
on the solar corona. W. Harkness. Ab-
stract HI 116
review of B. A. Gould's Uranometria Ar-
gentina. E. S. Holdon. Reference,
ill 119, 122
remarks on the total solar eclipse of Jan-
uary 11th, 1880. E. Frisby. Abstract,
ill 121
on a mechanical attachment for equatorial
mountings to facilitato sweeping in
right ascension. D. P. Todd. Abstract
and reference ill 142
on a simple method of deriving some equa-
tions used in the theory of the moon
and of the planets. W. F. McK. Ritter.
In fall lv 57
on the orbit of Swift's comet. E. Frisby.
Abstract iv 59
the solar parallax as derived from the
American photographs of the transit
of Venus, 1874, December 8-9. D. P.
Todd. Abstract and reference iv 168
the relative accuracy of different methods
of determining the solar parallax. W.
Harkness. Reference v 39
on the total lunar eclipse of June 11, 1881.
W. B. Taylor. Abstract v 90
the Florida expedition for observation of
the transit of Venus [1882]. J. R. East-
man. Abstract vi 21
note on the rings of Saturn. W. B. Taylor.
Abstract vi 41
the determination of the mass of a planet
from observation of two satellites. A.
Hall. Abstract vi 132
certain possible abbreviations in the com-
putation of the long-period perturba-
tions of the moon's motion due to the
direct action of the planets. G. W.
Hill. Abstract and reference vi 136
a now meteorite. J. R. Eastman. Ab-
stract vii 32
the formulae for computing the position of
a satellite. A.Hall. In full. I figure.
vii 93
a case of discontinuity in elliptic orbits.
W. B. Taylor. Abstract vii 122
Variations of latitude. A. Hall. Abstract
and reference viii 10
comets II and III, 1884. W. C. Winlock.
Title only viii 16
tho asteroids. G. L. Raven6. Title only,
viii 18, 64
27
37
Page
Astronomy, List of papers on—Cont'd,
flexures of transit instruments. W. Hark-
ness. Abstract viii
physical observations of Wolf's comet
(1884 III). W. C. Winlock. Abstract,
viii
the theory of Mercury. G. L. Ravene.
Abstract viii
secular perturbations of Polyhymnia by
Jupiter. W. F. McK. Ritter. Abstract,
viii
the new star in the nebula of Andromeda.
A. Hall. Reference ix
the images of stars. A. Hall. Rcference.Xx.
a comparison of the Boss and Auwers' de-
clination standards. II. Farquhar.
Abstract and reference ix
on a device for viewing the sun by light of
any desired wave length. W. Hark-
ness. Abstract x
on the representation of comet orbits by
models. W. Harkness. Reference x 28
The motion of Hyperion. G.W.Hill. Ab-
stract and reference x 90
the parallax of a'fauri. A. Hall. Ab-
stract x
the most prot able value of the latitude
and its theoretical weight from en-
tangled observations occurring in the
use of Talcott's method. Abstract x
Euler's theorem (generally called Lam-
bert's). A. Hall. Abstract x 101
the orbit of Hyperion. O. Stone. Abstract
and reference x 104
Atmospheric temperature determination..vi 24
Atomic motions v 143
philosophy, physical and metaphysical,
vii xxix
volume curve vii 15
volumes of crystallized and double salts..i 103
weights vii xlvii
Atoms vii 45
and molecules v 141
molecules and waves i 66
Attracting centre, Motion of a particle to-
ward i 88, ii 19, vii 122
Attraction, Infinite, of a finite maws..ii 19, viii 58
Auditing Committee. See Committee,
Audition, Binaural iii 69
Aurora, Height of iv 21
of February 4th, 1S72 i 47
Theories of i 43
Auwers' declination standards ix 53
Avicenna, cited on mineralogy i 77
Avogadro, Law of ..v 139
41
54
53
13
91
01
124 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Babcock, O. E., Death of vll 72
Bacillus malarise iv 39
Bache, A. D., Eulogy on i 35
Bacteria i 43
and spontaneous generation ii 109
Baer's law vii 21
Baeyer, cited on corrections to levelling for
deflection of the plumb line ii 25
Bagehot, cited on occult force "...vi xxxiii
Bailey, T., Death of. ii 109. Ill
Baird, S. F.,and scientific societies x 45
as an administrator x 49
communication on the decrease of fish on
the southern coast of New England.
Reference i 52
the artificial propagation of the cod.
Abstract iii 29
Death of. x 17, 20, 76
Meeting commemorative of. x 41
Personal characteristics of. x 71
remarks on archaeological collection by
G. Latimer ii 48
Scientific work of x 61
Bairdian school of ornithologists x 66
Baker, Frank, communication on modern
ideas of brain mechanism. Title only,
viii 17
remarks on audition viii 13
Baker, Marcus, communication on the his-
tory of Malfatti's problem. In full. 2
figures ii 113
a geometric problem, with bibliograph-
ical notes. In full. 4 figures iii 53, 55
the boundary line between Alaska and
Siberia. In full. Map iv 123
a geometrical question relating to
spheres. In full v 107
Benjamin Alvord. Head by E. B. Elliott.
In full vil 127
a collection of formufe for the area of a
plane triangle. Reference viii 37
a group of circles related to Feuerbach's
circle. In full, ^figures viii 45
What is a topographic map? Abstract.^. 11
a problem in probabilities. Abstract. ..x 87
a collection of solutions of the trisection
problem. Abstract x 96
remarks on Alaskan glaciers x 15
a geometrical problem v S8
graphics x 5
Benjamin Alvord vii 128
Balloon ascensions and air currents i 35
Bancroft, H. H., cited on diminution of In-
dians ii 175
Bank loans, Distribution of iv 31
Page.
Barker, Prof. G. F., cited on diatomic mole-
cules v 150
vital principle..' v 50
nerve currents v 61
Barnard, Gen., cited on precession and ter-
restrial rigidity ii 78
Barnes, J. K., Death of vi xvi
Barometric gradient as related to velocity
and direction of wind i 106
hypsometry v 48
New method of ii 131
observations modified by wind v 91
pressure and wind velocity x 10
and winds in relation to tides 1 53
Bartholin, cited on mineralogy i 77
Basaltic columns viii 19
Basch's experiments on the circulation of
the blood v 77
Base-line apparatus iii 35
at Kanab, Utah iii 34
measurement near Atlanta ii 50
Basketry ix 13
Bates, H. H., cited on gravitation formula,
viii 39, 40
communication on the motion of a particle
towards an attracting centre. Title
only i 89
movement of a particle attracted towards
a point. Abstract ii 19
the nature of matter. Reference vi 5
the physical basis of phenomena. In
full. 2 figures vii 40
remarks on wind-vane formula x 9
Bates, N. L., communication on organic
cells of unknown origin and form
found in human feces (two cases).
Title only ix 35
Baudin's method in thermometry ix 29
Bayma, Prof. J., cited on action at a dis-
tance v 158
Bay's Mountains, Tenn x 7
Bean, T. H., communication on the distri-
bution of fishes in the oceanic abysses
and middle strata. Title only ix 22
Bebb, M. S., cited on salices iv 110
Becquerel, A. E., cited on chemical rays....v 135
Bede, cited on cure of dumbness vl 53
Behring's Strait iv 123
Bell, A. G., communication on the tele-
phone. Abstract ii 103
binaural audition. Abstract iii 68, 69
the spectrophone. In full. Plate iv 142
a modification of Wheatstone's micro-
phone and its applicability to radio-
phonic researches. In full. Plate,
iv 183
INDEX TO VOLUMES I-X. 125
Page.
Bell, A. G., communications on—Cont'd,
fallacies concerning the deaf, and the
influence of such fallacies in prevent-
ing the amelioration of their condi-
tion. In full vi 48
the mechanism of "clicks" and
"clucks." Title only viii 18
remarks on temperature observations. ..vi 47
earthquake waves and sound waves..ix 42,43
Bellroth, cited on microscopic organisms,
li 110
Beman, Prof. W. W., Solution of a geometri-
cal problem by iii 65
Benedict, Prof. F. N., Survey by li 67
Benoit's coefficient of expansion of glass,
lx 32
Bentham and Hooker, cited on classification
of plants ivl08, 110, 113
Bergman, cited on mineralogy i 78
Bernstein, cited on mu.-cular contraction..v 58
nerve action '. v 61
Berzelius, cited on mineralogy i 78, 79
Bessel's method for computing positions of
satellites vii 94
Bessels, Emil, communication on some of
the results of the Polaris north pole
expedition. Title only i 92
the hygrometrical condition of the air
in high latitudes. Title only ii 66
the late English polar expedition. Ab-
stract ii 89
remarks on Arctic glaciers ii 36
Bibliographic notes on a geometrical prob-
lem iii 04
Bibliography of astronomy ii 95
Benjamin Alvord vii 128
S. F. Baird x 62
Great Basin ranges ix 6
Joseph Henry ii 360
Malfatti's problem ii 120
medical medals vi 40
meteorology x 20, 23
North American geology vii 71
G. A. Otis iv 181
science ii 302, x 38
trisection problem '. x 97, 98
Bigolow, Dr., cited on gaseous disinfec-
tion iv 38
Billings, J. S., communication on some mi-
nute fungi. Abstract i 42
the collection of a large library. Ab-
stract i 92
bacteria and spontaneous generation.
Abstract ii 109
the work of the National Board of
Health. Title only iii 50
Page.
Billings, J. S., communications on—Cont'd,
the scientific work carried on under the
direction of the National Board of
Health. Abstract iv 37
mortality statistics of the Tenth Census.
Abstract iv 103, 164
the ventilation of the House of Repre-
sentatives. Abstract v 99
composite photography applied to crani-
ology. Abstract vii 25
a collection of microscopes. No ab-
stract vii 73
the vital statistics of the Tenth U. S.
Census. Reference viii 4
anthropometric and reaction-time ap-
paratus. Abstract viii 25
germ cultures. Abstract viii 30
museum specimens illustrating biology.
Abstract ix 35
scientific men and their duties. Presi-
dential address. In full ix xxxv, 46
remarks on mosquital inoculation vi 10
bibliography vii 72
smell viii 28
care of pamphlets viii 29
Charleston earthquake ix 42
Bi-metallism iii 78, 107, iv 141
Binary arithmetic, Experiments in vi 3, 38
Binaural audition iii 69
Binocular microscopes iv 35
Biogen v 102
Biography, List of papers on :
on the life and scientific labors of the late
Alexander Dallas Baehe. J. Henry.
Reference i 35
biographical notice of Archibald Robert-
son Marvine. J. W. Powell. In full,
ii 83,(53)
life and character of Joseph Henry. J. C.
Welling. Infull ii 203
a memoir of Joseph Henry. A sketch of
his scientific work. W. B. Taylor. In
full ii 203, 230
address commemorative of Joseph Henry.
P. Parker. Infull ii 308
[address commemorative of] Joseph
Henry. B. Alvord. Infull ii 370
[remarks commemorative of Jonathan
Homer Lane.] J. E. Hilgard. In
full iii 122
a biographical sketch of the late Dr. [G. A.]
Otis. J.J.Woodward. Infull iv 171
[eulogy on A. A. Humphreys.] J. C. Well-
ing. Abstract vii 4
memorial [to Benjamin Alvord.] M. Baker
and E. B. Elliott. Infull vii 1:27
126 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Biography, List of papers on—Cont'd,
relations between Professor Baird and
participating societies. G. Mallery.
In full x 45
Professor Baird as an administrator. W.
B.Taylor. In full x 49
Professor Baird in science. W. H. Dall.
In full x 61
the personal characteristics of Professor
Baird. J.W.Powell. In full x 71
Biological Society, Invitation from. ...vil 5,
vlii 4
Biological Society of Washington x 47
Biology, List of papers on. (See also
Zoology and Botany :)
bacteria and spontaneous generation. J.
S. Billings. Abstract 11 109
principles of morphology. T. Gill. Refer-
ence lv 123
modern philosophical conceptions of life.
J. J. Woodward. Presidential address.
Infull v 49
on the organic compounds in their rela-
tions to life. L. F. Ward. Title only.rv 91
on the building up of organic matter. T.
Antisell. Title only v 97
on the possibilities of protoplasm. E.
Coues. Abstract and reference v 102
the three methods of evolution. J. W.
Powell. Presidential address. In full.
vi xxvii, 110
germ eultures. J. S. Billings. Abstract.
vili 30
organic cells of unknown origin and form
found in human foeees (two cases). N.
L.Bates. Title only ix 35
on museum specimens illustrating bi-
ology. Symposium. Abstract Ix 35
Black drop il 199, vi 23
Black Hills of Dakota Ill 125
Blair, H. W., Death of vii 81
Blindness, Color iv 54
Blood corpuscles of man and other animals
compared It 20,41
Blue Ridge, Fault in vl 30
Board of Bealth, National iv 37
Boerner, C. G., letter on a shower of the
Rocky Mountain grasshoppers. Com-
municated by J. Henry. Abstract 11 87
Bogosloff crater vll 34
Bolton, Prof. II. C, communication on count-
ing-out rhymes of children, their an-
tiquity, origin, and wide distribation.
Reference x 13
Bonneville, Lake 184, 11 103
Hoecovich's philosophy of matter. ....vll xlv, 49
Pagf>.
Boss' declination standards Ix 53
Botany, List of papers on. (See also Bi-
ology :)
on some minute fungi. J.S.Billings. Ab-
stract 1 42
descriptions of new species of fossil plants
from Alleghany Co., Virginia; with
some remarks on the rock seen along
the Chesapeake and Ohio Railroad,
near the White Sulphur Springs of
Greenbrier County, West Virginia. F.
B. Meek. Read by T. QUI. In full. 2
plates 162, 11 (20)
on the cause and remedy of the potato rot.
L. D. Gale. Title only 1 97
[plants common to Japan and eastern
America.] A. Gray. Abstract il 42
the climate of plants. L. D. Gale. Ab-
stract il 1S3
the natural system. of plants. L. F. Ward.
Title only 11 W, 187
field and closet notes on the flora of Wash-
ington and vicinity. L.F.Ward. Ab-
Stract lv 04
on the compass plant. B. Alvord. Refer-
ence v 106
the flora of the Laramie group. L. F.
Ward. Reference vlii 17
our city shade-trees, their foes and their
future. C. V. Riley. Reference x 7
•on the geographical distribution of fossil
plants. L.F.Ward. Reference x 28
Boundary line between Alaska and Siberia,
iv 123
Boutelle, C. O., remarks on deflection of
rivers vil 24
Bowditch, N., and the Mecanique Celeste,
vlii xxxvi
Bowyers and fletchers ix 44
Boyle, R., cited on atomic philosophy vil xlv
Boyle's law v 139
Brachisthode vi 124
on the helicoid x 90
Brain and phosphorus v 75
temperatures.^ v 75
Brainard's Arctic exploration ix 11
Bremiker, Dr., cited on alignment curves.
vl 124, 126
Brewer, Prof. W. H., remarks on the potato
rot i 97
Brianchon, cited on Feuerbach's circle,
viii 45
Brooks, W. K., communication on the em-
bryology of Lingula and the systematic
relations of the Brachiopods. Title
only tit 33
INDEX TO VOLUMES I-X. 127
Brown, Judge A., cited on difficulty of de-
termination of sound direction viii 12
Brown, W. R., cited on conservation of
energy vii 62
force and matter vii 31
Buccinum undatum iii 75
Buehan, cited on barometric pressures i 108
Bulletin, Cost of printing v 177
Distribution list of iii 159
of the Mathematical Section vi 121. -vii 87,
viii 37, ix 53, x 79
of the Society, Function of the i x
Rules for publication of. i ii, ii vii, iii vii,
iv 13, v 13, vi xxxiii, 135, vii xiii, viii
xiii, ix xiii, x xiii
Bulletins, Note on x 113
Bulwor, J, cited on visible speech vi 54
Buoys, Drifting vii 14
Burchard, H. N., communication on the sil-
ver question. Abstract iii 109
remarks on agricultural production vii 20
Burdon, W., Solution of a geometrical prob-
lem by iii 04
Bureau of Ethnology x 57
Burger, Franz, Electric investigations by..v 47
Burnott, S. M., communication on color per-
ception and color blindness. Abstract
and reference iv 54
refraction in the principal meridians of a
triaxial ellipsoid; regular astigmatism
and cylindrical lenses. Reference vi 4
the character of the focal lines in astig-
matism. Abstract vi 45
why the eyes of animals shine in the
dark. Abstract and reference vii 13
Are thore separate centres for light-,
form-, and color-perception ? Abstract
and reference vii 72
the Javal and Schiotz ophthalmometer.
Titleonly viii 11
Busey, S. C, communication on the gather-
ing, packing, transportation, and ex-
posure of fruits for sale. Title only. ..ii 16
the influence of the cardiac and respira-
tory movements upon the motion of
the lymph. Abstract and reference... .ii. 133
the relation of the meteorological condi-
tions to the summer diarrhoeal dis-
eases. Abstract and reference iv 165
the influence of the constant use of high-
heeled shoes upon the health and form
of the female, and upon the relation
of the pelvic organs. Abstract v 117
Butcher, H. B., communication on two im-
mense meteorites at Conception and
San Gregorio, Mexico. Reference i 24
Page.
Butler, J. D., communication on prehistoric
copper. Titleonly ii 185
Byasson, H., cited on phosphorus and cere-
bral activity v 75
By-Laws. See Standing Rules.
Calcium sulphide. Clock faces coated with,
iii 33
Calendar of the Society vii ixii, viii xxx,
ix xxvii, x xxxi
Calendars and Time Standards', List of
papers on
:
on a Gregorian calendar. E. Frisby. Ab-
stract i 75
onaproposed reformation of the Gregorian
calendar. J. E. Hilgard. Abstract.M 29, 30
calendar formulae. E. B. Elliott. Abstract,
ii 37
a calendar proposed by a Persian astrono-
mer in 1079. W. B. Taylor. Abstract.M 38
adjustment of the calendar. E. B. Elliott.
Abstract ii 59
standards of time— international, sec-
tional, and local. E. B. Elliott. Ab-
stract ii 137
meridional time for railway and tele-
graphic purposes. E. B. Elliott. Ab-
stract ii 202
on a system of standard time. A. S. Chris-
tie. Abstract v 112
the action of the International Geodetic
Association as to an initial meridian
and universal time. R. D. Cutts. Ab-
stract vi 106
California, Geology of northern ix 4
Latest volcano in ix 46
Cambrian system in the United States and
Canada vi 98
Campagna, Eucalyptus on the vi ^36
Capron, Horace, communication on Japan.
Title only ii 79
Death of. viii 8
Carbonate deposits of Leadville, Colo vi 32
Care of pamphlets viii 29
Carpenter, Dr. W. B., cited on binocular mi-
croscopes iv 35
Cartesian philosophy vii xli
Caspian Sea, Altitude of ii 34
Catalogue of astronomical papers ii 95
of stars prepared at U. S. Naval Observa-
tory i 74
Catlin, cited on color, number, and theology
of Indians Ii 175
Cells found in human fseces ix 35
Census, Mortality statistics of the Tenth,
iv 1G4
128 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Census, Vital statistics of the Tenth vlll 4
Centre of population of United States i 35
United SJates 1 22
Centres for light-, form-, and color-percep-
tion vll 72
Ceremonial institutions, Origin of certain..lx 19
Cernuschi, cited on bi-metallism iii 108
Chadwick. Lt. Com'd'r F. E., cited on sound
anomalies 34
Challis, Prof. J., cited on elasticity v 152, 154
force v 128
Chamberlin, T. C, communication on What
is a glacier? Abstract vll 38
the varying attitudes of former level
surfaces in the Great Lake region and
the applicability of proposed explana-
tions. Title only ix 15, 10
remarks on the loess of Iowa and Ne-
braska iv 121
Champlain, Ice on Lake 11 (22;
Changes of terrestrial level surfaces due to
variations in the distribution of super-
ficial matter vll 92. 101, ix 15, 53
Chapman's Flora of the Southern States,
iv 99
Charles, Law of v 139
Charleston earthquake 1x37,38, x 17,28
Charts of archaeology 11 72
Chase, Salmon P., Resolutions on death of..l 87
Chatard, T. M., remarks on earth tremors,
vlll 28
Chemical equivalency vil xlvii
rays v 135
side of vitality v 53
Society, Invitation from vlll 29, Ix 46
theory of volcanism vl 90, 93
Chemistry, Li»t of papers on :
[exhibition of apparatus for the genera-
tion of ozone.] B. F. Craig. No ab-
stract 1 52
on the cause and remedy of the potato rot.
L. D. Gale. Title only 1 97
on the chemistry of the Bessemer pro-
cess. C. E. Dutton. Title only 1 98
on the atomic volumes of crystallized and
double salts. F. W. Clarke. Refer-
ence 1 103
on the molecular heats of similar com-
pounds. F.W.Clarke. Abstract 1104
on the coloring agent of gems. F. M. End-
lich. Abstract 11 31
the estimation of manganese as pyrophos-
phate. C. E. Munroe. Communicated
by T. Antisell. Reference 11 132
chemical remarks on terrestrial geogony.
T. Antisell. Title only 11 132, 133, 134
Page.
Chemistry, List of papers on—Cont'd,
observations on 'chemical molecular
changes. T. Antisell. Title only Ill 28
the origin of the chemical elements. L.
F.Ward. Title only ..Ill 33
a case of peculiar corrosive action on me-
tallic tin. J.W.Osborne. Title only.MV 44
determination of the specific gravity of
solids by the common hydrometer.
C. E. Munroe. In full vl 26
the periodic law of chemical elements. F.
W. Clarke. Abstract vll 15
music and the chemical elements. M. H.
Doolittle. Abstract vll 26, 27
an attempt at a theory of odor. F. W.
Clarke. Abstract vlll 27
Chickering, J. W., communication on the
correlation of the winds and the tem-
peratures of the surface waters of tho
ocean along the coast of New Hamp-
shire. Abstract 11 17
Luray cave. Title only Ill 65
Roan Mountain, N. C. In full Iv 60
the thermal belts of North Carolina. Ab-
stract vl 11
the Muir glacier, Alaska. Title only...s. 15
Chesapeake and Ohio Railroad, Geology
along 11(26)
Chesapeake Bay geology x 16
Chico group in Northern California Ix 4
Chimsera, New species of 11 182
Chinese language 11 28
Chitonidse 11 193
Chlamydoconcha Orcuttl vlll 5
Chorography x 14
Christie, A. S., communication on a system
of standard time. Abstract v 112
a quasi general differentiation. Title
only vl 122
contact of plane curves. Abstract vl 157
a form of the multinomial theorem.
Title only vli 101
a problem in probabilities. Abstract...x 89
remark on infinitesimals vl 135
Christmas eve meteor 11 139
Chronograph readings, Relative frequency
of digits in 1 85
Circle, Quadrature of 1 57
Circles related to Feuerbach's circle vlll 45
Circular on the meteor of Dec. 24, 1873 11 139
Circumference, Ratio of, to diameter 1 57
Clark, Alvan, communication on the con-
struction of the lenses and other inter-
esting portions of the large telescope
now established at the Naval Observa-
tory. Title only 1 92
INDEX TO VOLUMES I-X. 129
Page.
Clarke, F. W., communication on the atomic
volumes of crystallized and double salts.
Reference 1 103
the molecular heats of similar com-
pounds. Abstract i 104
the periodic law of the elements. Ab-
stract vll 15
topaz from Stoneham, Maine. Abstract
and reference viii 5
an attempt at a theory of odor. Ab-
stract vlii 27
the Flood Rock explosion. AbstracL.xill 28
the present status of mineralogy. Title
only X 6
the Manchester meeting of the British
Association for the Advancement of
Science, 1887. Title only x 19
remarks on chemical theories of volean-
ism vi 93
Classification of insectivorous mammals ...v 118
literature of meteorology x 26
plants iv 108
Clausen, cited on computation of 7r i 58
Clausius' researches in molecular physics,
v 138, 140
Clerk-Maxwell. See Maxwell.
Clifford's philosophy vii liii
Climate and variations in solar radiation..vi 10
of plants ii 183
of Roan Mountain iv 62
Quaternary, of the Great Basin v 21
Climatic influence of land areas '....ii 46
Clingman, T. L., communication on the
earthquake phenomena recently ex-
perienced in Nerth Carolina. Abstract
and reference i 104
the falling of waterspouts in North Caro-
lina. Abstract ii 104
Cloud bursts in North Carolina ii 104
Coal, Formation of vi 28
Coastal plains ix 23
Coffin, J. H. C, cited on cyclonic motion...! 108
communication on maps prepared by G.
W. Hill for use in connection with the
transit of Venus in December, 1874.
Reference i 63
Sumner's method in navigation. In
full ii 105
remarks on calendars ii 29, 60
standard time ii 202, v 115
Cohesion v 127
and adhesion v 136
Coin, Amount of subsidiary silver ix 14
Coinage, International iil 38
of the Argentine Republic ii 65
Coincidences x 8
55
Page.
Coins, Exhibition of. v 22
Collier, Peter, communication on sugar from
sorghum. Abstract* iii 140
Color of Indians H 175
perception and color blindness iv 54
tests ill 54
Colorado of the West, Valley of the i 48
Coloring agent of gems ii 31
Columnar structure in the diabase of Orange
Mt.. N. J viii 19
Comet, Barnard's- viii 17
Encke's i 34, 35
1, 1871, Elements of. i 23
III, 1884, (Wolf 's) viii 37
Orbit of Swift's iv 59
orbits illustrated by models x 28
Spectrum of Encke's.. i 34
Tuttle's i 34
Comets and meteors I 94
Comet's orbit, Correction of. il 22
Comets' tails i 74
r.ommittee, auditing, Appointment of...v 84, 174,
vi 111, vii 82, viii 31, ix 47, x 39.
Report of....v 89, vi 5, vii 15, viii 3, ix 3, x 3.
