SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME 58. NUMBER 1 SMITHSONIAN PHYSICAL TABLES FIFTH REVISED EDITION PREPARED BY F. E. FOWLE AID, SMITHSONIAN ASTROPHYSICAL OBSERVATORY (Publication 1944) CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1910 ADVERTISEMENT. In connection with the system of meteorological observations established by the Smithsonian Institution about 1850, a series of meteorological tables was compiled by Dr. Arnold Guyot, at the request of Secretary Henry, and the first edition was published in 1852. Though primarily designed for meteorological observers reporting to the Smithsonian Institution, the tables were so widely used by physicists that it seemed desirable to recast the work entirely. It was decided to publish three sets of tables, each representative of the latest knowledge in its field, and independent of one another, but forming a homogeneous series. The first of the new series, Meteorological Tables, was published in 1893, the second, Geographical Tables, in 1894, and the third. Physical Tables, in 1896, In 1909 yet another volume was added, so that the series now comprises : Smithsonian Meteorological Tables, Smithsonian Geographical Tables, Smithsonian Physical Tables, and Smithsonian Mathematical Tables. The fourteen years which have elapsed since the publication of the first edition of the Physical Tables, prepared by Professor Thomas Gray, have brought such changes in the material upon which the tables must be based that it became necessary to prepare this almost wholly new set of tables for the present edition. Charles D. Walcott, Secretary, Smithsonian J?isiitution. yune, 19 10. PREFACE. The present Smithsonian Physical Tables are the outcome of a radical revision of the set of tables compiled by Professor Thomas Gray in 1896. Recent data and many new tables have been added for which the references to the sources have been made more complete ; and several mathematical tables have been added, — some of them especially computed for this work. The inclusion of these mathematical tables seems warranted by the demand for them. In order to pre- serve a uniform change of argument and to facilitate comparison, many of the numbers given in some tables have been obtained by interpolation in the data actually given in the papers quoted. Our gratitude is expressed for many suggestions and for help in the improve- ment of the present edition : to the U. S. Bureau of Standards for the revision of the electrical, magnetic, and metrological tables and other suggestions ; to the U. S. Coast and Geodetic Survey for the revision of the magnetic and geodetic tables ; to the U. S. Geological Survey for various data ; to Mr. Van Orstrand for several of the mathematical tables ; to Mr. Wead for the data on the musical scales ; to Mr. Sosman for the new physical-chemistry data ; to Messrs. Abbot, Becker, Lanza, Rosa, and Wood ; to the U. S. Bureau of Forestry and to others. We are also under obligation to the authors and publishers of Landolt-Bornstein- Meyerhoffer's Physikalisch-chemische Tabellen (1905) and B. O. Peirce's Mathe- matical Tables for the use of certain tables. It is hardly possible that any series of tables involving so much transcribing, interpolation, and calculation should be entirely free from errors, and the Smith- sonian Institution will be grateful, not only for notice of whatever errors may be found, but also for suggestions as to other changes which may seem advisable for later editions. F. E. FowLE. ASTROPHYSICAL OBSERVATORY OF THE Smithsonian Institution, June, 1910 TABLE OF CONTENTS Introduction on units of measurement and conversion factors Units of measurement : general discussion .... Dimension formulae for dynamic units ..... " " " heat units " of electric and magnetic units : general discussion " formulas in electrostatic system .... " *' " electromagnetic system Practical units of electricity, legalization of . PAGE XV XV xvii xxiii xxv xxvi xxix xxxiii TABLE I. 2. 4- 5- 6. 7- 8. 9- lO. 1 1. 12. i2a. 13- 14. 15- Formulae for conversion factors : (a) Fundamental units ... 2 (^) Derived units ... 2 I. Geometric and dynamic units 2 II. Heat units .... 3 III. Magnetic and electric units 3 Tables for converting U. S. weights and measures : (i) Customary to metric 5 (2) Metric to customary 6 Equivalents of metric and British imperial weights and measures : (i) Metric to imperial .7 (2) Multiples, metric to imperial 8 (3) Imperial to metric ........ 9 (4) Multiples, imperial to metric ...... 