Resolution on v 84
on communications i 21, ii viii, 101, iii 151,
iv 31, 39, v 14, 175, vi xiv, xv, vii xiv, xv,
viii xiv, xv, ix xiv, xv, x xiv, xv.
on mathematical papers vi 135, 161, vii 129,
viii 63, x 111
on mathematical papers, Resolution on..vi 135
on the meteor of December 24, 1873 i 94, 98,
ii 139
on papers and essays. See Committee on Com-
munications.
on publications i 21, ii viii, 161, iii 151, v 14,
175, vi xiv, xv, vii xiv, xv, viii xiv, xv,
ix xiv, xv, x xiv, xv.
to draft resolutions on the death of
L. Agassiz i 93, 94
F. B. Meek ii m
A. B. Eaton ii m
C. H. Davis ii m
T. Bailey
., ...ii m
J. Henry ii 196
A. R. Marvine ii 83
B. Peirce iv 21, 23
A. J. Myer iv 23, 31
G. A. Otis iv 120, 134
to draft resolutions on the discovery of the
satellites of Mars ii 186
to nominate officers of Mathematical Sec-
tion x 83
Communications, List of. See Acoustics,
Anatomy, Anthropology, Archaeology,
Astronomy, Biography, Biology, Botany,
130 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Calendars, Chemistry, Electricity, Geog-
raphy, Geology, Mathematics, Meteor-
ology, Microscopy, Mineralogy, Miscella-
neous, Oceanography, Optics, Physics,
Political Economy, Psychology, Seis-
mology, Social Science, Thermometry,
Zoology.
Statistics of. x 32
Compass plant v 100
Composite photography applied to crani-
ology vll 25
Composition of error v 100
Computation by method of least squares 1 02,
vt 150, vill 41
of a comet's orbit 11 22
planetary perturbations of the moon
vl 130
Computing the position of a satellite vll y:i
machine jt 102
Comte, AugUtte, cited on forces v 127
Conditioned observations, Adjustment of,
vlll 41
Conservation of energy vll 02
foreo i 27
Conservative element in disease It 111, 124
Consolidated list x 30
Constant Pin terrestrial magnetism x 102
Constitution. ..1 xv, It iii, lit iii, lv 5, v 0, vl vii,
-vit vii, vttl vii, lx vii, x vii
Adoption of t 80, 21
Amendment to tx 47, x :i9
Contact of plane curves vl 167
Contraction hypothesis vl 90, vlll 18
Corona of the sun 1 81, 111 116, 121
Corrections to normal thermometers lx 28
Corrigenda. ..11 p. 4 of cover. HI 148, vl 102, x 114
Coseismal map lx 39
Cosmos assembly hall x xxxi, 10, 31
Cosmos Club, Organization of x 47
Cotes, Roger, cited on ultimate causes v 163
Coues, Elliott, cited on Halrd's "Birds of
North America" x 66
poisoned wounds from arrows 11 182
communication on the structure and
homologies of the limbs, especially in
Aves. Title only 1 90
the use of poisoned arrows by North
American Indians. Title only 11 183
the possibilities of protoplasm. Abstract
and reference 102
remarks on poisoned arrows 11 183
Counting-out rhymes x 13
Cracks in ice on Lake Champlaln 11 (22)
Craig, B. F., communication on the fluctua-
tions of the temperature of the human
body. Reference 1 31
Page
Craig, n. F., communication on—Cont'd,
apothecaries' weights and measures.
Title only 1 34
thermometers. Title only 1 42
a method of verifying with exactness the
indications of a thermometer. Title
only 1 43
apparatus for the generation of ozone.
No abstract 1 62
the water supply of cities. Title only...i 65
Resolutions on J,he death of. 11 130
Craig, Thomas, communication on vortex
motion in ordinary fluids. Reference,
111 143
Crane, C. H., Death of. vl 41
Cranlology vll 25
Crello. Dr. A. L., cited on Malfatti's prob-
lem II 115
Croll, Prof. J., cited on action at a distance
v 156
Croll's theory 11 43, 45
Crookes, W., cited on matter v 129
Crookos' radiometer 11 80
Cross Timbers of Texas x 6
Crumpling of the earth's crust vlll 18
Crystalline state of matter Ill 39
Culture media vlll 30
Cumberland plateau lx 24
Currents shown by drifting buoys vll 14
Curtis, G. K., communication on tho rela-
tions between northers and magnotic
disturbances at Havana. Reference,
vll 25
Lieutenant Lockwood's expedition to
farthest north. Abstract lx 8
the theory of the wind-vane. Refer-
ence x 9
a problem in probabilities. No ab.
itract x 88
solutions of the trisection problem. Ab-
stract x 98
remarks on verification of weather pre-
dictions vlll 9
Curtis, Josiah, letter on Hayden's Survey.
Communicated by E. B. Elliott. No ab-
stract 1 03
Death of. vl 41
Curve of tho fourth degree 1 30
Curves, Alignment t vl 123
Contact of plane vl 157
similar to their evolutes vll 87
Customs of every day life lx 19
Cutts, R. D., communication on the misap-
plication of geographical terms, as
bearing especially on .the question of
the fishery right treaties. Abstract. ..I 39
INDEX TO VOLUMES I-X. 131
Page.
Cutts, R. D., communication on—Cont'd,
the results of astronomical observations
at Sherman Station, Wyoming Terr.
Abstract and reference i 70
the action of the International Geodetic
Association as to an initial meridian
and universal time. Abstract vi 106
Death of vi 111
Cyclones, Movement of 1 99
Retardation of v 108
Cyclonic storms, Laws of. 1 106
Dakota, Black Hills of. ill 125
calendar il 90
Dall.W. H., communication on the relative
value of Alaska to the United States, as
compared with that of other territorial
acquisitions. Abstract and reference..X 25
elevations and depressions in Alaska.
No abstract 11 27
the succession of the strata of the shell
heaps of the Aleutian islands. Ab-
stract 11 65
the results of recent investigations into
the natural history of the Chitonida9.
Abstract 11 193
the museums and zoological gardens of
Northern Europe. Title only ill 19, 21
the muscles of the oyster. Abstract. ..Ill 36
the deep sea dredgings in the Gulf of
Mexico and the West Indies in 1873-
1878, by Professors Louis and Alex-
ander Agassiz and the officers of the
U. S. Coast Survey. Title only ill 45
some recent observations on mollusks.
Abstract Ill 75
the boundary line between Alaska and
British America. Title only ill 77
recent discoveries in Alaska north of
Behring Strait. Abstract iv 163
some peculiar features of mollusks found
at great depths. Abstract .v 90
glaciation in Alaska. Abstract vi 33
recent advances in our knowledge of the
limpets. Abstract vii 4
certain appendages of the mollusca.
Reference vii 32
What is a glacier? Abstract vll 38
two remarkable forms of mollusks. Ab-
stract and reference viii 5
South Florida notes. Title only x 16
Professor Baird in science. In full x 61
remarks on the glacial period 11 36
Arctic tides 11 89
teredo borings v 98
glaciation and climate vl 11
Page.
Dall, W. H., remarks on—Cont'd.
tornadoes vii 3
drifting buoys vii 15
deflection of rivers vll 21
the Bogosloff eruption vii 34
Arctic exploration ix 12
Dalton's atomic philosophy vii xlvii
law v 139
Dana, J. D., cited on mineralogy i 78, 79
Darton, N. H., communication on the occur-
rence of copper ore in the Trias of the
Eastern United States. 'Title only...ix 46
Darwin's doctrine of gemmules vii liii
law of the distribution of volcanoes. ...vi 89, 91
Dase, cited on computation of" 1 58
Davidson, George, letter on transit of Venus,
1874. Communicated by Asaph Hall.
Abstract 11 32
Davidson, Lieut., cited on the co-ordinates
of Bald Head, Alaska iv 126
Davis, C. H., Death of ii 111
Dawson, Prof. J. W., cited on fossil plants
from Virginia ii (38), (42)
Deaf mutes, Fallacies concerning vi 48
Languages of iv 55
Death of L. Agassiz 1 93
B. Alvord vii 72, 127
O. E. Babcock vii 72
S. F. Baird x 17, 20 43, 76
T. Bailey ii 109, 111
H. W. Blair vii 81
H. Capron vlii 8
S. P. Chase i 87
B. F. Craig ii 130
C. H.Crane vi 41
J. Curtis vi 41
R. D. Cutts vi 111
C. H. Davis il 111
A. B.Eaton ii ill
E. Foote vl 48
L. D. Gale vi 48
W. B. Hazen x 6
J. Henry ii 19G, 203, 214, 358, 370
Mrs. J. Henry v 97
F. B. Hough viii 25
A. A. Humphreys vii 3, 4
F. Kampff. _ ii 1S9
W. C. Kerr viii 25
J. H. Lane Hi 122
E. P. Lull x 8
A. R. Marvine ii 83, (53)
F. B. Meek ii m
A. J. Myer iv 23, 31
G. A. Otis lv 120, 134, 171
T. R. Peale viii 10
B. Peirce lv 21, 23
132 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Death of—Cont'd.
J. C. Riley lii 28
J. Rodgers v 102
B. F. Sands vi 41
G. C. Shaeffer i 00
W. J. Twining v 102
J. J. Woodward vll 72, 75
M. Yarnall ill 28
Declination standards ix 53
Deep sea mollusks v 90
Definitions
y
vli 46
Degradation. See Erosion.
Delgarno, G., cited on instruction of the
dumb vi 71
Delta of the Mississippi river i (10)
Democritus' philosophy vii xxxiv
Denihilo nihil fit vii xxx, xxxiii
Denver, Altitude of 11 24
Department of science ix xlvi
Depauperation of Limnsea Ill 75
Derham, Dr. W., cited on echoes v 41
De Tocqueville, cited on destruction of In-
dians 11 175
Device for viewing the sun by light of any
desired wave length x 13
Devonian strata near Sulphur Springs, W.
Va 11(27)
Dewar, Prof., cited on the radiometer 11 81
Diagnosis of blood-stains 11 20, 41
Diarrhoeal diseases and weather Iv 165
Diatonic scale vll 26
Differential equations admitting periodic
integrals x 100
Diffraction fringes Ill 119
phenomena in the field of the micro-
scope 11 60
Diller, J.S., communication on the volcanic
sand which fell at Unalashka October
20, 1883, and some considerations con-
cerning its composition. Abstract.-vii 33
topaz from Stoneham, Maine. Abstract
and reference Till 5
the Keology of northern California. Ab-
stract lx 4
the latest volcanic eruption in northern
California and its peculiar lava. Refer-
ence lx 46
Mount Shasta contrasted with Mount
Rainier. No abstract x 11
remarks on geology of Cascade Moun-
tains lx 8
Krakatoan dust vll 35
Diorthode vi 123
Diptheria, Inoculation of iv 38
Direction of sound, Determination of ill 69,
viil 12, lx 43
Page.
Discontinuity in elliptig orbits vii 122
Discovery of the satellites of Mars.... 11 186
Disease and climate Iv 165
Conservative element in ii 111, 124
Disinfection by gases iv 38
of ships lii 51
Dismal Swamp, Geology of. vi 28
Displacement, Geologic ii 75
of the middlo Atlantic slope .x 16
Dissipation of energy vll 63
Distances on any spheroid vili 52
Distribution of fossil plants x 28
mammals ii 26
scientific men and institutions x 7
the surplus money of the United States
among the States vi 103
District of Columbia, Flora of iv 64
Diurnal variation of magnetic declination,
ill 46
Dixwell, G. B., communication on cylinder
condensation, steam jackets, and su-
perheated steam. Title only Ii 64
Doane, G. C, report of the Yellowstone ex-
pedition of 1870. Communicated by S.
F. Baird. Reference i 21
Dobson, Surgeon-Major, cited on insectivor-
ous mammals v 118, 120
Dog, Malformed ii 185
Doolittle, M. H., communication on the neb-
ular hypothesis and the inner moon
of Mars. Abstract ii 188, 190
the influence of aerolites on planetary
motion. Abstract 11 190
aerolithic disturbance of planetary mo-
tions. Abstract.. ii 190
a pile of balls. Abstract Ill 76
the silver question. Abstract Hi 103, 112
the geometrical problem to determine a
circle equally distant from four points.
Abstract v 88
substance, matter, motion, and force.
Title only vi 14
infinite and infinitesimal quantities.
Abstract vi 133
the rejection of doubtful observations.
Abstract vi 152
music and the chemical elements.
Abstract vii 26, 27
the verification of predictions. Ab-
stract vii 122
cause and chance in the concurrence of
phenomena. Title only viil 54
What is topography ? Abstract x 14
Newton's vis. Title only x 38
association ratios. Abstrlbt x 83
a problem in probabilities. Abstract. ..x 88
INDEX TO VOLUMES I-X. 133
Page.
Dooliltle, M. H., communication on—Cont'd.
association ratios. Abstract X93, 94
remarks on sesquisection Till 52
gravitation formula Till 40
phonetic alphabet ix 19
bi-metallism Ill 103
the need of abiomeier v 105
binary arithmetic vi 39
Dorsey, J. Owen, communication on the
gentile system of the Omahas. In full.
3 figures Ill 128
Drainage system and loess of eastern Iowa,
vl 93
of the Black Hills ill 125
systems 1 49
Draper, Prof. J. W., cited on photography. ..1 47
radiant energy v 135
Dreams in their relation with psychology..vi 37
Driftless region. vl 94
Drift of Iowa and Nebraska lv 120
Dry painting of the Navajos viil 14
Duane, Gen., cited on fog signals v 32, 43
phenomena of sound 11 (49), (50)
Du Bois-Raymond, Experiments in animal
electricity by v 57, 00, 01, 62
Dudley, P. II., communication on the uses
of the dynagraph, and the work per-
formed in determining the resistance
of trains, etc. Abstract Ill 29
Dulong and Petit, Law of v 139
Thermometric experiments of. v 91, 93
Dumbness of deaf children vl 48
Du Pr6, Warren, cited on earthquakes 1 101
Dutton, C. E., communication on the meas-
urement of the pressure developed by
the explosion of gunpowder in fire-
arms. Title only 1 52
some recent experiments on different
kinds of gunpowder at Fortress Mon-
roe. Titleonly 1 54
the causes of the elevations and subsi-
dences of the earth's surface. Title
only... 1 74
geological time. Titleonly 1 89
Mallet's theory of the formation of the
physical features of the earth. Title
only 1 90
recent improvements in the economy of
fuel. Titleonly i 96
recent improvements in the manufac-
ture of steel. Titleonly 1 97
the chemistry of the Bessemer process.
Title only.„ 1 98
the glacial period. Titleonly 11 26
the causes of glacial climate. Abstract,
1143,45 |
Page.
Dutton, C. E., communication on—Cont'd,
the geological character of the Colorado
river. Titleonly Ill 28
the succession of volcanic eruptions.
Title only ill 36, 37
the Permian formation of North Amer-
ica. Abstract Ill 65, 67
the silver question. In full Ill 78
the scenery of the Grand Canon district.
Title only lv 120
the Vermilion cliffs and the valley of
the Virgen in southern Utah. C. E.
Dutton. Titleonly lv 122
the geology of the Hawaiian islands.
Abstract vl 13
the volcanic problem stated. Abstract,
vl 87
What is a glacier ? Abstract vli 39
the volcanoes and lava fields of New
Mexico. Abstract vil 76
practical geology versus speculative
physics. Titleonly viil 4, 5
a recent visit to the scene of the Charles-
ton earthquake and resulting conclu-
sions. Titleonly x 16
the depth of earthquake foci. Abstract.
1 figure x 17
the speed of propagation of the Charles-
ton earthquake. Reference x 28
remarks on distribution of volcanic ac-
tion 1 102
wind and temperature observations 11 18
refraction of sound ii 58
geology of the Colorado region ii 76
the earth's interior ii 77
charcoal in the drift iv 122
separation of minerals by density vl 27
nebular hypothesis vi 45
temperature observation vl 48
outlines of continents vli 24
sun glows vli 35
Indian observation of nature vli 74
earthquake detonations viil 28
Charleston earthquake ix 42
Dynagraph, The iii 29
Dynamic hypothesis vi xxx
theories of force v 126
Eastman, J. E., cited on individual vocabu-
laries *i(21)
communication on a comparison of the
thermometers used to determine the
correction for atmospheric refraction
at the U. S. Naval Observatory. Ab-
stract i 68
134 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Eastman, J. R., communication on—Cont'd,
the frequency of the occurrence of the
zero and the nine digits in the tenths
of seconds as obtained from the chro-
nograph ic record of transit observa-
tions. Abstract i 85
the comparison of rain-gauges at differ-
ent, elevations. Abstract ii 49
a personal equation instrument. Ab-
stract ill 33, 37
some results from the discussion of the
observations of the transit of Mercury
of May 6, 1878. Abstract iii 43
the Florida expedition for observation
of the transit of Venus [1882]. Ab-
stract vi 21
the Rochester (Minnesota) tornado. Ab-
stract vii 3
a new meteorite. Abstract vii 32
remarks on vocabularies 11 28
Eaton, A. B., communication on the preser-
vation of foods. Title only 1 22
Death of 11 111
Eaton, Prof., cited on classification of ferns,
lv 110
Earth, Interior of. 11 76
tremors as shown by astronomical obser-
vations..... Ill 120
at Niagara Falls lv 186
Velocity of vill 28
Earthquake. See Seismology.
Earth's crust, Crumpling of vili 18
interior, Condition of viil 7
Easter, Computation of vi 15
Echo from surface of ocean 11 171
Echoes, Tyndall on , v 41
Eclipse of the moon, June 11, 1881 v 90
sun, January 11, 1880 iii 121
sun, July 29, 1878 11 202, ill 116
Economic phase of the English sparrow
question x 16
Economics. See Political Economy.
Education in Japan 11 69
Edwards, W. H., cited on the pupation of the
Nymphalidoe iii 42
Eidocenter viii 47
Eimbeck, Wm., cited on the diorthode vi 132
Elasticity v 130
Election of officers 1 20, 32, 64, 91, 11 16, 59,
86, 161, iii 17, 51, iv 29, v 84, 174, vi 111
vii 81, vill 80, ix 47, x 39.
officers of the Mathematical Section...vi 122,
vil 87, vili 37, lx 53, x 83
Electric receivers iv 153
researches by Joseph Henry ii 236
Electricity as a primitive force v 168
Page.
Electricity, List of papers on (See also
Acoustics) :
on the recording systems of the trans-
atlantic cables. J. E. Hilgard. Title
only 1 53
[a method of lighting gas jets by electric-
ity.] Dr. Van Sant. No abstract 1 56
on electricity engendered by the driving
belt of the machinery for ventilating
the Capitol at Washington. J. Henry.
Abstract 11 40
Jablokoff' s electric candle. J. E. Hilgard.
Title only ill 19
large area illumination by electricity. E.
B.Elliott. Title only iii 45
the storage of electric energy. C. H. Koyl.
Abstract v 46
units of force and energy, including elec-
tric units. E. B. Elliott. Title only,
vt 137
electric lighting. E. B. Elliott. Title only,
vii 80
[exhibition of a volt-meter.] T. C. Men-
denhall. Abstract vili 26
the electrometer as used in observation'*
of atmospheric electricity. C. F. Mar-
vin. Title only x 9
the mutual action of elements of electric
currents. E. B. Elliott. Abstract and
reference x 92
the quotients of space-directed lines. E.
B. Elliott. Abstract x 105, 106
Elements, Periodic law of. vii 15
Elevation. See Altitude.
Eliot and Storer, cited on atoms v 128
Elliott, E. B., calendar of the Society...vil xxii,
vill xxx, lx xxvii, x xxxi:
communication on the statistics of the
borrowing power of the United States.
Title only 1 29
the new coinage of Japan. Title only. ..I 31
the locus of the point of equal illumi-
nation by two unequal lights treated
by the quaternion analysis. Title only,
i 35
the adjustment of census returns. Title
only 1 63
life and annuity tables, based on the
census of 1870. Title only i 74
international coinage. Title only 1 75
change in value of dollar. No abstract,
I 91
the credit of the United States, as shown
by the value of its securities. Title
only 1 109
INDEX TO VOLUMES I-X. 135
Page.
Elliott, E. B., communication on—Cont'd,
the use of metric weights and balances
for postal purposes in the United
States. Abstract il 15
further remarks on metric weights and
balances for the postal service. Ab-
stract il 19
the transition in Germany, and the
Scandinavian nations of Sweden, Nor-
way, and Denmark, from the silver
standard of coinage and money of ac-
count to a gold standard 11 25
calendar formulae. Abstract 11 37
affected quantities of the first order.
Title only 11 42
the mutual relations as to price of gold,
silver bullion, silver coin, and green-
backs. Title only 11 50
the mutual relation as to price of gold,
greenbacks, silver bullion, and silver
coin. Infull 11 52
adjustment of the calendar. Abstract..U 59
two propositions, now before Congress,
for changing the coin of the United
States. Title only 11 68
force and momentum. Title only 11 84
monetary standards. Title only 11 85
mutual relations of gold and silver, and
of prices of commodities. Abstract...ii 87
the telephone. Title only il 111
a statistical diagram. No abstract 11 134
optional money standards. Title only...U 135
standards of time—international, sec-
tional, and local. Abstract 11 137
the telephote. Abstract ii 192
musical intervals. Abstract ii 199
the adjustment of the Carlisle tables of
reversions and annuities. Title only. .ii 201
meridional timo for railway and tele-
graphic purposes. Abstract Ii 202
the progress of international coinage in
France and America. Title only ill 27
the subject of international coinage.
Abstract ill 38
large area illumination by electricity.
Title only ill 45
the silver question. Abstract ill 103, 107
the construction of the Government
sinking fund. Abstract ill 113
bi-metallism. Abstract iv 141
accrued interest on Government secur-
ities. Title only v 21
the credit of the United States, past,
present, and prospective. Title only..-v 102
some formulae relating to Government
securities. Title only v 106
Page.
Elliott, E. B., communication on—Cont'd,
survivorships, with tables and formulas
of construction. Title only v 122
formulas for the computation of Easter.
In full vi 14
units of force and energy, including
electric units. Title only vi 137
a financial problem. Title only vi 149
electric lighting. Title only vil 80
Benjamin Alvord. Infull vii 127
example illustrating the use of a certain
symbol in the calculus of affected
quantity. Title only viii 37
quantity of United States subsidiary sil-
ver coin existing and in circulation.
Title only ix 14
annual profit to banks of national bank
note circulation. Title only ix 14
a problem in probabilities. No abstract,
x 88
the mutual action of elements of elec-
tric currents. Abstract and reference..x 92
a now computing machine. Abstract...x 102
the quotients of space-directed lines.
Abstract x 105, 106
remarks on auroras i 45, iv 22
calendar reform ii 30
bi-metallism ill 103
Benjamin Peirce Iv 24
small loans by banks iv 34
the metric system vi 4
standard time vi 110
infinitesimals „ vi 135
theory of errors vi 148
tornado vii 3
sun glows vii 17
irrigation vii 20
Poole's euharmonic organ vii 28
Elliott, H. W., communication on the habits
of the fur-bearing seals of the islands
of St. Paul and St. George, Behring Sea.
Reference 1 91
Elliptic integral of the third species Ix 54
integrals vil 102
Ellis, William, cited on the constant P x 102
Emmons, S. F., communication on ore de-
position by replacement. Abstract and
reference vl 32
What is a glacier? Abstract vii 37
remarks on glaciers vil 9
Emmons' Taconic system x 5
Encke's comet 134, 35
Endlich, F. M., communication on mineral
systems. Infull 1 77
electrical phenomena in the Rocky
Mountains. Title only 1 95
136 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Endlich, F. M., communication on—Cont'd,
two bricks from the great wall of China.
Title only i 98
specimens of meteoric iron from Chi-
huahua, Mexico, and the structure of
meteorites in general. Title only i 98
the occurrence of pure tellurium in cer-
tain gold mines of Colorado. Title
only 1 101
the coloring agent of gems. Abstract,
11 31
some interesting cases of metamor-
phism. Title only Ill 27
remarks on the glacial period 11 36
Endowment of research viil xli
Energy vll 61
Conservation and dissipation of 1 27
Engelman, Dr. G., cited on Quercus lv 110
English sparrow question x 16
Entomology. See Zoology.
Eotvos, cited on sounds produced by me-
teors .*..ll 157
Epicurus cited on philosophy vil xxx
Erie, Altitude of Lake ~. 11 23
Erosion as related to displacement 11 75
by drifting sand 1 57
Errata 11 p. 4 of cover, 111 148, vi 162, x 114
Errors, Composition of. v 106
respecting the North American Indians..ll 175
Theory of. vi 138, 152
Eruption, Latest, in Northern California,
ix 46
Theories of. vi 87
Eskimo shell heaps 11 65
Estimation of manganese as pyrophosphate,
11 132
Ether, Hypothesis of an vi xxix
Ethnology. See Anthropology.
Eucalyptus on tho Roman campagna vl 36
Eulcr ignored by Am. Phil. Soc vili xxxvii
Euler's theorem — x 101
Eulogy on A. D. Bache - 1 35
A. A. Humphreys vil 4
Evolutes vll 87
Evolution and phthisis 11 125
Methods of vl xxvii
of the bow and arrow Ix 44
elements _ vll 16
Expansion and buckling of ice fields 11 (22)
Experimentation 11 163, vll li
Explosion at Flood Rock.., vlii 28
" Explosion" of meteor explained- —11 143
Exposure of thermometers...-- ...vi 46, vll 80
Eye, Optical defects of 1 22
Eyes, Apparatus for testing Ill 53
shining in the dark ......vll 13
Page.
Falconidse, Natural arrangement of..... 11 41
Fall line T ix 23
Fallacies concerning the deaf vi 48
Fallacy as to the theory of gravitation v 85
Faraday, cited on matter vll 48
Farquhar, Edward, cited on personal vocab-
ulary. 11(18)
communication on certain remarkable
effects of lightning. Read by Joseph
Henry. Titleonly 1 42
dreams in their relation with psychol-
ogy. Abstract vi 37
remarks on the aurora iv 22
tornadoes vii 3
thunder storms vili 11
determining the direction of sound..vili 13
Farquhar, Henry, communication on exper-
iments in binary arithmetic. Abstract,
v 125, vi 3
further experiments in binary arith-
metic. Abstract vi 38
form of least-square computation. In
full vi 150
the problem discussed by Mr. Alvord.
Abstract* vi 152
the theoretical discussion in Prof. P. G.
Tait's "Encyclopedia Britannica"
article on mechanics. Abstract vii 29
empirical formulae for the diminution
of amplitude of a freely-oscillating
pendulum. Abstract vil 89
a Fonetic jElfabet. Abstract ix 17
a comparison of the Boss and Auwers
declination standards. Abstract and
reference Ix 53
a problem in probabilities. Abstract. ..x 88
a solution and generalization of a prob-
lem requiring the division of a rec-
tangle into parts which form a square.
No abstract x 96
remarks on standard time .v 114
infinitesimals- vi 135
drifting buoys vii 15
earth tremors vili 28
Fault at the base of the Wasatch Moun-
tains 11 105
near Harper's Ferry vl 30
scarps 11 195
Faults, Geologic 1175,76
In the Sierra Nevada- ix 4, 5
of the Great Basin ix 5
Ferguson, J., observation of supposed trans-
Neptunian planet ill 20
Ferrel, William, cited on deflection of rivers
by rotation- vll 22
law of storms- l 100
INDEX TO VOLUMES I-X. 137
Ferrel, William, cited on—Cont'd.
thermometry vi 25
communication on the effects of winds
and barometric pressure on the tides
of Boston, and on the mean level of
the sea. Abstract and reference i 53
the law connecting the velocity and di-
rection of the wind with the baro-
metric gradient. Abstract i 106
the conditions determining tempera-
ture. In full v90, 91
solar radiation at Sherman, Wyoming.
Title only v 101
Feuerbach's circle viii 45
Finance. See Political Economy.
Financial problem vi 149
Fish, Decrease of, on the southern coast of
New England i 52
fauna of Massachusetts 1 29
New species of ii 182
Remarkable ingestion of. ill 116
Fishes, Shoulder girdle of i 64
Fisheries exhibitions Til 26, x 56
of the world v 117
Fishery Commission's work x 52, 69
right treaties, Interpretation of 1 39
Fletcher, Robert, communication on recent
experiments on serpent venom. Ref-
erence vi 38
report as treasurer vi! 82, viii xxviii, 31, lx
xxx, 47, x xxxiv, 39
Fletchers and bowyers lx 44
Flexures of transit instruments vill 27
Flint, A. S., communication on the most
probable value of the latitude and its
theoretical weight from entangled ob-
servations occurring in the use of Tal-
cott's method. Abstract x 91
Flora of Laramie group viii 17
Roan Mountain iv 63
Washington and vicinity iv 64
Floras of America and Japan ii 42
different regions compared iv 99
Florida expedition for observation of the
transit of Venus vi 21
Submergence of iv 53
Flood Rock explosion viii 28
Focal lines in astigmatism vi 45
Fog signals and acoustics...„ii 37, 57, 60, 167, 345,
(45), iv 135, v 23, 39
Food adulteration iv 39
Foote, Elisha, communication on the laws of
condensation of aqueous vapor in the
atmosphere. Titltonly 1 74
a proposed method of observing astro-
nomical transits. Title only 1 75
Page.
Foote, Elisha, communication on—Cont'd,
some causes that produce rain. Title
only i 98
the causes of electrical developments in
thunder storms. Abstract ii 189
Death of. vi 48
Force i 27, v 126, vi xxviii, vli 47
and life v 57
matter vii 30
Forecasts, verification of viii 8
Formula for the length of a seconds-pendu-
lum vii 101
Formulae for area of a plane triangle viii 37
diminution of pendulum swing vii 89
Fort Yukon, Determination of position of...i 22
Fossil plants, Distribution of x 28
from Alleghany Co.,Va ii (26)
Fossils in aerolites v 66
Foster, M., cited on muscular contraction..v 60
nerve currents v 62
Fourier, cited on the temperature of space..ii 73
Forshey, C. G., communication on the allu-
vial basin of the Mississippi river
styled the delta. In full i 9S, (10)
Frank, F., cited on brain temperatures v 76
Franklin's scientific work viii xxxv
Free will iv 46
Fremont, Dr. H. F., Researches on inocula-
tion of diptheria by iv 38
Frisby, E., communication on a series for
the determination of the number ex-
pressing the ratio of the circumfer-
ence to the diameter. In full i 57
a Gregorian calendar. Abstract i 75
series. Title only ii 193
the total solar eclipse of January 11th,
1880. Abstract Hi 121
magic squares. Abstract. § figures ...Hi. \4Z
the orbit of Swift's comet. Abstract...iv 59
remarks on calendars ii 38
Frost limits in North Carolina vi 11
Fundamental distance in thermometry. ...ix 27
Fungi, Microscopic i 42
Gale, L. D., communication on the cause
and remedy of the potato rot. Title
only i 97
the geology of the lignite formation,
and on a hitherto undescribed de-
posit discovered in 1834 in New York
bay. Title only i 106
the failure of the wooden pavements of
Washington City. Abstract ii 26
the climate of plants. Abstract ii 183
remarks on the bowlders of Long Island. .ii 27
Death of. vi 48
138 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Galen, cited on life v 51
Galileo, cited on Saturn's rings vi 44
Gallaudet, E. St., communication on uncon-
scious cerebration. Title only ii 48
the international convention of the
teachers of the deaf and dumb, at
Milan. Abstract iv 55
remarks on gesture language and visible
speech -ri 77
Gamgee, A., cited on muscular contrac-
tion v59, 60
nerve currents v C2
Gardner, J. T., communication on the use of
railroad levellings in determining ele-
vations on the great lakes and rivers
in the United States and in the Rocky
Mountains. Abstract and referencc.il 23
Gases, Theory of. v 138
Gauss, cited on computation of t? i 59
Gauss' algorithm vii 102
method for computing variation of ele-
ments of an orbit -%riil 41
transformation vii 110
Gay-Lussac, Law of v 139
Gems, Coloring agent of ii 31
General committee rules. See Standing
Eules.
Gentile system of the Omahas iii 128
Geographical distribution of mammals ii 26
terms and fishery treaties i 39
Geography, List of papers on (see also
Oceanography and Seismology)
:
official report of the Yellowstone expedi-
tion of 1870. G. C. Doane. Communi-
cated by S. F. Baird. Reference i 21
[exhibition of map of the headwaters of
the Yellowstone and Lewis rivers.] M.
C.Meigs. No abstract 1 21
[geographical centre of the United States.]
J. E. Hilgard. Abstract i 22
on the results of travels in Alaska and the
determination of the position of Fort
Yukon. C. W. Raymond. Communi-
cated by T. L. Casey. Reference i 22
[exhibition of dust from Armenia.] T.
Antisell. No abstract i 25
on the relative value of Alaska to the
United States, as compared with that
of other territorial acquisitions. \V.
H. Dall. Abstract and reference i 25
on the distribution of the population of
the United States. J. E. Hilgard. Title
only i 29
on observations made on a journey to Cali-
fornia. J.Henry. Title only i 31
Pago.
Geography, List o£ papers on—Cont'd.
on the westward movement of the popula-
tion of the United States. J. E. Hil-
gard. Reference i 35
on the misapplication of geographical
terms, as bearing especially on the
question of the fishery right treaties.
R. D. Cutts. Abstract i 39
recent explorations in Syria under the
auspices of the Palestine exploration
fund. Prof. Porter. Title only i 54
on certain recent geological and geograph-
ical researches in Arizona and Nevada.
G.K.Gilbert. Abstract 1 64
[a visit to Egypt.] W. T. Sherman. No
abstract i 63
on the fluctuations of the river Nile. J.
Henry. Title only i 63
[letter on the Hayden Survey.] J. Curtis.
Communicated by E. B. Elliott. No ab-
stract 1 63
on some measurements of heights by a
pocket aneroid. W. Harkness. Title
only 1 64
[on the Goldschmidt aneroid barometer.]
J. E. Hilgard. No abstract i 65
[travels in Turkey and the Caucasus.] W.
T. Sherman. No abstract i 65
on the proceedings of the International
Metrological Commission. J. E. Hil-
gard. Title only i 68
on the habitability of the elevated plateaus
of the West. B. Alvord. Title only.. .i 74
on the use of the canons of the Colorado
for weighing the earth. G. K. Gilbert.
Title only i 88
on the recent determination of the longi-
tude between Paris and Greenwich.
J. E. Hilgard. Title only 1 89
on some of the results of the Polaris North
Pole Expedition. E. Bessels. Refer-
ence i 92
a method of describing and locating with
ease the approximate positions of geo-
graphical regions. J. M. Toner. Title
only 1 97
on two bricks from the great wall of China.
F. M. Endlich. Title only i 98
on the alluvial basin of the Mississippi
river styled the delta. C. G. Forshey.
In full i 98 (10)
on the use of railroad levellings in deter-
mining elevations on the great lakes
and rivers in the United States and in
the Rocky Mountains. J. T. Gardner.
Abstract and reference ii 23
INDEX TO VOLUMES I-X. 139
Page.
Geography, List of papers on—Cont'd.
on the geographical distribution of mam-
mals. T.Gill. Abstract 11 26
on the movements caused in large ice-
fields by expansion and contraction,
as illustrative of the formation of anti-
clinal and synclinal axes in geological
formations. M. C. Meigs. In full. 4
figures 11 33, (22)
on the Uintah Mountains. J. W. Powell.
Title only 11 34
the results of a recent determination of
the elevation of the Caspian and Aral
seas. A. Woeikoff. Abstract 11 34
account of progress of tho International
Metrical Commission. J. E. Hilgard.
Title only 11 41
the measurement of a base-line for the
primary triangulation of the United
States Coast Survey near Atlanta,
Georgia. J. E. Hilgard. Abstract and
reference 11 50
the watershed of the Adirondack region.
F. P. Judd. Abstract 11 67
[voyage of the U. S. S. Swatara.] W. Hark-
ness. No abstract 11 68, 69
Japan. H. Capron. Title only 11 79
the Adirondack watershed. F. F. Judd.
Abstract 11 82
the deviations of the plumb-line as deter-
mined in the survey of the 49th paral-
lel of latitude. F. V. Greene. Ab-
stract and reference 11 82
[route for] the interoceanic canal through
Nicaragua. E. P. Lull. Title only. ..11 83
[visit to Japan.] T. Antisell. No abstract,
11 84
the late English polar expedition. E.
Bessels. Abstract 11 89
a special method of barometric hypsome-
try. G. K. Gilbert. Abstract 11131
standard scales or measures of length. J.
E. Hilgard. Abstract 11 136
a proposed new leveling instrument. G.
K. Gilbert. Abstract 11 184
the recent history of Great Salt Lake. G.
K.Gilbert. Abstract 11187
the lands of the arid region of the United
States. J.W.Powell. Abstract 11 1S9
on the Eanab base-line, and a proposed
new method of base measurement.
G. K. Gilbert. Abstract Ill 34
the secular change in the magnetic decli-
nation in the United States and at some
foreign stations. C. A. Schott. Ab-
stract Ill 45
Page-
Geography, List of papers on—Cont'd.
[Luray cave.] J. W. Chickering. Title
Only Ill 65
on the boundary line between Alaska and
British America. W. H. Dall. Title
only Ill 77
a model of the basin of the Gulf of Mexico.
J. E. Hilgard. Abstract lv 52
notes on Roan Mountain, North Carolina.
J. W. Chickering. In full lv 60
the scenery of the Grand Cafion district.
C. E. Dutton. Title only lv 120
the Vermilion Cliffs and the valley of the
Virgen, in Southern Utah. C. E. Dut-
ton. Title only lv 122
boundary line between Alaska and Siberia.
M.Baker. In full. Map lv 123
recent discoveries in Alaska north of Behr-
ing strait. W. H. Dall. Abstract lv 163
on barometric hypsometry. G. K. Gilbert.
Reference v 48
alignment curves on any surface, with
special application to the ellipsoid. C.
H. Kummell. Abstract. 1 figure vl 123
graphic tables for computing altitudes
from barometric data. G. K. Gilbert.
Reference vi 136
the existing glaciers of the High Sierra of
California. I. C. Russell. Abstract and
reference, ^figures vil 5
some physical and economic features of
the Upper Missouri system. L. F.
Ward. Reference vll 20
the diversion of water courses by the rota-
tion of the earth. G. K. Gilbert. Ab-
stract and reference vll 21
What is a glacier ? Symposium. Ab-
stract vll 37
a concrete problem in hydrostatics. G. K.
Gilbert. Abstract vil 92
a formula for the length of a seconds-
pendulum. G. W. Hill. Reference,
vii 101
discussion of a concrete problem in hydro-
statics proposed by Mr. G. K. Gilbert.
R. S. Woodward. Title only vii 101
variations of latitude. A. Hall. Abstract
and reference viii 10
distances on any spheroid. C. H. Kum-
mell. Abstract and reference viii 52
some practical features of a field time de-
termination with a meridian transit.
R.S.Woodward. Abstract viii 55
Lieutenant Lockwood's expedition to
farthest north. G. E. Curtis. Ab-
stract lx 8
140 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Geography, List of papers on—Cont'd.
on the changes of terrestrial level surfaces
due to variations in distribution of
superficial matter. R. S. Woodward.
Reference lx 15
the physical-geographical divisions of the
southeastern portion of the United
States and their corresponding topo-
graphical types. G. Thompson. Ab-
stract lx 22
on the position and shape of the geoid as
dependent on local masses. R. S.
Woodward. Reference 1x53, 54
the topography and geology of the Cross
Timbers of Texas. R. T. Hill. Read
by W J McGee. Reference x 6
the topography and structure in the Bays
Mountains, Tennessee. B.Willis Ref-
erence x 7
development of a perspective map from a
contour map. B. Willis. Title only. ..tc 9
[exhibition of a new plane table.] W. D.
Johnson. No abstract x 9
Mt. Kainier and its glaciers. B. Willis.
Abstract x 10
What is a topographical map? M. Baker.
Abstract x 11
What is topography? Symposium. Ab-
stract x 14
the Muir glacier, Alaska. J. W. Ohicker-
ing. Title only x 15
South Florida notes. W. H. Dall. Title
only x 16
the progress of science as exemplified in
the art of weighing and measuring.
W. Harkness. Presidential address. In
full x xxxvii, 39
the most probable value of the latitude and
its theoretical weight from entangled
observations occurring in the use of
Talcott's method. A. S. Flint, Ab-
stract x 91
Geoidal deformation by local masses
vil 92, 101, lx 15, 53
Geology, List of papers on. (See also Seis-
mology.)
remarks on the structural geology of the
valley of the Colorado of the West. J.
W. Powell. Abstract 1 48
on certain recent geological and geograph-
ical researches in Arizona and Ne-
vada. G. K. Gilbert, Abstract I 54
on sand sculpture in the West. G. K. Gil-
bert. Abstract 1 57
descriptions of new species of fossil plants
from Alleghany County,Virginia; with
Pftge.
Geology, List of papers on—Cont'd.
some remarks on the rock seen along
the Chesapeake and Ohio railroad,
near the White Sulphur Springs of
Greenbrier County,West Virginia. F.
B. Meek. In full Iplates 162,11(20)
on the causes of the elevations and sub-
sidences of the earth's surface. C. E.
Dutton. Title only „ 1 74
on the glacial epoch in Utah and Nevada.
G. K. Gilbert. Abstract 1 84
on geological time. <'. E. Dutton. Title
only 1 89
on Mallet's theory of the formation of
the physical features of the earth. C.
E. Dutton. Title only 1 90
on the recent earthquakes in North Caro-
lina. B. Alvord. .Abstract 1 101
on a cold geyser or intermittent artesian
well in Ohio. G.K.Gilbert. Abstract,
t 103
on the geology of the lignite formation,
and on a hitherto undescribed deposit
discovered in 1831 in New York bay.
L. D. Gale. Title only 1 106
on the age of the Ton to sand- tones. G. K.
Gilbert. Abstract and reference 1 109
on the glacial period. C. E. Dutton. Title
only 11 26
[geological history of Lake Winnipeg.] G.
K. Warren. Abstract 11 27
[elevations and depressions in Alaska.]
W. H. Dall. No abstract 11 27
on the movements caused in large ice-
fields l>y expansion and contraction, as
illustrative of the formation of anti-
clinal and synclinal axes in geological
formations. M. C. Meigs. In full. 4
figures 11 33, (22)
on the Uintah Mountains. J.W.Powell.
Titleonly 11 34
the glacial theory. J. Henry. Abstract. .11 35
the causes of glacial climate. Symposium.
Abstract 1143, 45
ripple-marks. G. K. Gilbert. Abstract...11 61
some types of mountain building. J. W.
Powell. Titleonly 11 65
landslips and lakelets. G.K.Gilbert. Ab-
stract 11 69
monoclinal ridges. J. W. Powell. Ab-
stract 11 74
the distribution of thermal springs in the
United States. G. K. Gilbert. Title
only «. 11 80
[geologists versus physicists.] J. W. Pow-
ell. No abstract 11 85
INDEX TO VOLUMES I-X. 141
Geology, List of papers on—Cont'd.
Lake Bonneville. G. K. Gilbert. Abstract
and reference 11 103
the structure of the Henry Mountains. G.
K. Gilbert. Abstract and reference,
11 112, 113
chemical remarks on terrestrial geogony.
T. Antisell. Title only 11 132, 133, 134
the Wasatch a growing mountain. G. K.
Gilbert. Abstract 11 195
on some interesting cases of metamorph-
ism. F. M. Endlich. Title only Ill 27
the geological character of the Colorado
river. C. E. Button. Title only Ill 28
the succession of volcanic eruptions. C.
E. Dutton. Title only Ill 36, 37
on the Permian formation of North Amer-
ica. C. E. Dutton. Abstract ill 65, 67
the subject of the Permian formation in
North America. C. A. White. .46-
stract Ill 104
on the oscillations of Lake Bonneville. G.
K. Gilbert. Title only Ill 113
the drainage system of the Black Hills.
G.K.Gilbert. Abstract Ill 125
quaternary deposits of western Iowa and
eastern Nebraska. J. E. Todd. Ab-
stract iv 120
the Vermilion cliffs and the valley of the
Virgen in southern Utah. C. E. Dut-
ton. Title only Iv 122
the origin of the topographical features of
lake shores. G.K.Gilbert. Title only.iv 170
the quaternary climate of the Great
Basin. G. K. Gilbert. Reference v 21
on artesian wells on the Great Plains. C.
A. White. Reference v 101
geology of the Hawaiian islands. C. E.
Dutton. Abstract vi 13
the geology of Hatteras and the neighbor-
ing coast. W. C. Kerr. Abstract vl 28
topographical indications of a fault near
Harper'* Ferry. H. F. Walling. Ab-
stract vi 30
ore deposition by replacement. S. F. Em-
mons. Abstract and reference vl 32
glaciation in Alaska. W. H. Dall. .46-
stract vi 33
the volcanic problem, stated. C. E. Dut-
ton. Abstract vi 87
the drainage system and the distribution
of the loess of eastern Iowa. W J
McGee. Abstract vi 93
the Cambrian system in the United States
and Canada. C. D. Walcott. Abstract,
lfigure vi 98
Page.
Geology, List of papers on—Cont'd.
the existing glaciers of the High Sierra of
California. I. C. Russell. Abstract and
reference. 2 figures vii i
the mica mines of North Carolina. W. C.
Kerr. Abstract vii 9
deposits of volcanic dust in the Great
Basin. I. C. Russell. Abstract vii 18
the diversion of water courses by the rota-
tion of the earth. G. K. Gilbert. Ab-
stract and reference vii 21
the volcanic sand which fell at Unalashka
October 20, 1883, and some considera-
tions concerning its composition. J.
S. Diller. Abstract vll 33
the methods of modern petrography. G.
H. Williams. Abstract vll 36
What is a glacier? Symposium. Abstract,
vii 37
the strata exposed in the east shaft of the
water-works extension. T. Robinson.
Abstract vii 69
plan for the subject bibliography of North
American geologic literature. G. K.
Gilbert. Title only vii 71
plan for the subject bibliography of North
American geologic literature. J. W.
Powell. Title only vll 71
the volcanoes and lava fields of New Mex-
ico. C. E. Dutton. Abstract vii 76
a concrete problem in hydrostatics. G. K.
Gilbert. Abstract vii 92
discussion of a concrete problem in hydro-
statics proposed by Mr. G. K. Gilbert.
R. S. Woodward. Title only vii 101
practical geology versus speculative phys-
ics. C. E. Dutton. Title only viii 4, 5
geological and physical theories. W. B.
Taylor. Abstract
, vili 6
variations of latitude. A. Hall. Abstract
and reference viii 10
the flora of the Laramie group. L. F.
Ward. Reference vili 17
problems connected with the physics of
the earth's crust. H. M. Paul. Title
only viii 17, IS
the crumpling of the earth's crust. W. B.
Taylor. Abstract and reference viii 18
the columnar structure in the diabase of
Orange Mountain, N. J. J. P. Iddings.
Abstract. 4 figures viii 19
the terraces of the Potomac valley. W J
McGee. Title only viii 24
notes on the geology of northern Califor-
nia. J. S. Diller. Abstract ix 4
142 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Page.
Geology, List of papers on—Cont'd.
notes on the faults of the Great Basin and
of the eastern base of the Sierra Ne-
vada. I. C. Russell. Abstract Ix 5
recent changes of level in the basin of
Lake Ontario. G. K. Gilbert. Refer-
ence tx 8
on the changes of terrestrial level surfaces
due to variations in distribution of
superficial matter. R. S. Woodward.
Reference ix 15
on tho observed changes of level surfaces
in the Bonneville area, and their ex-
planation. G. K. Gilbert. Title only,
ix 15
on the varying attitudes of former level
surfaces in the Great Lake region and
the applicability (if proposed explana-
tions. T. C. Ohamberlin. Title only..Ix. 15, 16
the enlargement of mineral fragments as
a factor in rock alteration. R. D. Irv-
ing. Title only ix 16
the stibaerial decay of rocks and the ori-
gin of the red clay of certain forma-
tions. I. C. Russell. Title only ix 1G
on geological museums. G. P. Merrill.
Titleonly ix 3G
certain new and small mountain ranges.
G. K. Gilbert. Title only ix 45
on the occurrence of copper ore in the
Trias of the Eastern United States. N.
H. Barton. Titleonly ix 46
the latest volcanic eruption in northern
California and its peculiar lava. J. S.
Diller. Reference ix 46
on the position and shape of the geoid as
dependent on local masses. R. S.
Woodward. Reference ix 53, 54
the geologic age of the lowest formation of
Emmons' Taconic system. C. D. Wal-
cott. Reference i x 5
the topography and geology of the Cross
Timbers of Texas. R. T. Hill. Read
by W J McGee. Reference x 6
the topography and structure in the Bays
Mountains, Tennessee. It. Willis.
Title only x 7
Mt. Rainier and its glaciers. B. Willis.
Abstract x 10
[Mt. Shasta, contrasted with Mt. Rainier.]
J. S. Diller. No abstract x 11
the Muir glacier, Alaska. J. W. Chicker-
ing. Titleonly x 15
the quaternary deposits and tlie great dis-
placement of the Middle Atlantic
slope. W J McGee. Reference x 16
Page.
Geology, List of papers on—Cont'd.
South Florida notes. W. H. Dall. Title
only x 10
on the geographical distribution of fossil
plants. L. P. Ward. Reference x 28
Geometrical problems ill 55, 64, v 88, loT,
vi 157, viii 4">
Geometry, Grassmann's viii 53
Germ culture i 42, viii 30
Gesture language vi 63,84
Geyser, A cold i 103
Gilbert, G. K., cited on wind and barometric
observation v 108
verification of predictions vii 122, x 9t, 96
communication on certain recent geolog-
ical and geographical researches in
Arizona and Nevada. Abstract i 54
sand sculpture in the West. Abstract,
1 57
the glacial epoeh in Utah and Nevada.
Abstrant 1 84
the use of the cations of ilio Colorado for
weighing the earth. Titleonly i 88
a cold geyser or intermittent artesian
well in Ohio. Abstract i 103
the age of tho Tonto sandstones. Ah
stract and reference 1 109
ripple-marks. Abstract ii oi
the horarv oscillations of the tempera-
ture of the atmosphere. Abstract ii 07
horary oscillations of the atmosphere.
Abstract ii 69.
landslips and lakelets. Abstract ii 69
the distribution of thermal springs in
the United States. Titleonly 11 80
Lake Bonneville. Abstract and refer-
ence ii 103
the structure of the Henry Mountains.
Abstract and reference ii 112, 113
a special method of barometric hyp-
sometry. Abstract ii 131
a proposed new leveling instrument.
Abstract ii 184
the recent history of Great Salt Lake.
Abstract ii 187
the Wasatch a growing mountain. Ab-
stract ii 195
the Kanab base-line, and a proposed
new method of base measurement.
Abstract...'. iii 34
air currents on mountain slopes. Ab-
stract iii 38
the oscillations of Lake Bonneville.
Titleonly ill U3
the drainage system of the Black Hills.
Abstract iii 125
INDEX TO VOLUMES I-X. 143
Page.
Gilbert, G. K., communication on—Cont'd,
the origin of the topographical features
of lake shores. Title only iv 170
the quaternary climate of the Great
Basin. Reference v 21
barometric hypsometvy. Reference v 48
error? of barometric observations pro-
duced by wind. Reference v 91
a graphic table for computation. Ab-
stract v 120
the response of terrestrial climate to
secular variations in solar radiation.
Abstract vi 10
graphic tables for computing altitudes
from barometric data. Reference vi 136
the diversion of water courses by the
rotation of the earth. Abstract and
reference vii 21
the subject bibliography of North Amer-
ican geologic literature. Title only..vii 71
the problem of the knight's tour. Ab-
stract vil 88
a concrete problem in hydrostatics. Ab-
stract vii 92
recent changes of level in the basin of
Lake Ontario. Reference ix 8
the observed changes of level surfaces
in the Bonneville area, and their ex-
planation. Title only ix 15
certain new and small mountain ranges.
Title only ix 45
graphic methods in research. Abstract..*. 4
statistics of the Philosophical Society
from its foundation Abstract x 29
remarks on vocabularies ii 28
fresh water shells in brackish water. ..ii 181
the Permian of Utah iii 105
artesian wells on the Plains v 101
drainage system of Iowa vi 97
origin of pumice vii 25
verification of predictions vii 127
terrestrial rigidity viii 7
care of pamphlets viii 29
geology of northern California ix 7
earthquake waves and sound waves,
ix 43
Gilded thermometer bulbs ix 33
Gill, T. N., communication on the character-
istics and zoological relations of man.
Abstract i 24
additions to the fish fauna of Massachu-
setts, due to the researches of Prof. S.