10 Volume of a glass vessel from weight of its volume of water or mercury 1 1 Elementary differential coefficients and integrals . . . .12 Reciprocals, squares, cubes and square roots of natural numbers . 13 Logarithms, 1000-2000 ......... 22 Logarithms ........... 24 Antilogarithms ........... 26 Antilogarithms, .9000-1.0000 ........ 28 Circular (trigonometric) functions, argument (° , ' •) • • • '3° " " " argument (radians) . . '35 Factorials, n!, n= i to 100 38 Values of (hyperbolic sines), for values of x from o to 5 -39 e''— ^~^ Logarithms of (hyperbolic smes), for values of x from o to 5 . 40 Values of — (hyperbolic cosines), for values of x from o to 5 .41 VI CONTENTS. i6. Logarithms of £!+£! (hyperbolic cosines) for values of x from o to 5 42 17- 18. 19. 20. 21. 22. 23- 24. 25. 26. 27. 28. 29. 3°- 31- 32. Values of e' and e~' and their logarithms for x from o to 10 " ** log. e' for values of x from 10 to 30 " " ^' and ^"""^^ and their logarithms .... n —IT " " ^^'and^'* * u » » .... Vt — V" " «' ^^^and^"^"* " « . . . . " " ^ and e-"" and " " for fractional values of x Probability of errors of observations : probability integral . Values of 0.6745 ^^—[ 34- 35- 36. 37. 38. 39- 40. 41. 42. 43- 44. 45- 46. 47- °-^745 V«(;^«-i) " 0.8453 a/ / ^ \ " 0.8453 n\/n— I Inverse of probability integral. Diffusion Logarithms of the gamma function V{n) for values of n between i and 2 Values for the first seven zonal harmonics from ^=0° to ^:=9o° " " log. Mj^TT^Ja^ for facilitating the calculation of the mutual inductance between two coaxial circles 33. Value for /^(i—sin^^sin^^)^M$ for different values of 6; also the corresponding logarithms Moments of inertia, radii of gyration, corresponding weights British standard wire gauge : diameters, sections.... Birmingham wire gauge " " . . . . (For Brown and Sharp gauge, see tables 40 and 41) Cross section and weights of wires (copper, iron, brass), British units .< « u « « « u u .< metric units " " " " " aluminum wire: British and metric units Size, weight and electrical constants of copper wire, Brown and Sharp gauge : common units Same as table 40, but in metric measure Weight in grammes per square metre of sheet metal " " various common units of sheet metal . Strength of materials : {a) metals {b) stones {c) brick . {(i) concretes " " " timber tests (( (( <( <( (( Moduli of rigidity . . . CONTENTS. 47« 48. 49. 50. 51- 52- 53- 54- 55- 56. 57- 58. 59- 60. 61. 62. 63- 64. 65- 66. 67. 68. 69. 70. 71- 72. 73- 74- 75- 76. 77- 78. 79- 80. 81. 82. 83- 84. 85- 86. 87. 88. 89. 90. 91. 92. 93- , Variation of the moduli of rigidity with the temperature Young's modulus ...... Compressibility of the more important solid elements Hardness ....... Relative hardness of the elements Poisson's ratio ...... Elastic moduli of crystals, formulae '* " " " numerical results Compressibility of O, air, N, H at different pressures and temperatures " " ethylene " " " " (( (1 <( (( i( « u " " carbon dioxide at " " " " " gases, values of a . " " air and oxygen between 18° and 22°C Relation between pressure, temperature and volume of sulphur dioxide " " " «' '• " " ammonia Compressibility of liquids Specific gravities corresponding to the Beaume scale Densities of the solid and liquid elements . " " various woods . " " " solids . " " " alloys . " " " liquids . " " " gases . " " " aqueous solutions of salts, bases and acids Density of water between 0° and 36° C . . . . Volume of water at temperatures between 0° and 36° C in terms of its volume at the temperature of maximum density . . . . Density and volume of water at different temperatures from -10 to 250° C " " " mercury at " " " -10 " 36o°C Specific gravity of aqueous ethyl alcohol Density of aqueous methyl alcohol . . . . Variation of the density of alcohol with the temperature Velocity of sound in solids ...... " " " " liquids and gases Musical scales ........ Force of gravity at sea level and different latitudes Results of some of the more recent gravity determinations . Value of gravity at some of the U. S. C. and G. Survey stations Length of seconds pendulum for sea level and different latitudes Determinations of the length of the seconds pendulum Miscellaneous data as to the earth and planets . Terrestrial magnetism : secular change of declination " " dip or inclination .... " " secular change of dip . . * " " horizontal intensity 74 75 76 76 76 76 77 78 79 79 79 80 80 80 81 81 82 83 84 85 87 88 89 90 91 92 94 95 96 97 98 99 100 lOI 102 103 103 104 105 106 107 107 108 no 112 112 113 VIU CONTENTS. scales 94. Terrestrial magnetism : secular change of horizontal intensity 95. " " total intensity .... 