F. Baird, U. S. Fish Commissioner.
Reference i 29
the tapir of the Andes and its allied
forms. Title only i 39
Page.
Gill, T. N., communication on—Cont'd.
a tunny new to the American coast. Title
only i 47
the homologies of the shoulder girdle of
fishes. References i 64
tbe Scombrocottus salmoneus of Peters.
Title only ...i 68
the homologies of the arm in fishes, and
the development of the humerus in
ganoids. Title only I 73
the primates and their relations to man.
Title only t 96
the structure and shape of Palaeothe-
rium. Abstract i 99
the geographical distribution of mam-
mals. Abstract ii 26
the causes of the glacial climate. Ab-
stract ii 47
tho progress of the natural sciences dur-
ing the past century. Reference ii 56
the relations and sequences of the family
Centrarehoides. Title only ii 113
the morphology of the antlers of the
Cervidse. Abstract and reference ii 135
a new species of Chimoera found in Amer-
ican waters. Abstract ii 182
the family of Ceratiids. Title only ii 202
the Prodromus mcthodi mammalium of
Storr. In full ii 15, (3)
some remarkable instan ces of ingestion
among fishes. Abstract iii 116
principles of morphology. Refcrcnce..W 123
the classification of the insectivorous
mammals. In full v 118
analogues in zoo-geography. Title only,
vi 41
ichthyological results of the voyage of
the Albatross. Title only vi 48
remarks on the decrease of fish on the
southern coast of New England i 62
vocabularies ii 28
Peruvian fishes ii 35
geological climates ii 36, 48
calendars ii 38
Dakota calendar ii 94
marine fishes in fresh waters ii 181
resemblances in biology ii 187
an occurrence of the tarpa ii 202
ravages by teredo v 98
vital force v 104
Glacial epoch, Cause of. ii 35, 43, 45
in Utah and Nevada i 84
Glaciation in Alaska vi 33
Glacier tables vii 7
What is a? vii 37
Glaciers of Alaska x 15
144 PHILOSOPHICAL SOCIETY OP WASHINGTON.
Page.
Glaciers of the High Sierra vii 6
Mt. Rainier x 10
Glaisher, cited on barometric gradient™ i 107
Gley, E., cited on the pulse v 78
Goethe, cited on appHed science vii 12
Gold and silver and the prices of commodi-
ties i* 87
and silver coinage iii 78, 107
Gold-silver ratio iv 141
Goode, G. B., Bibliography of S. F. Baird
by ..x 62
communication on the swordfish and its
allies. Reference iv 162
the fisheries of the world. Reference...-? 117
fisheries exhibitions. Reference vii 26
the systematic care of pamphlets. Ab-
stract and reference. viii 29
the distribution of fishes in the oceanic
abysses and middle strata. Title only,
ix 22
museum specimens illustrating biology.
Title only ix 36
the geographical distribution of scien-
tific men and institutions in the United
States. Reference x 7
Goodfellow, E., remarks commemorative of
Benjamin Peirce.„ iv 25
Gould, B. A., letters on Cordoba Observatory.
Communicated by J. H. C. Coffin and J.
J. Woodward. No abstract i 57
letter on Cordoba Observatory. Commu-
nicated by J. J. Woodward. No ab-
stract i 88
communication on scientific culture in
the Argentine Republic. No abstract ii 15
the coinage of the Argentine Republic.
Read by E. B. Elliott. Abstract ii 65
Governmental endowment of research...viii xli
Graham, Law of v 138
Graphic methods in research x 4
table for computation v 120, vi 136
Grasshoppers, Shower of ii 87
Grassmann's system of geometry viii 53
Gravitation vii 43, 47
Fallacy concerning v 85
Modification of formula of viii 39
Gray, Asa, cited on the classification of
plants iv 108, 109, 110
communication on plants common to
Japan and eastern America. Ab-
stract ii 42
Gray, Elisha, communication on a telaphon.
Abstract ii 67
Gray, L. C, cited on brain temperatures....v 76
Great Basin, Fault3 of ix 5
Later geology of i 84
Page.
Great Basin, Quaternary climate of. v 21
ranges, Bibliography of. ix 6
volcanic dust in vil 18
Great Salt Lake, Fluctuations of ii 187, 188
Great Spirit, The, a mistake 11 170
Grecian atomic philosophy vii xxix
Greely, A. W., cited on bibliography of me-
teorology Jt 22
Green, H. J., cited on thermometry ix 25
Greene, B. F., communication on the Navy
compass. Title only ii 123
an adjustable binnacle for the correction
of a ship's compass. Title only ii 134
Greene, F. V., communication on the devia-
tions of the plumb-line as determined
in the survey of the 49th parallel of
latitude. Abstract and reference* ii 82
Gregorian calendar, A i 75
Proposed reformation of ii 29
Growth of stones and organisms v 67
Grunmach, Dr., cited on thermometry..ix 30, 32
Gudermann's notation vii 103
Gulf of Mexico, Model of. iv 52
Gulf stream, Channel of. iv 53
Gunnell, F. M., communication on yellow
fever disinfection. Abstract iii 51
Guthrie, Prof. F.. cited on attraction v 150
Guyot, Arnold, cited on the Appalachians,
iv 61
distribution of mountains and plains,
viii 19
Habits of fur-bearing seals i 91
llahn, O., cited on fossils in aerolites v 66
Hall, Asaph, communication on the elements
of the Comet I, 1871. Read by B. F.
Sands. Abstract i 23
astronomical photography. Abstract and
reference i 28
a curve of the fourth degree. Abstract
and reference i 30
the astronomical proof of the existence
of a resisting medium in space. Refer-
ence i 34
an historical note on the method of least
squares. Reference i 62
the experimental determination of the
ratio of the circumference to the
diameter, based on the principles of
the calculus of probabilities. Title
only i 62
the rectilinear motion of a particle
toward an attracting centre. Refer-
ence i 88
comets and meteors. Reference i 94
INDEX TO VOLUMES I-X. 145
Hall, Asaph, communication on—Cont'd.
the method adopted in writing the in-
ternational scientific telegrams. Ab-
stract , i 101
the operations of the several parties sent
from the United States to observe the
transit of Venus on the 8th of Decem-
ber, 1874. Abstract 1131,32
approximate quadratures. Abstract,
11 48
the appearance of Saturn's rings. Ab-
stract 11 94
a bright spot which has recently become
visible on the ball of Saturn. Ab-
stract .11 102
the position of the centre of gravity of
the apparent disk of a planet. Refer-
ence 11 181
the results of a search for satellites of
Mars. Abstract and reference 11 186
the supposed discovery of a trans-Nep-
tunian planet at the U. S. Naval Ob-
servatory in 1850. Abstract Ill 20
the satellites of Saturn. Abstract ill 26
the orbits of Titan and Hyperion. Ab-
stract Ill 40
inaugural address as chairman of the
Mathematical Section. In full vl 117
the determination of the mass of a
planet from observation of two satel-
lites. Abstract vl 132
the formulae for computing the position
of a satellite. In full. 1 figure vil 93
American scientific societies. Presiden-
tial address. In full viii xxxiii, 30
variations of latitude. Abstract and ref-
erence viil 10
the new star in the nebula of Andro-
meda. Reference ix 14
the images of stars. Reference ix 15
a problem in probabilites. Read by G.
W.Hill. No abstract x 88
the parallax of a Tauri. Abstract x 91
Euler's theorem (generally called Lam-
bert's). Abstract x 101
Longitude of Plover Bay by „lv 124, 126
remarks on planetary motions. ..11 188, 189, 192
transit of Mercury il 199
criteria for the rejection of observa-
tions vl 155
Grassmann's geometry vlll 53
time determinations viil 58
Hall, G. S,, communication on recent expe-
riments on reaction time and the time
sense. Title only viil 4
Hallcr, A. von, cited on nerve currents. .....v 61
56
Page.
Hallowell, Benjamin, letter on the meteor
of December 24, 1873. Communicated
by J. Henry. No abstract 1 95
Halo, A remarkable solar v 112
Hamilton, Sir W., cited on ultimate causes,
v 163, 166
Harkness, William, communication on the
physical constitution of the corona of
the sun. Reference 1 31
the spectrum of Encke's comet. Refer-
ence 1 34
the spectrum of Encke's comet, and the
appearance of Tuttle's comet. Refer-
ence 1 34
the density of the hypothetical resisting
medium in space. Title and refer-
ence 1 39
some measurements of heights by a
pocket aneroid. Title only 1 64
the power necessary to drive the pendu-
lum of an astronomical clock. Title
only 1 74
the distribution of temperature over the
surface of the globe. Reference 1 96
the apparatus to be used in the observa-
tions of the approaching transit of
Venus. Title only i 102
the transit of Venus in 1874. Communi-
cated by A. Hall. Abstract 11 32
the methods of measuring the inequali-
ties of the pivcts of the transit instru-
ment. Title only 11 68
the voyage of the U. S. S. Swatara. No
abstract 11 68, 69
the velocity of light and determination
of the solar parallax. Title only 11 201
tho color corrections of achromatic ob-
jectives. Abstract Ill 39
the number of lenses required in an
. achromatic objective, consisting of in-
finitely thin lenses in contact, in order
that, with any given law of dispersion
whatever, the greatest possible num-
ber of light-rays of different degrees
of refrangibility may be brought to a
common focus. In full Hi 65
the solar corona. Abstract iii 116
the relative accuracy of different meth-
ods of determining the solar parallax.
Reference v 39
the monochromatic aberration of the
human eye in aphakia. Reference,
vi 5
flexures of transit instruments. Ab-
stract viil 27
146 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Harkness, William, communication on—Cont'd,
the progress of science as exemplified
in the art of weighing and measuring.
Presidential address. In /wK....x xxxvii, 39
a device for viewing the sun by light of
any desired wave length. Abstract...x 13
the representation of comet orbits by
models. Reference x 28
the constant P in observations of terres-
trial magnetism x 102
remarks on the black drop 11 199
results from photographs of the transit
of Venus lv 169
vital force v 105
temperature observations vl 26
hygrometry vl 36
postulated continents vl 93
accidental and constant errors vl 133
glaciers vii 9
vision vll 13
problem in probabilities x 89
Harper's Ferry, Fault near vl 30
Hart, A. S., cited on Malfatti's problem..ll 117, 119
Harting, cited on mineral aggregates ill 39
Hartley, J., Solution of a geometrical prob-
lem by Ill 64
Hatteras, Geology of Cape vl 28
Hausen, C. A., cited on nerve currents v 60
Hauy, cited on mineralogy 1 77, 78
Havana magnetic disturbance and north-
ers vil 25
Hawaiian geology vl 13
Hayden, Everett, communication on the
Charleston earthquake. Abstract.
Map lx 38
Hayden, F. V., cited on base-line methods.JU 34
Hazen, H. A., communication on tho retarda-
tion of storm centres at elevated sta-
tions and high wind as a probable
cause. In full v 108
the coming winter of 1882-'83. Ab-
stract v 122
hygrometric observations. Abstract...-vi 36
thermometer exposure. Abstract vl 46
the sun glows. Abstractand reference..vil 17
thermometer exposure. Abstract. ....vll 80
thunderstorms of 1884. Abstract viii 10
the condensing hygrometer and sling
psychrometer. Abstract viil 25
effects of solar radiation upon thermom-
eter bulbs having different metallic
coverings. Abstract ;.lx 33
the sky glows of 1883. Title only x 6
relation between wind velocity and
pressure. Reference ~ x 10
remarks on deflection of rivers vll 24
Page.
Hazen, H. A., remarks, on—Cont'd.
.
weather prediction vill 9
care of pamphlets _ viii 29
graphics _ x 5
wind vanes x 9
the sparrow question x 16
Hazen, W. B., bibliography of meteorology
x 21
Death of .. x 6
Heat of the sun 1 31
Theory of v 133
Heats, Molecular 1 104
Hell Gate explosion viii 28
Hellmann, Dr. G., bibliographic work in
meteorology x 20, 21, 23, 25
Helmert cited on alignment curves....vl 124, 126
Henry, Joseph, Address on the life and char-
acter of li 203, 368, 370
cited on a telephonic experiment ii 104
adhesion and cohesion v 137
land and sea breezes v 29
Bound anomalies li 58, iv 135, v 33, 40, 43
the Philosophical Society x 45
Washington as a scientific center x 47
communication on phenomena of sound
and experiments with tuning forks.
Title only„ 1 22
observations made ou a journey to Cali-
fornia. Title only i 31
the organization and objects of the So-
ciety. Presidential address. In full,
lv,34
,
the life and scientific labors of the late
Alexander Dallas Bache. Reference. ..1 35
the expenditure of the income of the
Bache fund for 1872. Title only i 53
the fluctuations of the river Nile. Title
only 1 03
the condition of the Society. No ab-
stract i 64
Bound in relation to fog-signals, from in-
vestigations under the direction of the
U. S. Light House Board. In full......t 65,
li (45)
atmospheric electricity. Title only.. ..I 75, 87
experiments on fog signals during the
past summer. Title only i 90
a method of developing magnetism in
barsofsteeL Title only 1 97
meteor trains, and the upper atmos-
pheric currents. Tttleonly i 98
Giffard's injector. Title only ;i 99
audition. Title only„ 11 22
the glacial theory. Abttract _ 11 35
fog signals and abnormal conditions of
sound. Reference li 37
INDEX TO VOLUMES I-X. 147
Page.
Henry, Joseph, communication on—Cont'd.
electricity engendered by the driving
belt of the machinery for ventilating
the Capitol at Washington. Abstract.M 40
sound in connection with fog signals.
Reference ii 57
half-vision. Title only ii 60
researches on sound in its application
to fog signals. Presidential address.
Reference ii 60
illuminating materials. Title only ii 71
Crookes' radiometers. Abstract ii 80
[fog signals.] Abstract ii 85
paper made of asbestos. Title only ii 86
scientific method and its application to
acoustic researches in connection with
fog signals. Presidential address. In
full ii 162
Memoir on the scientific work of ii 230
Memorial services of iii 27
Portrait of ii frontispiece-
remarks on auroras i 46, 48
Japan ii 71
waterspouts ii 105
Resolutions on the deaih of ii 196
Henry, Mrs. Joseph, Death of v 97
Henry Mountains ii 113
Heraclitus, cited on philosophy vii xxxi
Herapath, J., cited on elasticity v 130
Hering's theory of color iv 54
Hermann, cited on muscular contraction
v 58, 59
nerve currents v 61
Hermaphrodite, Alleged i 24
Herschel, Sir John, cited on cohesion v 129
force v 151, 153
laws v 169
standard time v 115
satellites of Uranus i (30), (34)
temperature of space ii 73
theory of errors vi 138, 140
Herschel, Sir William, cited on relation of
light to heat v 135
satellites of Uranus i (30)
Saturn ii 102
Saturn's rings vi 43
High-heeled shoes v 117
High power definition i 47
High Sierra glaciers vii 5
Hilgard, J. E., cited on earthquake tides...v 144
communication on the distance trav-
ersed by approaching the North Pole
on a loxodromic curve. Title only i 21
a chronograph. No abstract i 22
the geographical centre of the United
States. Abstract i 22
Page.
Hilgard, J. E., communication on—Cont'd.
a chronoscope. No abstract i 23
the distribution of the population in the
United States. Title only i 29
an exponential formula having reference
to the tolerance allowed at the U. S.
mint. Title only i 31
the westward movement of the popula-
tion of the United States. Reference.,1 35
the aurora of February 4th. Abstract. ...i 47
Hindoo arithmetic. Title only i 53
the recording systems of the trans-At-
lantic cables. Title only i 53
the Goldschmidt aneroid barometer. No
abstract i 65
the proceedings of the International
Metrological Commission. Title
only 1 68
an inquiry into the law of probability.
Title only i 84
the air thermometer of Prof. Jolly. Title
only i 89
the recent determination of the longi-
tudo between Paris and Greenwich.
Title only i 89
recent experimental researches in
acoustics, by Prof. A. M. Mayer. Title
only i 90
the determination of the personal errors
in the observation of astronomical
transits. Title only i 92
a new apparatus for the investigation of
personal error in astronomical transit
observations. Title only i 106
a proposed reformation of the Gregorian
calendar. Abstract ii 29, 30
the proceedings of the International
Metrical Commission. Title only ii 41
iron facing copper plates. Abstract ii 42
the measurement of a base-line for the
primary triangulation of the United
States Coast Survey near Atlanta,
Georgia. Abstract and reference ii 50
standard scales, or measures of length.
Abstract ii 136
an optical salinometer. Abstract ii 185
Jablokoff's electric candle. Title
only m 19
phosphorescent clocks. Abstract iii 33
remarks commemorative of Jonathan
Homer Lane. In full iii 122
a model of the basin of the Gulf of Mex-
ico. Abstract iv 52
Siemens' deep sea thermometer and
Carr6's ice machine. Title only. v 100
remarks on auroras i 40, 43
148 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Hilgard, J. E., remarks on—Cont'd.
persistent observation of phenomena..ii 19
vocabularies H 28
calendar reform H 30
photographs of the sun ii 33
cause of glacial climate 11 36
a new meteorological instrument il 64
Dakota calendar 11 92
Peirce's Linear Associative Algebra. ..lv 24
unification of longitudes and time vl 109
Hilgard, Theodore, communication on the
number of the cepbalic vertebrae.
Reference 1 26
Hill, G. W., communication on certain pos-
sible abbreviations in the computation
of the long-period perturbations of
the moon's motion due to the direct
action of the planets. Abstract and
reference vl 136
a formula for the length of a seconds-
pendulum. Reference vii 101
a problem in probabilities. Abstract. ..x 88
the motion of Hyperion. Abstract and
reference x 90
the integration of differential equations
admitting periodic integrals. Abstract
and reference x 100
remarks on infinitesimals vl 135
gravitation formula vlil 40
adjustment of conditioned observations,
viii 41
Grassmann's geometry vill 53
density of Mercury .viii 45
problem in probabilities x 89
electric currents x 93
Hill, M., cited on visible speech vi 78, 80
Hill, R.T., communication on the topography
and geology of the Cross Timbers of
Texas. Read by W JMcOee. Reference,
x 6
Hillhouse, Dr. William, cited on trisection of
angles x 99
Hind, cited on supposed trans-Neptunian
planet ill 20
Historical note on binocular microscopes,
iv 35
on the method of least squares .....1 62
History of a geometrical problem ill 64
Malfatti's problem ii 113
Hitchcock, Romyn, communication on re-
cent improvements in microscopic ob-
jectives, with demonstration of the
resolving power of a new l-16th inch.
Title only ix 16
Hoffman, Dr. A. W., cited on ultimate
causes v 166
Page.
Hoffman, W. J., cited ©n the poisoning of
arrows ii 182
communication on the use of poisoned
arrows by North American Indians.
Title only ii 183
Holden, E. S., communication on the adopted
value of the sun's apparent diameter.
In full i95, (3)
Sir William Herschel's observations of
the satellites of Uranus. In full. ..i 106, (30)
the number of words used in speaking
and writing. In full ii 28, (16)
two drawings of nebulae, made with the
xxvi-inch telescope of the U. S. Naval
Observatory, by Mr. L. Trouvelot, of
Cambridge, Mass. Abstract il 51
search for Vulcan. Abstract ii 85
reference catalogues of astronomical
papers and memoirs. Abstract ii 95
the shadow of the ball of Saturn pro-
jected on the rings. Abstract ii 101
the brightness and the stellar magni-
tude of (he third Saturnian satellite,
Tethys. Read by A. N. Skinner. Title
only iii 18
B. A. Gould's Uranometria Argentina.
Reference iii 119, 122
Holmes, VV. H., remarks on glaciers vii 8
Homologies of the shoulder girdle of fishes..i 64
Homophenes vi 58, 76
Hooker, Thermometric observations by...v 94
Hooker, R., cited on natural law v 173
Hoosac tunnel. Acoustic features of ii 172
Hopkins, cited on the liquidity of the earth's
interior il 76, 78
temperature of space 11 73
Hough, F. B., communication on the culti-
vation of Eucalyptus on the Roman
Campagna. Reference vi 36
Death of viii 25
House of Representatives, Ventilation of,
v 99-
Howland, Dr. E. P., remarks on Charleston
earthquake ix 42-
Hubbard, G. G., remarks on visible speech,
vi 82
Hughes' microphone iv 184
Humboldt, Baron von, cited on transmission
of sound v 41
Humidity observations vi 36
Humphreys, A. A., Eulogy on vii 4
Death of vii 3, 4
Humphreys and Abbot, cited on the delta
of the Mississippi 1 (10), (12), (13)
Huron, Altitude of Lake il 23
Huxley, T. H., cited on vital principle v 78.
INDEX -TO VOLUMES I-X. 149
Page.
Hydrometer employed to determine Specific
gravity vl 26
Hygrometers vlii 25
Hygrometric observations vl 36
Hynoprs, J., cited on Malfatti's problem ii 118
Hyperion, Orbit of iii 26, 40, x 90, 104
Hypothesis, Use of. 11 164, vi xxxiii
Hypsometry, Barometric v 48
New method of M 11 131
lee fields, Anticlinal and synclinal axes
in 11 (22)
pyramids vii 6
Iddings, J. P., communication on the col-
umnar structure in the diabase of
Orange Mountain, N. J. Abstract. 4
figures vili 19
Illinois, Flora of lv 99
Illiteracy and rainfall 1 68
Illumination of objects for examination with
certain immersion objectives ii 126
Images of stars lx 15
Impressions on polished glass ii 39
Indexing scientific literature x 38
Indiau explanation of gravitation vl xxxi
Indians as observers of nature vii 73
Errors respecting ii 175
(See also Anthropology.)
Inductive reasoning vii lii
Inertia vii 48
Infinite and infinitesimal quantities vi 133
attraction ii 19, vili 5S
Ingestion among fishes lii 110
Initial meridian, Proposed vi 106
Inoculation of diphtheria iv 38
through mosquitoes vl 5
Insecticides vii 10
Insectivorous mammals v 118
Institutions, Evolution of vi xlviii
Integrals, Elliptic... vii 102, ix 54
Integration of differential equations admit-
ting periodic integrals x 100
Interior angle of objective iii 19
Intermarriage of the deaf. vl 83
International coinage iii 38
convention of teachers of the deaf and
dumb iv 55
Geodetic Association on standard time..vi 106
scientific telegrams i 101
symbols for archseologie charts ii 72
Intervals, Musical ii 199
Investigation, Methods of. ii 163
Iowa, Loess and drainage system of vi 93
Quaternary of iv 120
Irby, J. R. M., communication on the crys-
> talline state of matter. Abstract iii 39
Page.
Irving, R. D., communication on the en-
largement of mineral fragments as a
factor in rock alteration. Title only..lx 16
Isogram x 4
Isoseismal map ix 37, 39
Ivory, James, cited on action at no dis-
tance v 161
Jacobi's method for removing side-coeffi-
cients vili 41
notation vii 103
Jackson, President, cited on the distribution
of surplus among the States vi 103
Jackson, Dr., letter on autopsy of Agassiz.
Communicated by J. J. Woodward. No
abstract 1 93
Japan, Education in 11 69
Japanese coinage ill 38
dry painting vili 16
Jenkins, T. A., remarks on drifting buoy,
vll 15
Johnson, A. B., communication on the his-
tory of the light house establishment
of the United States. Abstract and
reference lv 135
recent investigations by the Light House
Board on the anomalies of sound from
fog-signals. In full. 2maps. 1 figurcv 23
some peculiar ravages of the Teredo
navalis. Title only v 98
some eccentricities of ocean currents.
Abstract
...vii 14
the difficulty in determining the direc-
tion of sound. Abstract viil 11, 12
Johnson, W. P., communication on a new
plane table. No abstract x 9
What is topography? Abstract x 15
Johnston, Gen., cited on the phenomena of
sound ii (48)
Jones, B., cited on phosphorus and brain
disease v 75
Jones, Rev. George, cited on zodiacal light,
i (19), (20), (21), (26)
Journals of mathematics vl 117
Judd, F. F., communication on the water-
shed of the Adirondack region. Ab-
stract it 67
the Adirondack watershed. AbstracL.ll 82
Jukes, cited on ripple marks H 61, 62
Juvet, .communication on a time globe.
Abstract lii 106
Kampf, Ferdinand, Death of ii 139
Kanab baseline iii 34
Keith, Reuel, communication on achro-
matic object glasses. Title only i 73
150 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Keith, Reuel, communication on—Cont'd,
the nature of the force of gravitation.
Title only 1 89
Kempe, A. B., Trisection linkage of. x 99
Kerosene oil test9 11 72
Kerr, M. B., remarks on glaciers "vii 8
Kerr, W. C, communication on the geology '
of Hatteras and the neighboring coast.
Abstract vi 28
the mica mines of North Carolina. Ab-
stract vii 9
Death of. vill 25
Kidder, J. H., communication on deep sea
temperature observations. Title only,
ix 14
the gilding of thermometer bulbs. Title
only lx 33
Kilauea ..vl 13
Kinematic theories of force v 126, vl xxviii
King, A. F. A., communication on the con-
servative element in disease. Ab-
stract 11 111
the conservative influence of disease as
illustrated in the phenomena of pul-
monary phthisis. Abstract 11 124
the prevention of malarial diseases, illus-
trating, inter alia, the conservative
function of ague. Abstract vl 5
King, C, cited on geology of Great Basin... 1 56
King, Major, communication on the con-
struction of the bridge across East
River between Brooklyn and New
York. Title only 1 23
the fatigue of metals. Title only 1 53
King, S. A., communication on the aerial
currents observed in fifty balloon as-
censions. Read by C. Abbe. Infull....i 35
Klaproth, cited on mineralogy t 78
Knight's tour vil 88
Knox, J. J., communication on the distribu-
tion of loans in the Bank of France,
the national banks of the United
States, and the Imperial Bank of Ger-
many. Abstract lv 31
the distribution of the surplus money of
the United States among the States..vl 103
Kolb, Baron, cited on population iv 28
Koyl, C. H., communication on the storage
of electric energy. Abstract v 46
Krakatoa and sun glows vil 35
Kummell, C. H., communication on compo-
sition of error from single causes of
error. Reference v 106
alignment curves on any surface, with
special application to the ellipsoid.
Abstract. J figure vl 123
Page.