96. " " secular change of total intensity 97. " " agonic line 98. Pressure of mercury and water columns .... 99. Reduction of barometer to standard temperature . 100. " '* " " " gravity, inch and metric loi. " " " " latitude 45° : inch scale 102. " " " " " " metric scale . 103. Correction of barometer for capillarity : inch and metric scale 104. Aerodynamics: data for wind pressures .... 105. " " " the soaring of planes 1 06. Coefficients of friction . 107. Viscosity of water at different temperatures 108. Coefficients of viscosity for solutions of alcohol in water 109. Specific viscosity of mineral oils ...... no. " " " various oils ...... 111. " " " " liquids 112. " '* " " " temperature variation 113. " " " solutions: variation with density and temperature 114. " " " " atomic concentrations . 115. " " •' gases and vapors ..... 116. " " " " " " temperature variation 117. Diffusion of an aqueous solution into pure water . 118. '* " vapors 119. " " gases and vapors 119a. " " metals into metals ...... 120. Solubility of inorganic salts in water: temperature variation 121. " " a few organic salts in water : temperature variation 122. " " gases in water....... 123. Absorption of gases by liquids 124. Capillarity and surface tension : water and alcohol in air 125. " " " " miscellaneous liquids in air 126. " " " " aqueous solutions of salts . 127. Capillarity and surface tension : liquids in contact with air, water or mercury.......... 128. Capillarity and surface tension : liquids at solidifying point . 129. " " " " thickness of soap films 130. Vapor pressures 131. " " of ethyl alcohol 132. " '• " methyl " 133. " " and temperatures : (a) carbon disulphide . (l>) chlorobenzine (<:) bromobenzine (ii) aniline . (e) methyl salicylate . (/) bromonaphthaline . (^) mercury CONTENTS. IX 134. Vapor pressures of solutions of salts in water .... 135. Pressure of aqueous vapor at low temperatures .... 136. " " " " 0° to 100° C (Broch).... 137. " " " " 100° to 230° C (Regnault) . 138. Weight in grains of aqueous vapor in a cubic foot of saturated air 139. •* " grammes of " " " " " metre of 140. Hygrometry, vapor pressure in the atmosphere . 141. " dew-points ....... 142. Relative humidity ........ 143. Values of o.378) Du Bois and Rubens' experiments (r) Drude's experiments ...... 168. Indices of refraction for rock salt 169. " " " " " " temperature coefficients . 170. " " " " sylvine 149 151 152 153 154 154 155 156 158 159 160 160 162 163 164 166 167 168 169 170 170 170 171 174 176 177 178 178 178 179 179 179 179 180 180 180 181 182 182 182 183 183 183 CONTENTS. 171. 172. 173- 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. ^93- 194. 195- 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207, 208. 209. 210. 211. 212. 213. of n Indices of refraction for fluorite " " " " " temperature coefficients " •' " " Iceland spar . " " " " nitroso-dimethyl-aniline " " " " quartz . " " " " various monorefringents . " " " " " uniaxial crystals biaxial crystals " " " " solutions of salts and acids {a) solutions in water \b) " " alcohol {c) " " potassium permanganate " " " " various liquids ... " " " " gases and vapors . Reflection of light, perpendicular incidence : various values " " " incidence varying : n near unity " " *' " " «=i,55 . Reflection from metals Transmission of Jena glasses " " " ultra-violet glasses " " alum, rock salt, sylvine, fluorite, Iceland spar, quartz Color screens (Landolt) ...... (Wood) " " (Jena glasses) ..... Rotation of the plane of polarized light by solutions . " " " " " " " sodium chlorate Colors of thin films, Newton's rings Thermal conductivity of metals and alloys . " " " various substances . " " " water and salt solutions " " " organic liquids " " " gases Heat of combustion ..... Heat values and analyses of various fuels : (a) coals . (^) peats . (J) liquid fuels Chemical and physical properties of explosives Heat of combination . . ' . Latent heat of vaporization . " " fusion .... Melting-points of the chemical elements Boiling-points " " " " Melting-points of various inorganic compounds Boiling-points " " " " Melting points of various mixtures of metals Low-melting-point alloys and quartz CONTENTS. XI 214. 215- 216. 217. 218. 219. 220. 221. 222, 223. 224. 225. 226. 227. 228. 229. 230. 231. 232, 233- 234- 235- 236. 237- 238. 239- 240. 241. 242. 243- 244. 245- 246. 247. 248. 249. 250. 251. 252. 253- 254. Densities, melting-points, boiling-points of organic compounds : (a) Paraffin series {b) define series (c) Acetylene series . (d) Monatomic alcohols ( ^= 1/30-48, and /= i ; .