Kummell, C. H., communication on—Cont'd,
the theory of errors* practically tested
by target-shooting. Abstract. 2 figures,
vl 138
curves similar to their evolutes. Ab-
stract „ vil 87
the quadrie transformation of elliptic
integrals, combined with the algo-
rithm of the arithmetico-geometrjc
mean. Abstract vil 101, 102
an artifice sometimes useful for the ad-
justment of conditioned observations.
Abstract viil 41
distances on any spheroid. Abstract and
reference viil 52
Can the attraction of a finite mass be in-
finite? Infull viii 58
the use of Somoff's theorem for evalua-
tion of the elliptic integral of the third
species. Reference ix 54
the brachisthode on the helicoid. Ref-
erence x 90
remarks on temperature readings vl 26
infinitesimals vl 135
conic sections vi 149
music and the elements vii 28
Feuerbach's circle viii 52
time determinations viii 58
problem in probabilities x 89
trisection of angles x 100
Lagrange ignored by the Am. Phil. Soc,
viii xxxviii
Lagrange's method vii 93
Lake Bonneville 1 84, li 103
and the geoid vii 92, 101, ix 15
Lake Champlain, Ice phenomena on li (22)
Lake Erie, Altitude of. 11 23
Lake, Great Salt H 187, 188
Lake Lahontan vii 18
Lake Michigan, Altitude of. ii 23
Lake Ontario, Changes of level in the basin
of. ix 8
Lakelets and landslips ii 69
Lancaster's classification of meteorological
literature x 26
Landen's transformation vil 107
Lands of the arid region 11 189
Landslips and lakelets il 69
Lane, J. H., cited on solar physics 1 31
Eulogy of. ill 122
Resolution on the death of Ill 123
Language, Evolution of. vi xlix
written and spoken Hi 139
Laplace cited on the solar atmosphere and
zodiacal light i (19), (27)
INDEX TO VOLUMES I-X. 151
Page.
Laplace ignored by the Am. Phil. Soc,
rill xxxviii
Laramie flora.- Till 17
Lassell cited on the satellites of Uranus,
1 (30), (34)
Observations of Hyperion by. Ill 40
Latent heat v 137
impressions on glass 11 39
Latimer, George, Legacy by 11 48
Latitude, A method of determining 11 105
computations x 91
of Lockwood's farthest north- ix 9
variations of. Till 10
Lava fields of New Mexico vil 76
Leadville ores vi 32
Least square computation vi 150, viii 41
squares 162, 89
Le Conte, John, communication on the mi-
croscopical structure of wool 11 62
Lee, W., communication on medallic medi-
cal history. Abstract -vi 39
Lefavour, E. B., remarks on infinitesimals,
vi 135
music and the elements vii 28
Lefroy, letter on changes of sea-level at Ber-
muda. Communicated by J. Henry.
No abstract 1 75
Legendre ignored by the Am. Phil. Soc,
viii xxxviii
Lehmus, Prof. D. C. L., cited on Malfatti's
problem *. 11 115
Leibnita cited on Newton's philosophy v 162
Leibnitz's philosophy vil xlii
Lenses, Achromatic combination of Ill 65
Cylindrical— vl 4
Le Sage's theory of cohesion v 129
Lesquereux, Prof. L., cited on fossil plants
from Virginia. il (38), (40)
Levees of the Mississippi delta i (14)
Levelling instrument, Proposed ii 184
Lewes, G. H., cited on action at a distanee..v 157
PEpee's instruction of the dumb vl 63
Ley cited on cyclonic motion 1 107
l'Hospital's trisection instrument x 99
Liagre's theory of target shooting vi 138
Library of the Surgeon General's Office. _...l 92
Lick, James, letter on proposed observatory.
Communicated by J. Henry. No ab-
stract 1 91
Life 1 27, v 49, 102
and electricity v 57
force v 57
Modern philosophical conceptions of......v 49
Light and sound iv 143
of the sun, passed through a narrow slit,
111 119
Page.
Light-house establishment of the United
States Iv 135
Lightning, Cause of. il 189
Limnsea megasoma, Depauperation of ill 75
Limpets vil 4
Linnseus, cited on growth of stones v G7
mineralogy 1 77
Lippman, G., cited on electricity v 168
List of deceased members ill xiv, viii xxv,
ix xxvi, x xxviii
members 1 19, (37), ii ix, ill ix, 153, lv 15,
vl5, vi xvi, vil xvi, viii xvi, lx xvi,
x xvi
members of the Mathematical Section.
vi 116, vil 86, viii 36, lx 52, x 82
recipients of the Bulletin ill 159
The consolidated x 36
Lister, Prof. J„ cited on germ culture il 109
Lithology. See Geology.
Littrow's telegraphic system i 101
Loans by banks in France, Germany, and
the United States lv 31
Lockwood's expedition to farthest north.Jx 8
Locusts, Shower of. ii 87
Lodge, Dr. O. J., cited on electricity v 168
Loess of eastern Iowa vi 93
Origin of the lv 121
Logical algebra 1 88
Lombard, J. S., cited on brain temperatures,
• v 75
Longitude computation viii 52
Loomis, Elias, cited on cyclonic motion,
1 107, 108
retardation of storm centres v 108
Lovering, Prof., cited on auroras 1 44
Loxodrome vi 124
Lucas, F. A., communication on museum
specimens illustrating biology. Title
only lx 36
Lucretius' philosophy vii xxxvii
Lull, E. P., communication on the inter-
oceanic canal through Nicaragua.
Title only ii 83
Death of. x 8
Lunar theory iv 57, vi 136
variation of magnetic declination ill 47
Lymph, Motion of the 11 133
McClellan, Gen., cited on phenomena of
sound 11 (48)
McCullough, Hon. H., remarks on U. S. sur-
plus given to the State of Indiana. ..vl 106
McDowell, S., cited on thermal belts vi 11
McGee, W J, communication on the drain-
age system and the distribution of the
loess of eastern Iowa. Abstract vi 93
152 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
McGee, W J, communication on—Cont'd.
What is a glacier 1 Abstract vil 38
the terraces of the Potomac valley.
Title only viii 24
the Charleston earthquake. Abstract..!*. 37
the quaternary deposits and the great
displacement of the middle Atlantic
slope. Reference x 1C
remarks on earthquakes ix 42
Machin, cited on computation of ir i 58
McKenney and Hall, cited on diminution of
Indians ii 175
McMurtrie, William, communication on the
meteorological conditions affectiug the
culture of the sugar beet. Reference,
111 142
Magic squares HI 143
Magnetic declination, Secular change in..lll 45
disturbance and northers vil 25
storms Ill 47
Magnetism. See Electricity.
Main, R., cited on Saturn's rings vi 42
Mairan, cited on auroras 1 44
Malarial diseases, Prevention of vl 5
Malfatti's problem 11 113
Mallery, Garrick, communication on a cal-
endar of the Dakota Indians. Abstract
and reference 11 90
some common errors respecting the
North American Indians. Abstract
and reference 11 175
customs of every-day life. Abstract. ..ix 19
relations between Professor Baird and
participating societies x 45
romarks on phonetic alphabets Ix 18
Mallet's contraction hypothesis vl 90
method of determining earthquake foci,
x 17, 19
Maloney, J. A., Electric investigations by..v 47
Mammals, Classification of 11 (3)
Distribution of. 11 26
Insectivorous v 118
Manganese, Estimation of. 11 132
Man, Zoological relations of 1 24
Mann, B. P., communication on reference
indexing. Abstract x 38
remarks on care of pamphlets vill 29
throvving-sticks Ix 14
Map of Charleston earthquake Ix 37, 39
Gulf of Mexico iv 52
path of meteor of December 24, 1873.. ..11 160
Topographic x 11
Maps for use in connection with the transit
of Venus, 1874 1 G3
Marcou, J., cited on paleozoic rocks vl 102
Mariotte, Law of... v 139
Page.
Mars, Satellites of. 11 181, 186, 188. 190, vl 45
Marsh, Hon. G. P., citad on individual vo-
cabularies 11 (16), (19), (21)
Marth's method vil 98
Martin, Artemas, communication on a prob-
lem in probabilities. Abstract x 80
methods of finding nth-power numbers
whose sum is an nth-power. Abstract..*. 107
Letter from vil 87
Marvin, C. F., communication on the Flood
Rock explosion. Title only vill 28
the electrometer as used in observations
of atmospheric electricity. Titleonly.jx, 9
Marvine, A. R., Biographical notice of 11 (53)
Resolutions on the death of 11 84
Mass of a planet determined from observa-
tions on two satellites vl 132
Mason, O. T., communication on archaeolog-
ical specimens. Title only 11 48
the classification of objects of archae-
ology. Title only 11 50
international symbols for charts of pie-
historical archaeology. Title only ...11 71, 72
the decipherment of some Aztec monu-
ments lately discovered in Guatemala.
Title only Ill 37
comparison of written language with
that which is spoken only. Abstract,
111 139
two examples of similar inventions in
areas widely apart. Abstract Ix 12
bowyers and fletchers. Abstract Ix 44
remarks on implements of Australia, Aleu-
tian Islands, and North America 11 66
the telephone 11 104
ancient Indian population 11 180
charcoal in the drift Iv 122
Indian observation of nature vil 74
origin of customs Ix 21
Mason, , communication on kerosene
oil tests. Abstract ii 72
Mathematical journals vi 117
Mathematical Section, Minutes of...vi 121, vil 87,
viii 37, ix 53, x 83
Organization of vi 28, 121
place of meeting vil 81
Statistics of x 34, 36
Mathematics, List of papers on (See also
Astronomy)
:
on the distance traversed by approaching
the North Pole on a loxodromic curve.
J. E. Hilgard. Title only 1 21
[exhibition of chronograph.] J. E. Hil-
gard. No abstract 1 22
on a curve of the fourth degree. A. Hall.
Abstract and reference i 30
INDEX TO VOLUMES I-X. 153
Page.
Mathematics, List of papers on—Cont'd.
on an exponential formula having refer-
ence to the tolerance allowed at the
U. S. Mint. J. E. Hilgard. Title only,
1 31
on the locus of the point of equal illumi-
nation by two unequal lights treated
by the quaternion analysis. E. B.
Elliott. Title only i 35
on Hindoo arithmetic. J. E. Hilgard.
Title only 1 53
on a series for the determination of the
number expressing the ratio of the
circumference to the diameter. E.
Frisby. In fall i 57
on the experimental determination of the
ratio of the circumference to the di-
ameter, based on the principles of the
calculus of probabilities. A. Hall.
Title only i 62
an historical note on the method of least
squares. A. Hall. Reference i C2
an inquiry into the law of probability. J.
E. Hilgard. Titleonly i 84
on logical algebra. C. S. Peirce. Refer-
ence i 83
on the mechanical representation of a
problem in least squares. S. New-
comb. Reference 1 89
on quaternions, as developed from the gen-
eral theory of the logic of relatives.
C. S. Peirce. Title only i 94
on affected quantities of the first order.
E. B. Elliott. Title only 11 42
approximate quadratures. A. Hall. Ab-
stract 11 48
some recent investigations on the theory
of invariants. J. J. Sylvester. Title
only 11 95
a trigonometrical formula. B. Alvord.
Title only 11 104
the history of Malfatti's problem. M.
Baker. In full. Zfigures 11 113
series. E. Frisby. Title only 11 193
the intersection of circles and the inter-
section of spheres. B. Alvord. Title
only 11 198
an adjustment of the Carlisle tables of re-
versions and annuities. E. B. Elliott.
Title only 11 201
new points respecting the intersections
of circles and the intersections of
spheres. B. Alvord. Title only 11 201
discussion of a geometrical problem, with
bibliographical notes. M. Baker. In
full. 4 figures 11153, 55
Page.
Mathematics, List of papers on—Cont'd.
on magic squares. E. Frisby. Abstract.
6 figures Ill 143
on the geometrical problem to determine
a circle equally distant from four
points. M. H. Doolittle. Abstract.. ..v 88
on some of the properties of Steiner's
power-circle. B. Alvord. Title only.rv 8tf
on composition of error from single causes
of error. C. H. Kummell. Reference,
v 106
on a geometrical question relating to
spheres. M. Baker. In full v 107
on a graphic table for computation. G. K.
Gilbert. Abstract v 120
experiments in binary arithmetic. H.
Farquhar. Abstract v 125, vl 3
formulas for the computation of Easter.
E. B. Elliott. In full vl 14
further experiments in binary arithmetic.
H. Farquhar. Abstract vl 38
inaugural address of the chairman of the
Mathematical Section. A. Hall. In
full vl 117
a quasi general differentiation. A. S.
Christie. Titleonly vl 122
infinite and infinitesimal quantities. M.
H. Doolittle. Abstract vl 133
certain possible abbreviations in the com-
putation of the long-period perturba-
tions of the moon's motion due to the
direct action of the planets. G. W.
Hill. Abstract and reference vl 136
the theory of errors practically tested by
target-shooting. C. H. Kummell. Ab-
stract. 2figurcs vl 138
a special case in maxima and minima. B.
Alvord. Abstract vl 149
form of least-square computation. H. Far-
quhar. In full vl 150
note on the problem discussed by Mr. Al-
vord. H. Farquhar. Abstract vl 152
the rejection of doubtful observations. M.
H. Doolittle. Abstract vl 152
the special treatment of certain forms of
observation-equations. R. S. Wood-
ward. Abstract vl 156
contact of plane curves. A. S. Christie.
Abstract vl 157
curves similar to their evolutes. C. H.
Kummell. Abstract vll 87
the problem of the knight's tour. G. K.
Gilbert. Abstract vll 83
empirical formulae for the diminution of
amplitude of a freely-oscillating pen-
dulum. H. Farquhar. Abstract vll 89
154 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Mathematics, List of papers on—Cont'd.
the formulae for computing the position of
a satellite. A.Hall. In full vii 93
a form of the multinomial theorem. A. S.
Christie. Title only vii 101
the quadric transformation of elliptic inte-
grals, combined with the algorithm of
the arithmetico-geometric mean. C.
H. Kummell. Abstract vii 101, 102
a case of discontinuity in elliptic orbits.
\V. B. Taylor. Abstract vii 122
the verification of predictions. M. H.
Doolittle. Abstract vii 122
methods of verifying weather predictions.
C. Abbe. Abstract viii 8
example illustrating the use of a certain
symbol in the calculus of affected
quantity. E.B.Elliott. Title only..-vill 37
a collection of formulae for the area of a
plane triangle. M. Baker. Reference,
viii 37
an artifice sometimes useful for the adjust-
ment of conditioned observations. C.
H. Kummell. Abstract viii 41
a group of circles related to Feuerbaeh's
circle. M. Baker. In full. 4 figures,
viii 45
distances on any spheroid. C. H. Kum-
mell. Abstract and reference viii 52
on Grassmann's system of geometry. A.
Ziwet. Reference viii 53
cause and chance in the concurrence of
phenomena. M. H. Doolittle. Title
only viii 54
Can the attraction of a finite mass be infi-
nite? C. H. Kummell. In full viii 58
on the use of Somoff's theorem for the
evaluation of the elliptic integral of
the third species. C. H. Kummell.
Reference ix 54
graphic methods in research. G. K. Gil-
bert. Abstract x 4
association ratios. M. H. Doolittle. Ab-
stract x 83
a problem in probabilities. Symposium.
Abstract x 87, 89
on the free cooling of a homogeneous
sphere initially heated to a uniform
temperature. R. S. Woodward. Ref-
erence x 90
on the brachisthode on the helicoid. C.
H. Kummell. Reference x 90
the motion of Hyperion. G. W. Hill. Ab-
stract and reference x 90
the parallax of a Tauri. A. Hall. Ab
struct * 91
Page.
Mathematics, List of papers on—Cont'd,
the most probable value of the latitude and
its theoretical weight from entangled
observations occurring in the use of
Talcott's method. A. S. Flint. Ab-
stract x 91
association ratios. M. H. Doolittle. Ab-
stract x 93, 94
[solution and generalization of a problem
requiring the division of a rectangle
into parts which form a square.] H.
Farquhar. No abstract x 96
a collection of solutions of the trisection
problem. M. Baker. Abstract x 96
[on the trisection problem.] G. E. Curtis.
Abstract x 98
the integration of differential equations
admitting periodic integrals. G. W.
Hill. Abstract and reference x 100
Euler's theorem (generally called Lam-
bert's). A. Hall. Abstract x 101
[a new computing machine.] E. B. Elliott.
Abstract x 102
on the constant P in observations of ter-
restrial magnetism. W. Harkness.
Abstract and reference x 102
the conditioned cooling of a homoge-
neous sphere. R. S. Woodward. Ref-
erence x 103
the orbit of Hyperion. O.Stone. Abstract
and reference x 104
the quotients of space-directed lines. E.
B. Elliott. Abstract x 105, 106
methods of finding n^-power numbers
whose sum is an nth-power. A. Martin.
Abstract x 107
Matter and force vii 30
Combination of. vi xxxv
Properties of. i 27,v 127, vi 5, vii 40
Three states of. v 136
Matteueci cited on muscular contraciion...v 59
Matthews, Washington, communication on
natural naturalists. Read by J. S. Bill-
ings. Abstract vii 73
mythological dry paintings of the Nava-
jos. Abstract viii 14
anthropometric and reaction-time appa-
ratus. Abstracts _..viii 25
Mauna Loa vi 13
Maxima and minima, Special case in..vi 149, 152
Maxwell, Prof. J. C, cited on matter v 128
on elasticity v 132
theories of heat v 13*4
radiant energy v 136
Boyle's law v 139
molecular orbits v 140, 147, 149
INDEX TO VOLUMES I-X. 155
Page.
Maxwell, Prof. J. C, cited on—Cont'd.
dissipation of molecular energy v 153
surface repulsion v 155
vortex rings vii liv
matter vii 44
Mayer, A. M., communication on a method
of determining a definite interval of
time, and its application to measuring
the number of vibrations of solid bod-
ies. Title only ii 64
Mayer's topophone viii 13
Mechanical representation of a problem in
least squares i 89
Medallic medical history vi 39
Medals, Exhibition of. v 22
Meehan, Thos., cited on the common names
of plants iv 113
Meek, F. B., communication on new species
of fossil plants from Alleghany Co.,
Virginia; with some remarks on the
rock seen along the Chesapeake and
Ohio railroad, near the White Sulphur
Springs of Greenbrier county, West
Virginia. Read by T. Gill. In full. 2
plates-..: i 62, ii (26)
Death of. „ ii 111
Meigs, M. C, communication on a map of
the head waters of the Yellowstone
and Lewis rivers. No abstract i 21
the movements caused in large ice-fields
by expansion and contraction, as illus-
trative of the formation of anticlinal
and synclinal axes in geological for-
mations. In full. 4 figures ii 33, (22)
remarks on glacial period ii 37
Members. See List of Members.
Membership statistics of scientific socie-
ties x 29
Memoir on the scientific work of Joseph
Henry ii 203
Memorial to B. Alvord vii 127
(See also Biography.)
Mendenhall, T. C, communication on the
measurement of temperature at dis-
tant points. Title only viii 18
the Charleston earthquake. Abstract,
ix 37
remarks on Japanese customs ix 21
Mercadier, M., cited on radiophony iv 158
Mercury, Theory of. viii 41
Transit of. ii 199, iii 43
Meridian, Proposed initial vi 106
Meridian transit time determinations...viii 55
Merriam, C. H., communication on the eco-
nomic phase of the English sparrow
question. Reference x 16
Page.
Merrill, G. P., communication on geological
museums. Title only ix 36
Metaphysic philosophy vi xxx
Metaphysics vii xxix
Metcalf, Capt. H., cited on theory of target
practice vi 145
Meteor, Explanation of explosion of ii 143
of December 24, 1873 i 94, ii 123, 139
(See also Meteors.)
Meteoric matter and planetary motions,
ii 1S8, 190
Meteorite, A new vii 32
Meteorites at Concepcion and San Gregorio,
New Mexico i 24
Meteorological work by Joseph Henry ii 236
of the Smithsonian Institution ii 295
Meteorology, List of papers on (See also
Thermometry)
:
on the aerial currents observed in fifty
balloon ascensions. S. A. King. Com-
municated by C. Abbe. In full i 35
[on aerial currents observed in balloon
ascensions.] C. Abbe. Abstract i 38
on certain remarkable effects of lightning.
E. J. Farquhar. Communicated by
J. Henry. Title only i 42
on the aurora. W. B. Taylor. Abstract. ,.i 43
on the aurora of February 4th [1872]. J. E.
Hilgard. Abstract 1 47
on the effects of winds and barometric
pressure on the tides of Boston, and
on the mean level of the sea. W. Fer-
rel. Abstract and reference 1 53
on the meteorology of Japan. T. Autisell.
Title only i 70
on the results of astronomical observa-
tions at Sherman Station, Wyoming
Terr. R. D. Cutts. Abstract and refer-
ence i 70
on the laws of condensation of aqueous
vapor in the atmosphere. E. Foote.
Title only i 74
on the meteorology of Russia. A. Woeikof.
Reference i 75
on atmospheric electricity. (3 papers.) J.
Henry. Title only 175,87
on electrical phenomena in the Kocky
Mountains. F. M. Endlich. Title only,
i 95
on the distribution of temperature over
the surface of the globe. W. Hark-
ness. Reference 1 96
on some causes that produce rain. E.
Foote. Title only 1 98
on the laws governing the movement of
storm centres. C. Abbe. Abstract... 1 99
156 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Meteorology, List of papers on—Cont'd,
on the law connecting the velocity and di-
rection of the wind with the barometric
gradient. W. Ferrel. Abstract i 106
on the correlation of the winds and the
temperatures of the surface waters of
the ocean along the coast of New
Hampshire. J. W. Chickering. Ab-
stract ii 17
meteorological observations in Peru, and
some of the meteorological conditions
of that country. A. Woeikof. Title
only ii 38
the glacial theory. J. Henry. Abstract.Xi 35
the causes of glacial climate. Symposium.
Abstract ii 43, 45
the comparison of rain-gauges at different
elevations. J. R. Eastman. Abstract.Xi 49
a new meteorological instrument. J. W.
Osborne. Abstract ii 63
the hygrometrical condition of the air in
high latitudes. E. Bessels. Title only,
11 66
the horary oscillations of the temperature
of the atmosphere. G. K. Gilbert. Ab-
stract ii 67
horary oscillations of the atmosphere. G.
K. Gilbert. Abstract ii 69
facts relating to the falling of waterspouts
in North Carolina. T. L. Clingman.
Abstract ii 104
the causes of electrical developments in
thunderstorms. E. Foote. Abstract..Ii 189
suggestions respecting the study of mete-
orology in regard to the causes of yel-
low fever. J. W. Osborne. Title only,
lii 21, 27
a curious manifestation of force by the
wind. J. VV. Osborne. Title only....ill 27
air currents on mountain slopes. G. K.
Gilbert. Abstract ill 38
on the meteorological conditions affect-
ing the culture of the sugar beet. W.
McMurtrie. Reference iii 142
[the aurora boreatis.] C. Abbe. Abstract.Xv 21
on the' conditions determining tempera-
ture. W. Ferrel. In full v 90, 91
on errors of barometric observations pro-
duced by wind. G. K. Gilbert. Refer-
ence v 91
on solar radiation at Sherman, Wyoming.
W. Ferrel. Title only v 101
on the retardation of storm centres at ele-
vated stations, and high wind as a
probable cause. H. A. Hazen. In
full v 108
Page.
Meteorology, List of gapers on—Cont'd,
[a remarkable halo.] W. B. Taylor. Ab-
stract v 112
on a graphic table for computation. G. K.
Gilbert. Abstract v 120
on the coming winter of 1882-'83. H. A.
Hazen. Abstract v 122
the response of terrestrial climate to secu-
lar variations in solar radiation. G. K.
Gilbert. Abstract vi 10
the thermal belts of North Carolina. J. W.
Chickering. Abstract vi 11
hygrometric observations. H. A. Hazen.
Abstract vl 36
the Rochester (Minnesota) tornado. J. R.
Eastman. Abstract vii 3
the sun-glows. H. A. Hazen. Abstract
and reference vll 17
the relations between northers and mag-
netic! disturbances at Havana. G. E.
Curtis. Reference vll 25
methods of verifying weather predictions.
C. Abbe. Abstract viil 8
thunderstorms of 1884. H. A. Hazen. Ab-
stract vlli 10
the condensing hygrometer and sling psy-
chrometer. H. A. Hazen. Abstract,
viii 25
normal barometers. T. Russell. Title
only lx 46
the sky-glows of 1883. H. A. Hazen. Title
only x 6
the theory of the wind-vane. G. E. Curtis.
Reference x 9
the electrometer as used in observations
of atmospheric electricity. C. F. Mar-
vin. Title only x 9
relation between wind velocity and press-
ure. H. A. Hazen. Reference x 10
the Signal Service bibliography of meteor-
ology. C. Abbe. In full x 20
memorandum on the Signal Service bibli-
ography of meteorology and terrestrial
magnetism. C. J. Sawyer. Read by
C. Abbe. In full x 23
Meteors and comets 1 94
Method of least squares..i 62, 89, vl 150, vlli 41
research 11 163, vl xxxiii, vll li
Methods of evolution vi xxvii
modern petrography vll 36
verifying predictions vll 122
verifying weather predictions viil 8
Metric system vl 4
advocated by Geodetic Commission. ...vl 109
for postal purposes ii 15, 19
in microscopy ill 22
INDEX TO VOLUMES I-X. 157
Mexico, Gulf of. iv 52
Meyer's atomic volume curve vil 15
Mica mines of North Carolina vii 9
Michelson.A. A.,communication on the mod-
ifications suffered by light in passing
through a very narrow slit. Abstract.iii 119
Michigan, Altitude of Lake li 23
Micrometry, Standard for ill 22
Micron itt 23
Microphone, Hughes' iv 184
Modification of Wheatstone's iv 183
Microscopy, List of papers on (See also
Optics)
:
on the desirability of reproducing photo-
graphs of scientific objects and espe-
cially of magnified microscopical prep-
arations in a permanent form by some
photo-mechanical method. J. J.Wood-
ward. Abstract i 41
on the use of monochromatic sunlight as
an aid to high power definition. J. J.
Woodward. Abstract and reference i 47
on micrometric writing on glass. J. J.
Woodward. Title only i 93
on the modern microscope, Nobert's lines,
and the attempts of others to construct
them. J. J. Woodward. Title only.. .ii 25
diffraction phenomena in the field of the
microscope. J. J. Woodward. Abstract
and reference ii 60
the microscopical structure of wool. J. J.
Woodward and John Leconte. Title
only ii 62
the use of photography in connection with
the micrometer measurement of blood
corpuscles. J. J. Woodward. Title
only ii 79
a simple device for the illumination of
balsam-mounted objects for examina-
tion with certain immersion objectives
whose "balsam angle" is 90° or up-
wards. J. J. Woodward. In full. 1
figure ii 126
on the apertometer of Prof. E. Abbe, of
Jena, Germany. J. J. Woodward. Ab-
stract iii 18
on a standard for micrometry. J. J. Wood-
ward. Abstract iii 22
on the oil-immersion objectives of Zeiss,
and on convenient methods of obtain-
ing oblique illumination for these and
similar objectives. J. J. Woodward.
Abstract iii 25
a new apertometer for microscopic ob-
jectives. J. J. Woodward. Title
only Hi 37
microscopy, List of papers on—Cont'd.
Riddell's binocular microscopes—an his-
torical notice. J. J. Woodward. Ab-
stract and reference iv 35
[exhibition of a collection of microscopes.]
J. S. Billings. No abstract vii 73
recent improvements in microscopic ob-
jectives, with demonstration of the
resolving power of a new l-16th inch.
R.Hitchcock. Title only ix 16
Milneria minima viii 5
Mills, cited on thermometry ix 30
Mind and body v 72
Mineralogy, List of papers on :
on mineralogical systems. F. M. Endlich.
In full i 77
on specimens of meteoric iron from Chi-
huahua, Mexico, and the structure of
meteorites in general. F. M. Endlich.
Title only I 98
on the occurrence of pure tellurium in
certain gold mines of Colorado. F. M.
Endlich. Title only i 101
on some interesting cases of metamorph-
ism. F. M. Endlich. Title only iii 27
some observations on the crystalline state
of matter. J. R. M. Irby. Abstract...iii 39
topaz from Stoneham, Maine. F.W. Clarke
and J. S. Diller. Abstract and refer-
ence viii 5
the enlargement of mineral fragments as
a factor in rock alteration. R. D.
Irving. Title only ix 16
the present status of mineralogy. F. W.
Clarke. Title only x 6
Misapplication of geographical terms i 39
Miscellaneous Papers, List of:
anniversary address, Nov. 18, 1871 ; [on the
organization and objects of the Soci-
ety.] J.Henry. In full i v, 34
on the preservation of foods. A. B. Eaton.
Title only i 22
[exhibition of a chronoscope.] J. E. Hil-
gard. No abstract i 23
on the construction of the bridge across
East River between Brooklyn and New
York. Major King. Title only i 23
on the new coinage of Japan. E. B. Elliott.
Title only i 31
on apothecaries' weights and measures.
B. F. Craig. Title only i 34
on the measurement of the pressure de-
veloped by the explosion of gun-
powder in firearms. C. E. Dutton.
Title only * 62
158 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
miscellaneous Papers, List of—Cont'd.
on the expenditure of the income of the
Bache fund for 1872. J. Henry. Title
only 1 63
an account of some recent experiments on
different kinds of gunpowder at Fort-
ress Monroe. C. E. Dutton. Title
only 1 54
[the Woodbury photo-relief process.] J.
J. Woodward. Abstract i 57
[the condition of the Society.] J. Henry.
No abstract 1 64
on the water supply of cities. B. F. Craig.
Title only 1 65
on the collection of a large library. J. S.
Billings. Abstract i 92
a description of a new spirometer. G. A.
Otis. Title only i 94
on recent improvements in the economy
of fuel. C. E. Dutton. Title only i 96
on recent improvements in the manufac-
ture of steel. C. E. Dutton. Titleonly,
1 97
on Giffard's injector. J. Henry. Title
only i 99
on the method adopted in writing the in-
ternational scientific telegrams. A.
Hall. Abstract I 101
[on scientific culture in the Argentine Re-
public] B. A. Gould. No abstract...ll 15
on the present state of the sciences. C.
W. Shields. Abstract and references...U 16
on the gathering, packing, transportation,
and exposure of fruits for sale. S. C.
Busey. Titleonly 11 16
on the failure of the wooden pavements of
Washington City. L. D. Gale. Ab-
stract 11 26
on latent impression* on polished glass
plates produced by heating the plates
in close connection with engraved me-
tallic plates. A. C. Ross. Abstract...11 39
iron facing copper plates. J. E. Hilgard.
Abstract 11 42
the progress of the natural sciences dur-
ing the past century. T. N. Gill. Ref-
erence 11 56
cylinder condensation, steam jackets, and
superheated steam. G. B. Dixwell.
Title only 11 64
the coinage of the Argentine Republic.
B. A. Gould. Communicated by E. B.
Elliott. Abstract 11 65
the progress which [has] been made in
educational matters in [Japan.] D.
Murray. Abstract 11 69
Page.
miscellaneous Papers, List of—Cont'd.
illuminating materials. J. Henry. Title
only 11 71
[kerosene oil tests.] Mason. Ab-
stract 11 72
paper made of asbestos. J. Henry. Title
only 11 86
the burning of theatres and public halls.
'J. M. Toner. Reference 11 95
the rulings on glass by Mr. Rogers, of
Cambridge. J. J.Woodward. Abstract,
11 130
the uses of [the] dynagraph, and the work
performed in determining the resist-
ance of trains, etc. P. H. Dudley. Ab-
stract Ill 29
phosphorescent clocks. J. E. Hilgard.
Abstract HI 33
the work of tho National Board of Health.
J.S.Billings. Titleonly Ill 50
[yellow fever disinfection.] F. M. Gun-
nell. Abstract Ill 51
[exhibition of a time globe.] Juvet.
Abstract Ill 106
sugar from sorghum. P.Collier. Abstract,
111 140
the scientific work carried on under the
direction of the National Board of
Health. J. S. Billings. Abstract,
lv 37
the history of the light house establish-
ment of the United States. A. B.
Johnson. Abstract and reference lv 135
relation of meteorological conditions to
the summer diarrhoeal diseases. S. C.
Busey. Abstract and reference lv 165
[exhibition of a panoramic photograph.]
W. B. Taylor. Abstract v 21
[exhibition of coins and medals.] J. M.
Toner. Abstract v 22
on the ventilation of the House of Repre-
sentatives. J. S. Billings. Abstract,
v 99
on the philosophical order of the sciences.
C. W. Shields. Reference v 105
on the fisheries of the world. G. B. Goode.
Reference v 117
the cultivation of eucalyptus on the
Roman Campagna. F. B. Hough. Ref-
erence vi 36
sketches from medallic medical history.
W. Lee. Abstract vl 39
fisheries exhibitions. G. B. Goode. Ref-
erence vll 26
American scientific societies. A. Hall.
Presidential address. JnfulL.-vUi xxxiii, 30
INDEX TO VOLUMES I-X. 159
Page.
Miscellaneous Papers, List of—Cont'd,
the systematic care of pamphlets. G.
Brown Goode. Abstract and reference,
viii 29
the systematic care of pamphlets. C. V.
Riley. Abstract viii 29
scientific men and their duties. J. S. Bill-
ings. Presidential address. In full,
ix xxxv, 46
when I first saw the cholera bacillus. R.
D. Mussey. Title only ix 22
the frequency of coincidences. L. F.
Ward. Abstract x 8
Manchester meeting of the British Asso-
ciation for the Advancement of Sci-
ence, 1887. F. W. Clarke. Title only...x 19
on reference indexing. B. P. Mann. Ab-
stract x 38
Mississippi delta 1 (10)
Missouri, Valley of the Upper vii 20
Mivart, St. G., cited on life v 52
Model of the basin of the Gulf of Mexicc.lv 52
Mohs, cited on mineralogy i 78, 79
Molecular excursions v 140, 141
heats of similar compounds i 104
kinetics v 133
physics. See Physics.
Molecules, atoms, and waves i 66
size of v 141
complexity of v 147
Mollusks, Appendages of vii 32
found at great depths v 90
Observations on iii 75
Two remarkable viii 5
Moore, Commander, cited on Plover Bay..iv 124
Moon, Theory of iv 57, vi 136
Moon's eclipse of June 11, 1S81 v 90
motion, Computation of. vi 136
Money, Gold and silver iii 78, 107
Mono craters vii 19
Monochromatic aberration in aphakia vi 5
sunlight as an aid to high definition i 47
Monoclinal ridges ...ii 74
More, Henry, cited on matter vii xlii
Morphology, Biologic —iv 123
of the antlers of the Cervidse ii 135
Morse, E. S., cited on disparity of sexes in
Buccinum iii 75
Mortality among army officers „ ii 49
statistics of the tenth census iv 164
Mosher, Experiments of ». ii 40
Mosler, cited on phosphorus and cerebral
activity _ v 75
Mosquito inoculation vi 5
Mosso, Plethysmograph of. v 77
Motion, Laws of vii 56
Page.
Motion, Modes of._ vi xxxviii
of a particle toward an attracting centre,
i 88, 11 19, vii 122
Transmutation of vi xxviii
Mount Dana glacier vii 5
Mount Lyell glacier vii 6
Mount Rainier and its glaciers x 10
Mount Taylor, Geology of vii 77
Mount Washington meteorological observa-
tions v 108
Movement of storm centres 1 99
Muir's glacier observations vii 8
Munroe, C. E., communication on the esti-
mation of manganese as pyrophos-
phate. Read by T. Antisell. Referenccit 132
the determination of the specific gravity
of solids by the common hydrometer.
In full vi 26
Murdoch, John, remarks on throwing-
sticks Ix 13
Murray, David, communication on the pro-
gress which has been made in educa-
tional matters in Japan. Abstract.. ..11 69
Muscular contraction v 58
Museum, National Ii 292
Museum specimens illustrating biology...ix 35
Music and the chemical elements vii 26
Musical intervals 11 199
Mussey, R. D., communication on the appli-
cation of physical methods to intel-
lectual science. Abstract vii 18
when I first saw the cholera bacillus.
Title only Ix 22
remarks on artesian wells v 101
phonetic alphabets ix 18
Myer, A. J., Death of. Iv 23
Resolution on the death of. iv 31
Mythological dry painting of the Navajos,
viii 14
Mythology of the Numas i 96
National Academy of Sciences viii xl
National Board of Health, Scientific work by
the iv 37
National Museum 11 292, x 57
Natural naturalists vii 73
Navajo dry painting viii 14
Naval Observatory, New telescope of. 1 62, 63
star catalogue 1 74
Navigation, Sumner's method in ii 105
Nebraska, Quaternary of iv 120
Nebula of Andromeda ix 14
Nebulsa, Drawings of ii 51
Planes of certain i 109
Nebular hypothesis and the satellites of
Mars- ii 186, 188, 190, vi 45
160 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Necks of volcanoes vll 78
Nerve currents v 60
Neve and glacier denned vii 37
Nevada, Glacial epoch in i 84
Physical features of i 54
Volcanic activity in 1 99
New Hampshire, Relation of winds to sea
temperature on the coast of. ii 17
New Mexican volcanoes and lava-fields. ..vii 76
New star .*..ix 14
Newberry, Dr. J. 8., cited on fossil plants
from Virginia ii (38), (42)
Newcomb, Simon, communication on the
transits of Venus, past and future.
Title only i 29
the possibility of a universal atmos-
phere. Title only i 52
the progress of the construction of the
new telescope for the Naval Observa-
tory. Reference 1 62, 63
the proceedings of the commission to
arrange for the observation of the next
transit of Venus. Title only i 65
the mechanical representation of a
problem in least squares. Reference..! 89
the transit of Venus. Title only ii 41
tt thermodynamic theory of the spec-
trum. Title only iii 41, 43
the cosmogony. Titleonly ii 113
the recent transit of Mercury [1878].
Abstract- ii 199
observations of the total solar eclipse,
July 29, 1878. Abstract ii 202
the recurrence of eclipses. Titleonly. .iii 33
a recent visit to California to inspect a
site for the new Lick observatory.
Title only iii 45
the future of the human race regarded
from the standpoint of evolution.
Presidential address, 1879. Title only.Ml 52
the principles of taxation. Title only,
iii 119
the relation of scientific method to so-
cial progress. Presidential address, 1880.
In full iv 40
the speed of propagation of the Charles-
ton earthquake. Reference x 28
remarks on auroras i 46
the radiometer ii 81
passage of light through a narrow slit,
iii 120
auroras iv 22
Benjamin Peirce... iv 26
Newton, Henry, Researches in the Black
Hills by iii 125
Newton, Prof. H. A., cited on the aurora...iv 22
Page.
Newton, Sir Isaac, eked on action at a dis-
tance V 159
atoms vii xliv
elasticity v 130
laws of orbits v 146
the spectrum v 142
the ultimate v 165, 167
trisection of angles x 97
Newton's rings v 155
Newtonian formula of gravitation, Modifica-
tion of. viil 39
philosophy vii 45
Niagara Falls, Earth tremors at iv 186
Nichol, J. P., Thermometric experiments
of v 93
Nicholson, W. L., report of the committee
to collect information relative to the
meteor of December 24th, 1873. In full.
Map and 2 figures ii 139
remarks on the effect of magnetism on
the length of magnetic bars ii 373
Nomogram x 4
Normal section in geodesy vi 123
North American Indians, Errors respecting,
ii 175
North Carolina coast, Geology of. vl 28
earthquakes i 101, 104
mica mines vii 9
thermal belts vi 11
waterspouts ii 104
Northers and magnetic disturbance vii 25
Nt&-power numbers whose sum is an n">.
power x 107
Numas, Genesis and demonology of i 104
Mythology of. i 96
Nymphalidse, Pupation of. iii 41
Objective, Interior angle of iii 19
Achromatic iii 65
Objectives, Color corrections to achromatic,
iii 39
Oil-immersion iii 25
Oblateness of the earth, Change in viil l!i
Oblique illumination in microscopy iii 25
Observation and experimentation, Princi-
ples of. ~ ii 163, vii Ii
Observation equations, Special treatment of
certain vi 156, viii 41
Observations of the meteor of Dec. 24, 1873..U 1 1
1
Occult force vi xxxiii
qualities WO
Oceanography, List of papers on :
on the effects of winds and barometric
pressure on the tidws of Boston, and
on the mean level of the sea. W. Fer-
rel. Abstract and reference i 53.
INDEX TO VOLUMES I-X. 161
Oceanography, List of papers on—Cont'd.
[letter on changes of sea-level at Ber-
muda.] J. H. Lefroy. Communicated by
J. Henry. No abstract i 75
on the tides of the Bay of Fundy. Mr.
Ramsay. Communicated by J. J.Wood-
ward. Title only t 94
Sumner's method in navigation. J. H. C.
Coffin. Infull 14 105
the navy compass. B. F. Greene. Title
only 11 123
an adjustable binnacle for the correction
of a ship's compass. B. F. Greene.
Title only 11 134
optical salinometer. J. E. Hilgard. Ab-
stract 11 185
temperatures of the Pacific OEean. T.
Antisell. Abstract 11 192
the deepseadredgingsin the Gulf of Mex-
ico and the West Indies in 1873-1878,
by Professors Louis and Alexander
Agassiz and the officers of the U. S.
Coast Survey. W. H. Dall. Title only,
iii 45
on Siemens' deep sea thermometer and
Carre's ice machine. J. E. Hilgard.
Title only v 100
some eccentricities of ocean currents. A.
B.Johnson. Abstract vii 14
historical sketch of deep sea temperature
observations. J. H. Kidder. Title
only Ix 14
Odor, Theory of. viii 27
Office, Rotation in v 49
Officers, Duties of. (See Standing Rules.)
for 1871 1 20
1872 1 32, 33
1873 1 64
1874 1 91
1875 11 16
1870 11 x, 59, 84
1877....'. 11 86
1878 11 161
1879 ill 17
1880 11151,53,151
1881 lv 30
1882 v 14, 85, 112
1883 v 175, vl xiv, 41, 122
1884 vl xv, vii xiv, 36, 85
18S5 -vii xv, viii xiv, 30
1886 .-viii xv, ix xiv, 52
1887 ix xv, x xiv, 82
1888 x xv
of the Army and Navy as scientific admin-
istrators Ix xlix
57
Page.
Ogden, H.G., communication on What is to-
pography? Abstract x 15
Oil-immersion objectives Ill 25
Oldberg. R., The Flora Columbiana of lv 65
Omaha Indians, Gentile system of. Ill 128
Omar Cheyam, Calendar proposed by il 38
Onatsevich, Lt. M. S., Co ordinates of Plover
Bay by lv 128
Ontario Basin, Changes of level in Ix 8
Ophthalmology. (See Optics.)
Optical salinometer 11 185
Optics, List of papers on (see also Micros-
copy) :
on a new method for detecting and
measuring the optical defects of the
eye. W.Thomson. Reference i 22
on achromatic object glasses. R. Keith.
Title only 1 73
[exhibition of spectra and spectroscopes.]
J. J. Woodward. No abstract 1 89
half-vision. J. Henry. Title only 11 60
the markings on Navicula rhomboides. J.
J.Woodward. Title only 11 69
the color corrections of achromatic object-
ives. W. Harkness. Abstract Ill 39
a thermodynamic theory of the spectrum.
S. Newcomb. Title only ill 41, 43
some apparatus recently brought into use
by the medical department of the
Army for the examination of the eye.
J. J. Woodward._ Abstract Ill 53
the number of lenses required in an ach-
romatic objective, consisting of infi-
nitely thin lenses in contact, in order
that, with any given law of dispersion
whatever, the greatest possible num-
ber of light-rays of different degrees
of refrangibility may be brought to a
common focus. W. Harkness. In
full Ml 65
the modifications suffered by light in pass-
ing through a very narrow slit. A. A.
Michelson. Abstract Ill 119
color perception and color blindness. S.
M. Burnett. Abstract and reference,
lv 54
refraction in the principal meridians of a
triaxial ellipsoid, regular astigmatism
and cylindrical lenses. S. M. Burnett.
Reference vi 4
the monochromatic aberration of the
human eye in aphakia. W. Harkness.
Reference vl 5
the character of the focal lines in astig-
matism. S. M. Burnett. Abstract,
vl 45
162 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Optics, List of papers on—Cont'd,
why the eyes of animals shine in the dark.
S. M. Burnett. Abstract and reference,
vii 13
the Javal and Schiotz ophthalmometer.
S. M. Burnett. Title only vlil 11
on a device for viewing the sun by light
of any desired wave length. W. Hark-
ness. Abstract x 13
Orange Mountain, N. J viil 19
Orbit of comet, Correction of ii 22
Hyperion x 90, 104
Swift's comet iv 59
Orbits illustrated by models x 28
of Titan and Hyperion Hi 2C, 40
Special case in elliptic vii 122
Ore deposition by replacement vi 32
Organization of the Society i v, 19, 20, 21
Orthocenter viii 47
Osborne, J. A., cited on the pupation of the
Nymphalidse Hi 41
Osborne, J. W., communication on a new
meteorological instrument. Abstract,
ii 63
the study of meteorology in regard to
the causes of yellow fever. Title only,
Hi 21, 27
a curious manifestation of force by the
wind. Title only Hi 27
a case of peculiar corrosive action on
metallic tin. Title only i Hi 44
remarks on auroras iv 22
Otis, G. A., Biographical sketch of iv 171
Bibliography of. iv 181
communication on fractures of the inner
table of the cranium. Title only 1 73
a new spirometer. Title only i 94
Death of. iv 120
Resolutions on the death of. iv 134
Ox-eye daisy as an insecticide vU 12
Pacific Ocean, Temperatures and currents
of H192
Painting with dry colors viii 14
Paleontology. (See Zoology and Botany.)
Palaeotherium, Structure and shape of. i 99
Pamphlets, Care of viii 29
Papers read to the Society. (See Acoustics,
Anatomy, Anthropology, Archaeology,
Astronomy, Biography, Biology, Botany,
Calendars, Chemistry, Electricity, Geog-
raphy, Geology, Mathematics, Meteor-
ology, Microscopy, Mineralogy, Miscella-
neous, Oceanography, Optics, Physics,
Political Economy, Psychology, Seis-
Page.
mology, Social Science, Thermometry,
Zoology.)
Statistics of the Society's x 32
Papyrus Ebers ii 64
Parallax of aTauri x 91
Methods of measuring v 39
Parker, Peter, communication on the me-
teor of December 24, 1873. No ab-
stract i 94
Joseph Henry. In full ii 368
remarks on Chinese vocabularies ii 28
calendars ii 30
electrical treatment ii 40
origin of the American Indians ii 94
report of the committee to collect infor-
mation relative to the meteor of De-
cember 24th, 1873. In full. Map and
2 figures ii 139
resolutions on the death of Salmon P.
Chase i 87
Patterson, H. N., cited on the flora of Illi-
nois iv 99
Paucker, Prof. M. G., cited on Malfatti's
problem H 116
Paul, H. M., communication on earth trem-
ors as shown by astronomical observa-
tions. Abstract Hi 120
problems connected with the physics of
the earth's crust. Title only viii 17, 18
the Flood Rock explosion. Title only,
viii 28
the Charleston earthquake. Abstract.Xx. 41
remarks on sun glows vH 35
earthquakes vii 73, ix 42
the topophone viii 13
dry painting by the Japanese viU 16
time determinations viii 58
graphics x 5
Pavements, Failure of wooden ii 26
Peale, T. R., Death of. viii 10
Peirce, Benjamin, cited on curves similar
to their evolutes vii 87
communication on the heat of the sun.
Abstract i 31
the theories of the nature of comet's
tails. Reference i 74
Death of. It 21, 23
Remarks commemorative of iv 23
Resolutions on death of. iv 23
Peirce, C. S., cited on verification of predic-
tions vii 124
communication on the appearance of
Encke's comet as seen at Harvard Col-
lege Observatory. Reference i 35
stellar photometry. Reference i 63
INDEX TO VOLUMES I-X. 163
Page.
Peirce, C. S., communication on—Cont'd,
the coincidence of the geographical dis-
tribution of rain fall and illiteracy, as
shown by the statistical maps of the
ninth census reports. Abstract i 68
logical algebra. Reference i 88
quaternions, as developed from the gen-
eral theory of the logic of relatives.
Title only i 94
various hypotheses in reference to
space. Title only i 97
Peirce's criterion , vi 155
Pendulum formulae vii 89, 101
Perception of color, form, and light vii 72
Periodic integrals .x 100
law of the chemical elements vii 15
Permian formation of North America. ..iii 67, 104
Persian calendar ii 38
Perturbations of moon's motion, Computa-
tion of -vi 136
Polyhymnia by Jupiter Tiii 54
Peru, Meteorology of ii 35
Peters, Prof. C. H. F., cited on supposed
trans-Neptunian planet Hi 20
letter on transit of Venus, 1874. Commu-
nicated by A. Hall. Abstract ii 31
Petrographic methods vii 36
Phenomena, Physical basis of. vii 40
Philosophical Society of Washington viii xlv
Growth of x 47
why this name wai chosen i v, x 45
Phonetic alphabet ix 17
Phosphorescent clocks iii 33
Phosphorus and cerebral activity v 75
Photo-engraving i 41
Photographic panorama v 21
Photographing the sun's corona iii 117
transit of Venus, 1882 vi 21
Photographs of transit of Venus, 1874 ii 31
Photography as an aid to astronomy i 28
an aid to research i 41
Composite vii 25
Photometry, Stellar i 63
Photophone iv 143
Phthisis ii 124
Physical geography. (See Geography and
Geology.)
Physical-geographical divisions of the south-
eastern portion of the United States,
lx 22
Physical investigations by Joseph Henry..ii 271
method in intellectual sciences vii 18
Physics, List of papers on (see also Acous-
tics, Optics, Electricity)
:
on the nature and origin of force. W. B.
Taylor. Abstract and reference i 27
Page.
Physics, List of papers on—Cont'd.
on the fatigue of metals. Major King.
Title only i 53
on waves, molecules, and atoms. W. B.
Taylor. Abstract i 66
on the rectilinear motion of a particle
toward an attracting centre. A. Hall.
Reference i 88
on the motion of a particle towards an at-
tracting centre. H. H. Bates. Title
only i 89
on the nature of the force of gravitation.
R. Keith. Title only i 89
on a method of developing magnetism in
bars of steel. J. Henry. Title only,
i 97
on the movement of a particle attracted
towards a point. H. H. Bates. Ab-
stract ii 19
a method of determining a definite inter-
val of time, and its application to meas-
uring the number of vibrations of solid
bodies. A. M. Mayer. Title only ii 64
Crookes' radiometers. J. Henry. .46-
stract _ ii 80
force and momentum. E.B.Elliott. Title
only ii 84
a thermodynamic theory of the spectrum.
S. Newcomb. Title only iii 41, 43
vortex motion in ordinary fluids. T.
Craig. Reference iii 143
curious fallacy as to the theory of gravita-
tion. B. Alvord. In full v 85
on physics and occult qualities. W. B.
Taylor. Presidential address. In full,
v 125, 126
the three methods of evolution. J. W.
Powell. Presidential address. In full,
vi xxvii, 110
the nature of matter. H. H. Bates. Ref-
erence vi 5
substance, matter, motion, and force. M.
H. Doolittle. Title only vi 14
the atomic philosophy, physical and meta-
physical. J. C. Welling. Presidential
address. In full vii xxix, 81
music and the chemical elements. M. H.
Doolittle. Abstract vii 26, 27
review of the theoretical discussion in
Prof. P. G. Tait's " Encyclopaedia Brit-
annica" article on mechanics. H.
Farquhar. Abstract vii 29
the physical basis of phenomena. H. H.
Bates. Infull vii 40
a formula for the length of a seconds-
pendulum. G. W. Hill. Reference..iril 101
164 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Physics, List of paper9 on—Cont'd,
a slight modification of the Newtonian
formula of gravitation. W. B. Taylor.
Abstract viii 39
Can the attraction of a finite mass be infi-
nite? C. H. Kummell. In full viii 58
Newton's vis. M. H. Doolittle. Title only,
x 38
the free cooling of a homogeneous sphere
initially heated to a uniform tempera-
ture. R. S. Woodward. Reference x 90
the conditioned cooling of a homogeneous
sphere. R. S. Woodward. Reference.* 103
Physics of the Mississippi river i (13)
Piedmont region ix 24
Pile of balls Hi 76
Piles bored by teredo v 98
Pisciculture x 55
Plains, Artesian wells on the v 101
Plane curves, Contact of vi 157
Planet, Centre of apparent disk of ii 181
search for intra-Mercurial ii 85
supposed discovery of a trans-Neptunian,
iii 20
Planetary mass determined from two satel-
lites vi 132
motion as affected by meteoric matter,
ii 18S, 189, 190
motions iii 26, vi 41
perturbations of the moon vi 136
Planets, Theory of iv 57
Plants, Climate of. ii 183
on Roan Mountain.. iv 03
Plateau region .• i 55, vii 76
Plato cited on philosophy.. vii xxxvi
Plethysmographs v 77
Pleurotomaria, Notch in shell of. iii 70
Plover Bay, Alaska ..iv 124
Plucker, Prof. J., cited on Malfatti's problem
ii 118
Plumb-line deflection. ..ii 82, vii 92, 101, ix 15, 53
Poggendorf corrections in thermometry...ix 29
Poinsot, Louis, cited on impact of inelastic
bodies v 131
Poisoned arrows ii 180, 1S2
Poisson cited on temperature of space ii 7:;
Polar expedition ii 89
Polaris expedition i 92
Polarization of light by a narrow slit.iii 119, 124
Pole, Shifting of the earth's viii 10
Political Economy, List of papers on ;
on the statistics of the borrowing power of
the United States. E. B. Elliott. Title
only i 29
on international coinage. E. B. Elliott.
Tifa only 1 75
Page.
Political Economy, List of papers on
—
Cont'd.
[change in value of dollar.] E. B. Elliott.
No abstract i 91
on the credit of the United States, as
shown by the value of its securities.
E. B. Elliott. Title only 1 109
on the transition in Germany, and the
Scandinavian nations of Sweden, Nor-
way, and Denmark, from the silver
standard of coinage and money of ac-
count to a gold standard. E. B. Elli-
ott ii 25
the mutual relations as to price of gold,
silver bullion, silver coin, and green-
backs. E.B.Elliott. Title only ii 50
mutual relation as to price of gold, green-
backs, silver bullion, and silver coin.
E.B.Elliott. In full ii 52
two propositions, now before Congress, for
changing the coin of the United States.
E. B. Elliott. Title only ii 68
monetary standards. E. B. Elliott. Title
only ii 85
mutual relations of gold and silver, and of
prices of commodities. E. B. Elliott.
Abstract ii 87
optional monetary standards. E. B. Elli-
ott. Title only ii 135
the progress of international coinage in
France and America. E. B. Elliott.
Title only iii 27
the subject of international coinage. E.
B. Elliott. Abstract iii 38
the silver question. C. E. Dutton. In
full iii 78
the silver question. Symposium. Ab-
stract iii 107
the construction of the Government sink-
ing fund. E. B. Elliott. Abstract...lU 113
the principles of taxation. S. Newcomb.
Title only iii 119
the distribution of loans in the Bank of
France, the national banks of the
United States, and the Imperial Bank
of Germany. J. J. Knox. Abstract,
iv 31
[bi-metallism.] E. B. Elliott. Abstract,
iv 141
accrued interest on Government securi-
ties. E.B.Elliott. Title only v 21
on the credit of the United States, past,
present and prospective. E.B.Elliott.
Title only v 102
on some formulae relating to Government
securities. E. B. Elliott. Title only..jv 106
INDEX TO VOLUMES I-X. 165
Page.
Political Economy, List of papers on—
Cont'd,
the distribution of tho surplus money of
the United States among the States.
J. J. Knox. Abstract vi 103
a financial problem. E. B. Elliott. Title
only vi 149
annual profit to banks of national bank
note circulation. E. B. Elliott. Title
only ix 14
quantity of United States subsidiary silver
coin existing and in circulation. E.
B.Elliott. Title only ix 14
Polyhymnia, Perturbations of. viii 54
Poncelet, cited on Feuerbach's circle....viii 45
Population, Animal, of the globe iv 27
of the earth lv 28
Westward movement of i 35
Porter, communication on recent ex-
plorations in Syria under the auspices
of the Palestine Exploration Fund.
Title only i 54
Porter, Miss S., cited on the instruction of
the deaf. vi 81
Porter, R. P., cited on statistics of sheep...lv 28
Portrait of S. F. Baird x 41
of Joseph Henry 11 frontispiece.
Potato rot 1 97
Pouillet, cited on temperature of space. ....11 73
Pouillet's formula for rate of cooling v 91
Powell, J. W., communication on the struct-
ural geology of the valley of the Colo-
rado of the West. Abstract 1 48
the mythology of the Numas. Refer-
ence 1 96
the genesis and demonology of the
Numa tribe of Indians. Reference 1 104
the UiDtah Mountains. Title only 11 34
the causes of the glacial climate. Ab-
Stract 11 44, 45
some types of mountain building. Title
only 11 65
monoclinal ridges. Abstract 11 74
life of Archibald Robertson Marvine. In
full 11 83, (53)
geologists versus physicists. No abstract,
11 85
the philosophy of the North American
Indians. Title only 11 109, 110
poisons among the North American In-
dians. Abstract 11 182
the lands of the arid region of the United
States. Abstract 11 189
the evolution of language. Title only..ii 199
limitations to the use of some anthro-
pologic data. Reference iv 134
Page.
Powell, J. W., communication on—Cont'd,
the three methods of evolution. Presi-
dential address. In full vi xxvii, 110
plan for the subject bibliography of
North American geologic literature.
Title only vii 71
the personal characteristics of Professor
Baird. In full x 71
remarks on auroras 1 48
volcanism in Arizona and Nevada 1 99
distribution of volcanic action 1 102
the vocabulary of the Utes 11 28
ripple marks 11 62
khivas 11 66
landslip lakes 11 69
interior of the earth 11 79, 85
aboriginal historical charts 11 93
fallacies concerning Indians ....11 180
mounds as evidence of population 11 181
western Permian strata ill 106
organization of primitive society ill 137
plants of Washington and vicinity iv 119
auroras lv 22
uniformity of peak altitudes in the Ap-
palachians lv 64
force and vital principle v 104
eruption and elevation vi 92, 93
drainage system of Iowa vi 97
glaciers vii 8
distribution of volcanic eruption vii 79
Precession and terrestrial rigidity 11 77, 78
Precipitation measured at different heights,
11 49
Preece, cited on photophonic experiments,
lv 149
radiophony lv 183
Predictions of weather and their verifica-
tion vii 122, vili 8
Presidential address. See Address.
Pressure and temperature, Diurnal changes
of 11 67, 69
Prevost's theory of exchanges v 140
Prico, cited on infinite attraction viii 58
Price-Edwards E., cited on refraction of
sound iv 137
Prices of gold, greenbacks, and silver 11 52
Probabilities, Meteorologic v 122
Problem concerning spheres v 107
Financial
, vl 149
in hydrostatics vii 92, 101, ix 15, 53
probabilities x 87, 89
Problems in geometry Hi 55, 64, v 88, 107,
vi 157, viii 45, x 96
Proctor, Richard, cited on the zodiacal light,
i (20), (22)
Prodromus Methodi Mammalium 11 (3)
166 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Prognostication for the winter of 1882-83....v 122
Proorthode , vi 123
Protagon v 75
Protoplasm, Possibilities of v 102
Psychical research x 8
Psychology v 72
Psychology, List of papers on :
on logical algebra. C. S. Peirce. Refer-
ence i 88
on the number of words used in speaking
and writing. E. S. Holden. In full,
ii 28, (1G)
unconscious cerebration. E. M.Gallaudet.
Title only ii 48
dreams in their relation with psychology.
E. J. Farquhar. Abstract vi 37
the atomic philosophy, physical and meta-
physical. J. C. Welling. Presidential
address. In full vi! xxix, 81
the application of physical methods to* in-
tellectual science. R. D. Mussey. Ab-
stract vii 18
Are there separate centers for light-, form-,
and color-perception ? S. M. Burnett.
Abstract and reference...... vii 72
recent experiments on reaction time and
the time sense. G. S. Hall. Title
only viii 4
modern ideas of brain mechanism. P.
Baker. Title only viii 17
anthropometric and reaction-time appa-
ratus. J. S. Billings and W. Matthews.
Abstract viii 25
an attempt at a theory of odor. F. W.
Clarke. Abstract viii 27
the frequency of coincidences. L. F.
Ward. Abstract x 8
Psychrometer, Sling viii 25
Publication of mathematical papers. ..vi 115, 135
of bulletin. See Bulletin.
Publications of scientific societies. ..viii xxxvii
the Philosophical Society x 114
Pumpelly, Prof. R., Researches on sewage in
soils by iv 38
Pupation of the Nymphalidse iii 41
Pyrethrum puwder vii 10
Pythagorean philosophy vii xxxiii
Quadrature of circle i 57
Quadratures, Approximate ii 48
Quadric transformation of elliptic integrals,
vii 102
Quaternary climate of the Great Basin v 21
deposits of western Iowa and eastern Ne-
braska iv 120
of the middle Atlantic slope x 16
Page.
Quimby, Prof., cited on the aurora of Feb.
14, 1872 i 48
Quotients of space-directed lines x 105, 106
Radcliffe, C. B., cited on muscular contrac-
tion .-. v 59, 61
Radiometer ii 80
Radiophony iv 143, 183
Railroad levellings and their hypsometric
value ii 23
trains, Resistance of iii 29
Rain-fall and illiteracy i 68
Rain-gauges at different elevations ii 49
Rainier and its glaciers x 10
Ramsey,
,
letter on the tides of the Bay
of Fundy. Communicated by J. J. Wood-
ward. Title only i 94
Rankine, W. J. M., cited on reconcentration
of energy v 172
Ratio of circumference to diameter i 57
Ravenfi, Gustave, communication on the as-
teroids. Title only viii 18, 54
the theory of Mercury. Abstract viii 41
Rayleigh, Lord, cited on sound produced by
heat iv 150, 183
Raymond, C. W., communication on the re-
sults of travels in Alaska and the de-
termination of the position of Fort
Yukon. Communicated by T. L. Casey.
Reference i 22
letter on transit of Venus, 1874. Commu- .
nicated by A. Hall. Abstract ii 31
Reaumur cited on the pupation of the Nym-
phalidte iii 41
Reed, Henry, communication on the physi-
ology of civilization. Title only ill 20
Reference indexing x 38
Refraction in the principal meridians of a
triaxial ellipsoid vi 4
of sound ii 57, 167 (48), v 35, 39, 44
Uncertainty of correction for atmos-
pheric i 69
Rejection of doubtful observations vi 152
Religion and science ii 16, 224
Removal of place of meeting x xxxi, 10, 31
Remsen, Prof. Ira, Researches on impure air
by iv 37
Report of committee to collect information
relative to the meteor of December
24th, 1873 ii 139
Representation of comet orbits by models,
x 28
Research, Endowment of. viii xli
Method of ii 163, iv 40, vii li, x 4
Resistance of railway trains iii 29
Resisting medium in space 134, 39
INDEX TO VOLUMES I-X. 167
Page.
Resolution on acceptance of membership,
ill 149
auditing committee v 84
committees on mathematical papers..vi 135
discovery of the satellites of Mars ii 186
resigned and dropped members v 84
the title "Mr." i 104, x 46
providing for presidential address iv 30
Resolutions of the International Geodetic
Commission on unification of longi-
tudes and time vi 107
on the death of L. Agassiz i 94
B. Alvord vii 127
S.P.Chase i 87
B. F. Craig ii 130
J. Henry ii 196
J. H. Lane iii 123
A. R.Marvine ii 83
A. J. Myer.., iv 31
G. A.Otis iv 134
B. Peirce iv 23
J. Rodgers v 105
G. C. Schaeffer i 90
J. J. Woodward vii 75
Review of Tait's article on mechanics vii 29
Reynolds, Prof., cited on refraction of sound,
ii 58, v 40, 44
Rhymes, Counting out x 13
Richardson, J. G„ communication in regard
to the diagnosis of blood-stains. Read
by J. J. Woodward. Reference ii 41
Riddell, Dr. J. L., Discovery in microscopy
by iv 35
Ridges, Monoclinal ii 74
Ridgway, Robert, cited on Baird's " Birds
of North America" x 65
communication on a natural arrangement
of the Faleonidse. Read by T. Gill.
Reference ii 41
Rigidity of the earth ii 76
Riley, C. V., communication on the pupation
of the Nymphalidse. Abstract iii 41
the issuance of silk worms from their
cocoons and some striking departures
from normal habits in insects. Title
only iii 44
recent advances in economic entomol-
ogy. Abstract vii 10
the systematic care of pamphlets. Ab-
stract viii 29
our city shade-trees, their foes and their
future. Reference x 7
Riley, J. C, Death of iii 28
Rings of Saturn ii 94, 102, 188, vi 41
Ripple marks ...ii 61
Ritter, J. W., cited on the chemical rays...v 135
Page.
Ritter, W. F. McK., communication on a
simple method of deriving some equa-
tions used in the theory of the moon
and of the planets. In full iv 57
secular perturbations of Polyhymnia by
Jupiter. Abstract viii 54
Rivers and terrestrial rotation vii 21
of Iowa vi 93
Roan Mountain iv 60
Robinson, J., Flora of Essex Co., Mass., by
iv 95
Robinson, T., communication on the strata
exposed in the east shaft of the water-
works extension. Abstract vii 69
Was the earthquake of September 19th
[1884] felt in the District of Columbia ?
Abstract vii 73
remarks on deflection of rivers vii 24
measuring earth tremors viii 28
Robison, Prof. J., cited on elasticity v 132
Newton's rings v 155
Rochester tornado vii 3
Rockwood, C. G., communication on the
Charleston earthquake. Abstract. ..ix 37
Rodgers, John, Death of. v 102, 105
Rogers, Prof. H. D., cited on the Devonian
in Pennsylvania 11 (34), (38)
Rogers, Prof. W. B., cited on geology at Sul-
phur Springs, W. Va ii (27), (30)
Rogers' rulings on glass ii 130
Ross, A. C, communication on latent im-
pressions on polished glass pjates pro-
duced by heating the plates in close
connection with engraved metal lie-
plates. Abstract ii 39
Rotation and rivers vii 21
in office v 49
Rowland, cited on thermometry ix 30
Riicker, Prof. A. W., cited on the constant P,
x 102
Rule on communications from sections...vi 38
Rules for Publication of Bulletin. See
Bulletin.
Standing. See Standing rules.
Rulings on glass ii 130
Rumford, Count, cited on theories of heat..v 133
Russell, I. C, communication on the exist-
ing glaciers of the High Sierra of Cali-
fornia. Abstract and reference. 2 fig-
ures vii 5
deposits of volcanic dust in the Great
Basin. Abstract vii 18
What is a glacier? Abstract vii 37
the faults of the Great Basin and of the
eastern base of the Sierra Nevada.
Abstract ix 5
168 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Russell, I. C, communication on—Cont'd,
the subaerial decay of rocks and the
origin of the red clay of certain forma-
tions. Title only ix 16
Russell, Thomas, communication on tem-
peratures at which differences be-
tween mercurial and air thermometers
are greatest. In full. I figure lx 25
normal barometers. Title only ix 46
Russian meteorology i 75
Rutherford, cited on computation of tt i 58
Sabine, Gen., cited on Plover Bay iv 125
St. George Island, Seals on i 91
St. Louis directrix, Altitude of ii 24
St. Paul Island, Seal3 on i 91
Salinometer ii 185
Sand sculpture i 57
Sanderson, Dr. Burden, cited on bacteria..ii 109
Sands, B. F., Death of„ vi 41
Sandwich Islands, Geology of. vi 13
Satellites, Computations concerning vii 93
of Mars ii 181, 186, 188, 190, vi 45
Saturn iii 26, 40
Uranus- i (30)
Saturday-NightClub x 45
Saturn and its rings, Revolution of ii 188
Bright spot on ii 102
Rings of ii 94, 102, 188, vi 41
Satellites of. iii 26, 40
Shadow of. ii 102
Saville, J. H., communication on the new
Japanese coinage. Title only i 51
Sawyer, C. J., communication on the Signal
Service bibliography of meteorology
and terrestrial magnetism. Head by
C. Abbe. In full x 23
Schaeffer, G. C, Resolutions on the death
of. i 90
Schellbach, Prof. K. H., cited on Malfatti's
problem ii 118
Schools of Japan ii 69
Schott, C. A., communication on a new eye-
piece for observing personal equations.
Title only ii 200
the secular change in the magnetic de-
clination in the United States and at
some foreign stations. Abstract iii 45
remarks on calendars ii 38
rigidity of the earth ii 77
Sciences, Philosophic order of. v 105
Present state of ii 16
Progress of. ii 56
Scientific administrators ;.ix xliii
experimentation ii 163, vii li
Page.
Scientific men and their duties ix xxxv
Distribution of. ^. x 7
method ii 163, vi xxxiii, vii li
and social progress- iv 40
societies i vi, viil xxxiii
of Washington, and Professor Baird x 45
of Washington, Proposed federation of,
v 102
of Washington, Statistics of x 29
work by state aid viii xli
Scrope, G. P., cited on columnar structure,
Viii 24
Sea level influenced by winds and baro-
metric pressure i 53
Seals, Fur-bearing i 91
Secchi, Angelo, cited on elasticity v 130
Saturn's rings vi 43
Seconds-pendulum formula vii 101
Secretaries' report...vi 111, vii xxiii, viii xxvii,
ix xxix, x xxxii
Secular change in magnetic declination. ..iii 45
perturbations of Polyhymnia by Jupiter,
viii 54
Seebach's method of determining earth-
quake foci x 17
Seitz, E. B., cited on Malfatti's problem ii 118
Seismology, List of papers on :
on the earthquake phenomena recently
experienced in North Carolina. T. L.
Clingraan. Abstract and reference i 104
earth tremors as shown by astronomical
observations. H.M.Paul. AbstracL.itl 125
earth vibrations at Niagara Falls. J. M.
Toner. Abstract iv 186
seismographic record obtained in Japan.
E.Smith. Title only vi 87
Was the earthquake of September 19th
[1884] felt in the District of Columbia?
T.Robinson. Abstract vii 73
the Flood Rock explosion. F. W. Clarke,
C. F. Marvin, and H. M. Paul. Ab-
stract viii 28
the Charleston earthquake. Symposium.
Abstract. Map ix 37, 38
a recent visit to the scene of the Charles-
ton earthquake and resulting conclu-
sions. C. E. Dutton. Title only x 16
on the depth of earthquake foci. C. E.
Dutton. Title only x 17
the speed of propagation of the Charleston
earthquake. C. E. Dutton and S. New-
comb. Reference x 28
Series for determining the ratio of circum-
ference to diameter i 57
Serpent venom vi 38
Sewage in soils iv 38
INDEX TO VOLUMES I-X. 169
Page.
Sexes, Disparity of, in mollusks ill 75
Shade trees and their foes x 7
Shanks, cited on computation of t 1 58
Shasta, Mount x 10
Shastina, Volcanic sand from vii 33
Shell heaps of the Aleutian islands it 65
Shelters for thermometers vi 46
Sherman, W. T., communication on a visit
to Egypt. No abstract i 63
travels in Turkey and the Caucasus.
No abstract i 65
Sherman, Wyoming, as a site for an astron-
omical observatory i 70
Shields, C.W., communication on the present
state of the sciences. Abstract and
references ii 16
the philosophical order of the sciences.
Reference v 105
Shoes, high-heeled v 117
Shoulder girdle of fishes i 64
Shrinkage cracking in basalt viii 20
Siberia-Alaska boundary iv 123
Sibscota, G., cited on dumbness aud deaf-
ness vi 49
Side-coefficients, Removal of. viii 41
Siemens, C. W., cited on conservation of
solar energy v 172
Sierra Nevada, Geology of. ix 4, 5
glaciers vii 5
Sign language vi 63, 84
Signal Service bibliography of meteorology,
x 20, 23
Silver coin, Quantity of. ix 14
Silver-gold ratio iv 141
Silver question, The, iii 78, 107
Similar inventions in areas widely apart,
ix 12
Sinking fund, The United States iii 113
Siren 1185,(51)
Skinner, A. N., communication on the pre-
cession of stars in right ascension.
Title only ill 21
Sling psychrometer viii 25
thermometer vi 46, vii 80
Smart, Dr. Chas., Researches on food adult-
eration by iv 39
Smith, Edwin, communication on a seismo-
graphic record obtained in Japan.
Title only vi 87
Smithsonian bonds of State of Arkansas...vi 105
edition of the Bulletin x 113
Smithsonian Institution under administra-
tion of S.F. Baird x 49
under administration of Joseph Henry,
ii 285
Bnake venom vi 38
\
Page.
Social evolution vi xlviii
progress and scientific method iv 40
Social Science and Statistics, List of
papers on :
on the adjustment of census returns. E.
B.Elliott. Title only 1 63
on the coincidence of the geographical
distribution of rainfall and of illiter-
acy, as shown by the statistical maps
of the ninth census reports C. S.
Peirce. Abstract* 1 '68
on life and annuity tables, based on the
census of 1870. E. B. Elliott. Title
only 1 74
on the use of metric weights and balances
for postal purposes in the United
States. E. B. Elliott. Abstract 11 15
further remarks on metric weights and
balances for the postal service. E. B.
Elliott. Abstract 11 19
on proposed reforms in spelling the Eng-
lish language. A. R. Spofford. Title
only..., 11 42
the mortality among army officers. B.
Alvord. Reference Ii 49
[proposed governmental insurance.] B.
Alvord. No abstract ii 49
[a statistical diagram.] E. B. Elliott. No
abstract ii 134
animal population of the globe. L. F.
Ward. Abstract.... iv 27
the relation of scientific method to social
progress. S. Newcomb. Presidentivl
address. In full iv 40
the international convention of the teach-
ers of the deaf and dumb, at Milan.
E. M. Gallaudet. Abstract iv 55
mortality statistics of the Tenth Census.
J. S. Billings. Abstract Iv 163, 164
on survivorships, with tables and formulas
of construction. E. B. Elliott. Title
only v 122
fallacies concerning the deaf, and the in-
fluence of such fallacies in preventing
the amelioration of their condition.
A. G. Bell. In full vl 48
the vital statistics of the Tenth U. S. Cen-
sus, J.S.Billings. Reference viii 4
a fonetio sslfabet. H. Farquhar. Abstract.
ix 17
the geographical distribution of scientific
men and institutions in the United
States. G. B. Goode. Reference x 7
the economic phase of the English spar-
row question. C. H. Merriam. Refer-
ence x 16
170 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Social Science and Statistics, List of
papers on—Cont'd,
statistics of the Philosophical Society from
its foundation. G. K. Gilbert. Ab-
stract ...x 29
the progress of science as exemplified in
the art of weighing and measuring.
W. Harkness. In full x xxxvii, 39
association ratios. M. H. Doolittle. Ab-
stract x 83
association ratios. M. H. Doolittle. Ab-
stract x 94
Societies, American scientific vlii xxxiii
Scientific 1 vi
and Professor Baird x 45
Statistics of x 29
Soils and sewage lv 38
Solar corona 1 31, 111 110, 121
eclipse, Jan. 11, 1880 ill 121
July 29, 1878 11 202, 111 116
heat variations and climate vi 10
parallax derived from transit of Venus,
1874 lv 168
from the velocity of light Hi 74
methods v 39
Solid, liquid, and gas defined v 136
Somoff 's theorem ix 54
Sondhauss, cited on refraction of sound. ...11 57
Sorghum sugar ill 140
Soul v 103
Sound, Abnormal phenomena of. 11 37
and fog signals 11 57, 60, (45), lv 135, v 23, 39
heat iv 143, 183
light iv 143
Determination of direction of...ill 69, viii 12
from two syrens ii 85
Joseph Henry's researches on ii 344
Refraction of ii 57, 167, (48), v 35, 39, 44
velocity and air temperature vi 47
waves and earthquake waves ix 42, 43
(See also Acoustics.)
Sounds accompanying and following meteor
of December 24, 1873 ii 157
South Mountain fault vi 30
Space vli 56
Resisting medium in 1 34, 39
Temperature of. ii 73
Space-directed lines x 105, 106
Sparrows, English x 16
Specific gravity method vi 26
Spectrophone _ iv 143, 101
Spectrum of Pneke's comet i 34
corona Hi 117
Speech, Visible iv 55, vi 60
Speed of propagation of the Charleston
earthquake... x 17, 28
Page.
Spencer, Herbert, cited on ceremonies ix 20
growth of crystals.* v 67
motion vii 57
nerve currents v 62
the ultimate v 164, 166
Spheres, Problem concerning v 107
Spheroid, Distances on any viii 52
Spofford, A. R., communication on proposed
reforms in spelling the English lan-
guage. Title only 11 42
Spontaneous generation ii 109, ^» 64, 103
Standard for micrometry Hi 22
Standard time ii 137, 202, vi 106
adopted by the society vii 18
A system of v 112
Standards of declination ix 53
length ii 136
value ill 78, 107
Standing rules of the General Committee, i
xvii, il vi, ill vi, 149, lv 11, v 11, vi xii,
vii xii, vili xii, ix xii, x xii
Standing rules of the Mathematical Section,
vl 115, vii 85, viii 35, ix 51, x 81
Standing rules of the Society..i xvi, li iv, Hi
iv, 149, iv 7, 30, 38, v 7, vi ix, vii ix,
viii ix, ix ix, x ix
Star catalogue prepared at U. S. Naval Ob-
servatory i 74
New ix 14
Stars, Arrangement of HI 76
Images of. ix 15
Station errors H 82
Statistics. (See Social Science.)
Steam as a disinfectant Hi 51
Steiner, Prof. J., cited on Malfatti's problem,
ii 115
on Feuerbach's circle vili 46
Stellar photometry i 03
Steno, cited on crystallography i 77
Sternberg, Dr. G. M., Researches on Bacillus
malarise iv 39
Stokes, Professor, cited on refraction of
sound H 58, (47), v 40
Stone, Ormond, communication on the de-
termination of the errors of a pro-
visory catalogue of fundamental stars.
Title only i 02
the correction of a comet's orbit. Refer-
ence H 22
a problem in probabilities. Abstract...x 89
the orbit of Hyperion. Abstract and ref-
erence x 104
Stoneham, Me., Topaz from vili 5
Stoney, cited on the radiometer H 81
Storage of electric energy v 46
Storm centres, Movement of. i 99
INDEX TO VOLUMES I-X. 171
Page.
Storm centres, Retardation of. v 108
Storms and auroras i 45
Law of i 106
Thunder ii 189
Storr, Dr. G. C. C, cited on the classification
of mammals li (3)
Strata exposed in shaft of water-works ex-
tension vii 69
Struve, Otto, cited on determination of
planet's mass from observations on
satellites vi 132
satellites of Uranus i (35)
Saturn's rings vi 42
Stryker artesian well i 103
Substance vl 14, vii 41
Sugar beet culture and climate iii 142
from sorghum iii 140
Sumner, W. G., cited on bi-metallism iii S4
Sumner's method in navigation ii 105
Sun, Heat of i 31
viewed by light of any desired wave
length x 13
Sun-glows vii 17, 35
Sun's apparent diameter i (3)
corona i 31, iii 116, 121
Surplus, Proposal to distribute the vi 103
Sweeping mechanism iii 142
Swift, Dean, cited on the scientific crank,
viii xl
Swift's comet, Orbit of iv 59
Swordfish and its allies iv 162
Sylvester, J. J., communication on the
theory of invariants. Title only ii 95
Trisection linkage of. x 99
Symbols, Archeologic ii 72
Symons, Prof. G. J., Bibliographic work of,
x 21, 23
Symposium on the cause of the glacial cli-
mate ii 43, 45
the silver question iii 78, 107
What is a glacier ? vii 37
the Charleston earthquake ix 37, 38
What is topography ? x 14
a problem in probabilities x 87, 89
Systems of mineralogy i 77
Taconic system of Emmons x 5
Tainter, S., Photophonic experiments by.
iv 145, 150
Tait, Prof. P. G., cited on forcc.v 128, 152, vii 29
Talbot, H. F., cited on the history of Mal-
fatti's problem ii 114
Talcott's method x 91
Target-shooting and the theory of errors..vi 138
Taxonomic terms of Storr ii (7)
Taylor, F. W., Analysis by vii 32
Page,
Taylor, W. B., communication on the nature
and origin of force. Abstract and ref-
erence i 27
the aurora. Abstract 1 43
our present knowledge of the planet
Jupiter. Title only i 62
waves, molecules, and atoms. Abstract,
i 66
a calendar proposed by a Persian astron-
omer in 1079. Abstract ii 38
the causes of the glacial climate. Ab-
stract ii 43, 46
acoustic refraction. Abstract li 57
the temperature of space. Abstract ii 73
Joseph Henry. A sketch of his scientific
work. In full ii 203, 230
a panoramic photograph. Abstract v 21
the total lunar eclipse of June 11, 1881.
Abstract v 90
a remarkable halo. Abstract v 112
physics and occult qualities. Presiden-
tial address. In full v 125, 126
the rings of Saturn. Abstract vi 41
a case of discontinuity in elliptic orbits.
Abstract vii 122
geological and physical theories. .46-
stract viii 6
the crumpling of the earth's crust. Ab-
stract and reference viii 18
slight modification of the Newtonian
formula of gravitation. Abstract...viii 39
Professor Baird as an administrator. In
full x 49
remarks on calendar reform ii 30
interior of the earth ii 76, 77
radiometer ii 80
planetary motions ii 1S8, 189
amplitude of light waves iii 120, 125
death of J. H. Lane iii 124
taboo iii 138
Henry's acoustic researches iv 140
radiophony iv 162
anomalies of sound v 37
binary arithmetic vi 4
sling thermometer vi 47
satellites' orbits vi 133
infinitesimals vi 135
sun glows vii 35
topophone viii 13
resolutions on the death of G.C. Schaeffer,
i 90
Telephone, Exhibition of ii 67, 103
Comments on ii 111
Telephonic study of binaural audition iii 09
Telephote ii 102
Telescope for Naval Observatory i 02, 83
172 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Temperature and pressure, Diurnal changes
of it 67, 69
Conditions determining v 91
distribution over the surface of the globe,
i 96
Measurement of atmospheric vl 46
of sea water as related to winds on the
coast of New Hampshire ii 17
brain v 75
space ii 73
the air vi 24
the human body i 31
(See also Meteorology and Thermometry.)
Temperatures at which differences between
mercurial and air thermometers are
greatest ix 25
of the Pacific Ocean ii 192
Tenth census mortality statistics... iv 164
Teredo navalis v 98
Terrestrial magnetism, Bibliography of..x 23, 27
Constant P in observations of. x 102
Terquem, cited on Feuerbach's circle. ..viii 46
Texas Cross Timbers x 6
Thanhoffer, cited on the pulse v 77
Theatres, Burning of ii 95
Theology v 103
of the American Indians ii 176
Theory of errors vi 152
practically tested by target-shooting...vi 138
Thermal belts of North Carolina vi 11
Thermometry, List of papers on
:
on thermometers. B. F. Craig. Title
only i 42
a method of verifying with exactness the
indications of a thermometer. B. F.
Craig. Title only i 43
a comparison of the thermometers used to
determine the correction for atmos-
pheric refraction at the U. S. Naval
Observatory. J. R. Eastman. Ab-
stract i 68
on the air thermometer of Prof. Jolly. J.
E. Hilgard. Title only i 89
determining the temperature of the air.
C. Abbe. Abstract vl 24
hygrometric observations. H. A. Hazen.
Abstract vi 36
thermometer exposure. H. A. Hazen. Ab-
stract vi 46
thermometer exposure. H. A. Hazen. Ab-
stract vii SO
the measurement of temperature at dis-
tant points. T. C. Mendenhall. Title
only _..viii 18
the condensing hygrometer and sling psy-
chrometer. H. A. Hazen. Abstract..-viil 25
Pagt-.
Thermometry, List of papers on—Cont'd,
temperatures at which differences between
mercurial and air thermometers are
greatest. T. Russell. In full. 1 fig-
ure ix 25
the gilding of thermometer bulbs. J. H.
Kidder. Title only ix 33
effects of solar radiation upon thermome-
ter bulbs having different metallic
coverings. H. A. Hazen. Abstract. ..Ix 33
Thompson, Gilbert, communication on the
physical-geographical divisions of the
southeastern portion of the United
States and their corresponding topo-
graphical types. Abstract ix 22
What is topography? Abstract x 15
remarks on glaciers vii 8
Indian paintings viii 16
Thompson, Prof. S. P., cited on eleetricity..v 168
Thomson, Sir William, cited on rigidity of
the earth ii 78
Sumner's method ii 107
Volt-meter of. viii 26
Thomson, William, communication on a
new method for detecting and measur-
ing the optical defects of the eye.
Reference i 22
Three methods of evolution vi xxvii
Throwing-sticks ix 13
Thunderstorms in 1884 viii 10
Electrical phenomena of ii 189
Tidal retardation and consequent crumpling,
viii 19
Tides at Boston influenced by winds and
barometric pressure i 53
Tillo, Col., cited on levellings in Asia ii 34
Time, A system of standard v 112
determination with a meridian transit..viii 55
globe iii 107
Standard U137, 202, vl 106
Titan and Hyperion iii 26, 40, x 104
Titicaca, Climate at Lake il 35
Todd, D. P., communication on solar paral-
lax from the velocity of light. Refer-
ence iii 74
a mechanical attachment for equatorial
mountings to facilitate sweeping in
right ascension. Abstract and refer-
ence iii 142
the solar parallax as derived from the
American photographs of the transit
of Venus 1874, December 8-9. Abstract
and reference iv 168
Todd, J. E., communication on quaternary
deposits of western Iowa and eastern
Nebraska. Abstract iv 120
INDEX TO VOLUMES I-X. 173
Page.
Todd, J. E., remarks on charcoal in the
drift iv 122
Toner, J. M
,
communication on a method
of describing aud locating with ease
the approximate positions of geo-
graphical regions. Title only i 97
the burning of theatres and public halls.
Reference li 95
a malformed dog. No abstract ii 185
earth vibrations at Niagara Falls. Ab-
stract iv 186
coins and medals. Abstract v 22
remarks on care of pamphlets viii 29
Tonto Sandstone, Age of i 109
Topaz from Stoneham, Me vlii 5
Topographic map defined x 11
types in the southeastern States ix 22
Topography and geology of the Cross Tim-
bers of Texas x 6
and structure x 7
defined x 14
Topophone viii 12
Tornado at Rochester, Minn vii 3
Torreya in Southern States and Japan ii 42
Townley, K., cited on transmission of sound,
v 42
Transit flexures viii 27
Meridian viii 55
of Mercury ii 199
Mercury, May, 1878 lit 43
Venus, 1874 i 63, ii 31, 33, iv 168
Venus, 1882 vi 21
Trap of Orange Mt., N. J viii 24
Treasurer's report v 176, 180, vi xii, vii xxiv,
viii xxviii, ix xxx, x xxxiv
Tremors detected by astronomical observa-
tions iii 120
Triangle, Formulae for the area of viii 37
Problem concerning iii 55
Trisection of angles x 96
Trouvelot, L., Drawings of nebulae by ii 51
Tucker, R., Solution of a geometrical prob-
lem by iii 65
Tupman, , letter on solar eclipse. Com-
municated by W. JIarkness. No ab-
stract 4 56
Twining, W. J., Death of. v 102
Tyndall, John, cited on photophonie experi-
ments iv 152
sound anomalies v 33, 41
heat absorption by the air v 94, 96
Introduction of i 65
letter on fog signals. Communicated by
J.Henry. No abstract i 91
Uinta Mountains, Permian rocks of ill 106
Pago.
Unalashka volcanic sand vii 33
Unification of longitudes and time vi 106
Uniformitaiianism viii 6
United States, Centre of population of. i 35
Geographic centre of. i 22
Urara v 62
Uranometria Argentina iii 122
Uranus, Satellites of i (30)
Utah, Glacial epoch in i 84
Permian formation of. iii 68, 105
Ute language ii 28
Vacant offices, Filling of. ii 84, iii 53, v 112,
vi 41, vii 36
Valentin, cited on mineralogy i 77
Valleys, Classification of. i 49
Values at different times ii 87
Relative, of gold, greenbacks, and silver,
ii 52
Van Sant,
, communication on a method
of lighting gas-jets by electricity. No
abstract i 56
Variations of latitude viii 10
Vauquelin, cited on mineralogy i 78
Velocity of earth tremors viii 28
earthquake waves ix 41. x 17, 28
Venom of serpents vi 38
Ventilation of the House of Representatives,
v 99
Venus, Transit of, 1874 i 63, ii 31, 33, iv 168
1882 vi 21
Verification of weather predictions vii 122,
viii 8, x 83, 94
Vertebrae, Cephalic i 26
Virginia, Fossil plants from ii (26)
Visible speech iv 55, vi 53
Vision vii 72
Apparatus for testing iii 53
Vital principle 127,v50, 102
statistics of the tenth U. S. census viii 4
Vocabulary of an individual ii 28, (16)
Volt-meter viii 26
Volcanic dust in the Great Basin vii 18
necks vii 78
problem, The vi 87
sands vii 33
Volcano, Latest, in northern California ix 46
Volcanoes of New Mexico vii 76
Von Cronstedt, cited on mineralogy i 78
Von Jherling, Dr. H., cited on the Chito-
nidce ii 193
Vortex motion iii 143 .
Vulcan, Search for ii 85
Wagner, cited on the sun's diameter i (4)
Waite, ChiefJustice M. R., letter announcing
the death of Joseph Henry ii 196
174 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Walcott, C. D., communication on the Cam-
brian system in the United States aud
Canada. Abstract. I figure vl 98
the geologic age of the lowest formation
of Emmons' Taconic system. Refer-
ence x 6
Discovery of Permian fossils by ill 68, 105
Wallerius, cited on mineralogy i 78
Walling, H. F., communication on topo-
graphical indications of a fault near
Harper's Ferry. Abstract vl 30
Ward, Lester F., communication on the nat-
ural system of plants. Title only.M 186, 187
the origin of the chemical elements.
Title only Ill 33
animal population of the globe. Abstract,
Iv 27
field and closet notes on the flora of
Washington and vicinity. Abstract.Xv 64
the organic corn pounds in their relations
to life. Title only v 91
some physical and economic features
of the Upper Missouri system. Refer-
ence vil 20
the flora of the Laramie group. Refer-
ence vlil 17
the frequency of coincidences. Abstract,
x 8
the geographical distribution of fossil
plants. Reference x 28
remarks on vital force v 105
Dismal Swamp vl 30
deflection of rivers vli 23
Indian observation of nature vil 74
care of pamphlets vlil 29
Warren, G. K., cited on abnormal phenom-
ena of sound 11 (48)
communication on the geological history
of Lake Winnipeg. Abstract 11 27
Warner, A. J., communication on the silver
question. Abstract Ill 112
Wasatch Mountains fault 11 103
Growth of 11 195
Washington a scientific centre... .1 xi, vlil xlvi,
x 47
Flora of iv 64
Watershed of the Adirondack region ii 67, 82
Waterspouts in North Carolina ii 104
Watson, J. C, communication on the discov-
ery of new planets having especial ref-
erence to the asteroids. Title only... .1 53
Watson, Sereno, cited on the Great Basin
flora iv 99
the classification of plants iv 108, 110
Wave lengths of light '. v 142
Waves, Earthquake x 17
Page.
Waves, molecules and at»ms i 66
Weather forecasts v 122, vlil 8
Webb, Capt., cited on phenomena of sound,
ii (40), (50)
Weiss, Prof., cited on mineralogy i 78, 79
Welling, J. C, communication on the life
and character of Joseph Heniy. In
full 11 203
anomalies of sound signals. In full v 39
the atomic philosophy, physical and
metaphysical. Presidential address.
In full vii xxix, 81
eulogy on Gen. A. A. Humphreys. Ab-
stract vii 4
remarks on vocabularies ii 2S
drifting buoys vil 15
Indian observation of nature vil 75
Wells, D. A., cited on medium of exchange,
iil 101
Wenham. cited on microscope apertures. .ill 19
Werner, cited on mineralogy 1 78, 79
Wernich, cited on contamination of air by
sewage iv 38
What is a glacier? vil 37
Wheatstone's microphone, Modification of,
iv 183
Whewell, Dr. W., cited on attraction v 161
Greek philosophy vii xxxviii
White, C. A., cited on the loess of Iowa iv 121
communication on the evolutional history
of the North American Unionidce.
Title only ii 181
asymmetry in the form of the human
cranium. Title only ii 190
the fresh-water shell-heaps of the in-
terior rivers of North America. Title
only ill 32
the subject of the Permian formation in
North America. Abstract ill 104
artesian wells on the Great Plains. Ref-
erence v 101
remarks on the relations of plants to
geology iv 119
loess of the Mississippi valley iv 122
teredo .v 99
theory of permanence of oceans vi 93
drainage system of Iowa vi 97
White, Prof. I. C, Discovery of Permian fos-
sils by iil 105
Whitfield, R. P., Observations on Limnsea
by ill 75
Whitney, Prof. J. D., cited on geology of
Great Basin i 56
Whitney, Prof. W. D., cited on individual
vocabularies 11 (19)
Wiebe, H. F., cited on thermometry ix 26
INDEX TO VOLUMES I-X. 175
Page.
Wild, Prof., cited on thermometry ix 33
Williams, G. H., communication on the
methods of modern petrography. Ab-
stract vli 36
Willis, Bailey, communication on the topog-
raphy and structure in the Bays
Mountains, Tennessee. Reference x 7
development of a perspective map from
a contour map. Title only x 9
Mount Rainier and its glaciers. Ab-
stract x 10
remarks on geology of Cascade Mount-
ains ix 8
Winchell, Alexander, communication on the
progressive dispersion of mankind
over the surface of the earth. Title
only ill 32
Wind and hygrometry vl 30
railway traction iii 31
retardation of storm centres v 108
as related to barometric gradient i 106
velocity and pressure x 10
Winds and barometric pressure in relation
to tides 1 53
as related to ocean temperatures on the
coast of New Hampshire il 17
observed in balloon ascensions 1 35
on mountain slopes iii 38
Wind-wrought errors in barometric observa-
tion v 91
Wind-vane, Theory of. x 9
Winlock, W. C, communication on comets
II and III, 1884. Title only vtii 16
physical observations of Wolf's comet
(1884, III). Abstract vlii 37
Winter of 1882-83, Prognostication for v 122
Woeikoff, Alexander, communication on the
meteorology of Russia. Reference 1 75
the results of a recent determination of
the elevation of the Caspian and Aral
seas. Abstract 11 34
meteorological observations in Peru, and
some meteorological conditions of that
country. Title only 11 35
Wood, Dr. H. C, Researches on inoculation
of diphtheria by lv 38
Woodbury process of photo-printing 1 42, 57
Wooden pavements, Failure of il 26
Woodward, J. J., communication on the al-
leged hermaphrodite described by
Drs. Accly, Blackman, aud Jackson.
Abstract and reference 1 24
he desirability of reproducing photo-
graphs of scientific objects, and espe-
cially of magnified microscopical
preparations, in a permanent form by
Page.
Woodward, J. J., communication on—Cont'd,
some photo-mechanical method. Ab-
stract 1 41
the use of monochromatic sunlight as
an aid to high-power definition. Ab-
stract and reference 1 47
the Woodbury photo-relief process. Ab-
stract 1 57
spectra and spectroscopes. No abstract,
1 89
micrometrie writing on glass. Title
only 1 93
the similarity between the red blood-
corpuscles of man and those of certain
other mammals, especially the dog;
considered in connection with the di-
agnosis of blood stains in criminal
cases. Abstract and reference 11 20
the markings on Navicula rhomboides.
Title only 11 69
the rulings on glass by Mr. Rogers, of
Cambridge. Abstract 11 130
the modern microscope, Nobert's lines,
and the attempts of others to con-
struct them. Title only 11 25
diffraction phenomena in the field of
the microscope. Abstract and refer-
ence ii 60
the microscopical structure of wool.
Title only ii 62
the Papyrus Ebers. Abstract 11 64
the use of photography in connection
with the micrometer measurement of
blood corpuscles. Title only ii 79
a simple device for the illumination of
balsam-mouuted objects for examina-
tion with certain immersion objectives
whose "balsam angle" is 90° or up-
wards. In full. 1 figure 11126
theapertometerof Prof. E. Abbe, of Jena,
Germany. Abstract ill 18
a standard for micrometry. Abstract,
ill 22
the oil-immersion objectives of Zeiss,
and on convenient methods of obtain-
ing oblique illumination for these and
similar objectives. Abstract ill 25
a new apertometer for microscopic ob-
jectives. Title only iii 37
some apparatus recently brought into
use by the Medical Department of the
Army for the examination of the eye.
Abstract* ill 53
Riddell's binocular microscope—an his-
torical notice. Abstract and refer-
ence „ iv 35
176 PHILOSOPHICAL SOCIETY OF WASHINGTON.
Page.
Woodward, J. J., communication on—Cont'd.
a biographical sketch of the late Dr.
Otis. In full iv 171
modern philosophical conceptions of
life. Presidential address. In full v 49
Death of. vil 72
remarks on malformed dog i 185
diagnosis of blood-stains ii 41
a new meteorological instrument il 64
poisoned arrows ii 180, 182
Resolutions on the death of vii 75
Woodward, R. S., cited on infinite attraction,
viii 59
communication on the special treatment
of certain forms of observation-equa-
tions. Abstract vi 150
a concrete problem in hydrostatics pro-
posed by Mr. G. K. Gilbert. Titleonly,
vii 101
some practical features of a field time
determination with a meridian transU.
Abstract viii 55
the changes of terrestrial level surfaces'
due to variations in distribution of
superficial matter. Reference ix 15
the position and shape of the geoid as
dependent on local masses. Reference,
ix 53, 54
the free cooling of a homogeneous sphere
initially heated to a uniform tempera-
ture. Reference x 90
the conditioned cooling of a homogene-
ous sphere. Reference x 103
remarks on deflection of plumb-line. ...vii 92
Grassmann's geometry viii 53
infinite attraction viii 63
problem in probabilities x 89
Wolf's comet (1884 III) viii 37
Wooiara _ v 62
Words in an individual vocabulary ii 28, (1C)
Written language and speech iii 139
Wyandottes, Social and political organiza-
tion of iii 137
Yards. Standard ii 136
Yarnall, Mordecai, communication on the
general star catalogue prepared from
the observations at the Naval Observ-
atory since 1845. Reference i 74
Death of iii 28
Yeast ferment as an insecticide vii 11
Yellowstone expedition of 1870 t 21
valley vii 20
Young, C. A., cited on observations at Sher-
man, Wyo i 71, 73
zodiacal light i (21)
Page.
Young, C. A., communication on the expe-
dition to Pekin for observing the late
transit of Venus. Abstract ii 33
Young, Dr. T., cited on superficial repul-
sion v 155
theories of heat and light v 134
Young-Helmholtz theory of color iv 54
Ziwet, Alexander, communication onGras-s-
mann's system of geometry. Reference.
viii 53
remarks on problem in probabilites x 89
Zodiacal light i (19)
Zoological work of S. F. Baird x 62
Zoology, List of papers on (See also Bi-
ology) .
on the characteristics and zoological rela-
tions of man. T. Gill. Abstract i 24
on the number of the cephalic vertebrae.
T. Hilgard. Reference i 26
on additions to the fish fauna of Massachu-
setts, due to the researches of Prof. S.
F. Baird, U. 8. Fish Commissioner. T.
Gill. Reference i 29
on the tapir of the Andes and its allied
forms. T.Gill. Titleonly i 39
on a tunny new to the American coast. T.
Gill. Titleonly i 47
on the decrease of fish on the southern
coast of New England. S. P. Baird.
Reference i 52
on the homologies of the shoulder girdle
of fishes. T.Gill. Reference i 64
on the Scombrocottus salmoneus of Peters.
T. Gill. Title only i <;8
on the homologies of the arm in fishes,
and the development of the humerus
in ganoids. T. Gill. Title only 1 73
on the habits of the fur-bearing seals of the
islands of St. Paul and St. George,
Behring Sea. H. W. Elliott. Refer-
ence I 91
on the primates and their relations to
man. T.Gill. Titleonly i 96
on the structure and homologies of the
limbs, especially in Aves. E. Coues.
Title only i 96
on the structure and shape of Palseothe-
rium. T.Gill. Abstract i 99
on the "Prodromus methodi mammal-
ium " of Storr. T. Gill. Infull...U 15, (3)
on the similarity between the red blood-
corpuscles of man and those of certain
other mammals, especially the dog
;
considered in connection with the
diagnosis of blood-stains in criminal
INDEX TO VOLUMES I-X. 177
Page.
Zoology, List of papers— Cont'd.
cases. J. J. Woodward. Abstract and
rtfcrence it 20
on the geographical distribution of mam-
mals. T.N.Gill. Abstract ii 26
explanatory note on the diagnosis of
blood stains. J. G. Richardson. Read
by J. J. Woodward. Reference 11 41
outlines of a natural arrangement of the
Falcon idee. R. Ridgway. Communi-
cated by T. Gill. Reference 11 41
the microscopical structure of wool. J. J.
Woodward and John Leconte. Title
only 11 02
the markings on Navicula rhomboides.
J.J.Woodward. Title only 11 69
shower of the Rocky-Mountain grasshop-
pers. C. G. Boerner. Communicated
by J. Henry. Abstract 11 87
the relations and sequences of the family
Centrarchoides. T. N. Gill. Title
only 11 113
the morphology of the antlers of the Cer-
vidse. T. Gill. Abstract and reference,
11 135
some phases of the evolutional history of
the North American Unionidee. C. A.
White. Title only 11 181
a new species of Chimsera found in Amer-
ican waters. T.Gill. Abstract 11182
[exhibition of malformed dog.] J. M.
Toner. No abstract 11 185
the results of recent investigations into
the natural history of the Chitonidse.
W. H. Dall. Abstract 11 193
a fish found on the Florida coast. W. S.
Abbey. Letter, read by C. Abbe. No
abstract \ 11 202
the family of Ceratiids. T. N. Gill. Title
only 11 202
notes on the museums and zoological
gardens of northern Europe. W. H.
Dall. Title only ill 19. 21
the artificial propagation of the cod. S. F.
Baird. Abstract ill 29
the embryology of Lin^ula and the sys-
tematic relations of the Braehiopods.
W.K.Brooks. Title only ill 33
the muscles of the oyster. W. H. Dall.
Abstract ill 30
Page.
Zoology, List of papers on—Cont'd.
pupation of the Nymphalidse. C. V. Riley.
Abstract Ill 41
the issuance of silkworm moths from their
cocoons, and some striking departures
from normal habits in insects. C. V.
Riley. Title only Ill 4t
some recent observations on mollusks.
W. H. Dall. Abstract ill 75
some remarkable instances of ingestion
among fishes. T. N. Gill. Abstract.Hi UO
animal population of the globe. L. F.
Ward. Abstract lv 27
the swordfish and its allies. G. B. Goode. •
Reference iv 1C2
on some peculiar features of mollusks
found at great depths. W. H. Dall.
Abstract v 90
on some peculiar ravages of the Teredo
navalis. A. B. Johnson. Title only..-v 98
on the classification of the insectivorous
mammals. T.Gill. In full v 118
the prevention of malarial diseases, illus-
trating, inter alia, the conservative
function of ague. A. F. A. King. Ab-
stract vl 5
recent experiments on serpent venom.
R. Fletcher. Reference vi 33
analogues in zoo-geography. T. N. Gill.
Title only vl 41
ichthyological results of the voyage of the
Albatross. T.N.Gill. Title only vi 48
recent advances in our knowledge of the
limpets. W. H. Dall. Abstract vil 4
recent advances in economic entomology.
C.V. Riley. Abstract vll 10
certain appendages of the mollusca. W.
H. Dall. Reference vll 32
two remarkable forms of mollusks. W.
H. Dall. Abstract and reference viii 5
the distribution of fishes in the oceanic
abysses and middle strata. G. B.
Goode and T. H. Bean. Title only...ix 22
our city shade-trees, their foes and their
future. C.V.Riley. Reference x 7
the economic phase of the English spar-
row question. C. H. Merriam. Refer-
ence x 16
Zornow, Prof. A. R., cited on Malfatti's prob-
lem 11 118






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