-. w/^/-^ = i/453-59 X 30-48*, and io«/«/V-*= 107453.59 X 30-48^= 2.373. (c) If gravity produces an acceleration of 32.2 feet per second per second, how many watts are required to make one horse-power ? One horse-power is 550 foot pounds per second, or 550 X 32.2 = 177 10 foot poundals per second. One watt is 10'' ergs per second, that is, 10^ dyne centi- metres per second. The conversion factor is mPt"^, where m = 453.59, /= 30.48, and t=-i, and the result has to be divided by 10^, the number of dyne centime- tres per second in the watt. Hence, 17710 w/2/-7io^= 17710 X 453-59 X 30-48710''= 746.3- (d) How many gramme centimetres per second correspond to 33000 foot pounds per minute ? The conversion factor suitable for this case \sflt~'^, where/ is 453-59, / is 30.48, and / is 60. Hence, 33000 //~^= 33000 X 453-59 X 30.48/60=: 7604000 nearly. * It is important to remember that in problems like that here given the term "pound" or " gramme " refers to force and not to mass. INTRODUCTION. XXIU HEAT UNITS. I. If heat be measured in dynamical units its dimensions are the same as those of energy, namely ML^T~^. The most common measurements, however, are made in thermal units, that is, in terms of the amount of heat required to raise the temperature of unit mass of water one degree of temperature at some stated temperature. This method of measurement involves the unit of mass and some unit of temperature ; and hence, if we denote temperature-numbers by and their conversion factors by 0, the dimensional formula and conversion factor for quan- tity of heat will be M0 and mO respectively. The relative amount of heat com- pared with water as standard substance required to raise unit mass of different substances one degree in temperature is called their specific heat, and is a simple number. Unit volume is sometimes used instead of unit mass in the measurement of heat, the units being then called thermometric units. The dimensional formula is in that case changed by the substitution of volume for mass, and becomes L^0, and hence the conversion factor is to be calculated from the formula Pd. For other physical quantities involving heat we have :— 2. Coefficient of Expansion.— The coefficient of expansion of a substance is equal to the ratio of the change of length per unit length (linear), or change of volume per unit volume (voluminal) to the change of temperature. These ratios are simple numbers, and the change of temperature is inversely as the mag- nitude of the unit of temperature. Hence the dimensional and conversion-factor formulae are ©~^ and 6~^. 3. Conductivity, or Specific Conductance.— This is the quantity of heat transmitted per unit of time per unit of surface per unit of temperature gradient. The equation for conductivity is therefore, with H as quantity of heat, ,\=T and the dimensional formula 7:rr^= r-n-, which gives m/~^i ^ for conversion factor.0LT LI' ^ In thermometric units the formula becomes UT~^, which properly represents diffusivity. In dynamical units H becomes ML^T~*, and the formula changes to MLT~*0~^. The conversion factors obtained from these are Pf~^ and m/t~^0~^ respectively. XXIV INTRODUCTION. 4. Thermal Capacity. — This is the product of the number for mass and the specific heat, and hence the dimensional formula and conversion factor are simply M and m. 5. Latent Heat.— Latent heat is the ratio of the number representing the quantity of heat required to change the state of a body to the number represent- ing the quantity of matter in the body. The dimensional formula is therefore M©/M or 0, and hence the conversion factor is simply the ratio of the tempera- ture units or $. In dynamical units the factor is Pt~''-.* 6. Joule's Equivalent. — Joule's dynamical equivalent is connected with quantity of heat by the equation ML2T-''= JHor JM0. This gives for the dimensional formula of J the expression L^T~'0~^. The conver- sion factor is thus represented by IH~'^B~^. When heat is measured in dynamical units J is a simple number. 7. Entropy.— The entropy of a body is directly proportional to the quantity of heat it contains and inversely proportional to its temperature. The dimen- sional formula is thus M0/0 or M, and the conversion factor is m. When heat is measured in dynamical units the factor is mlH~^d~^. Examples, (a) Find the relation between the British thermal unit, the calorie, and the therm- Neglecting the variation of the specific heat of water with temperature, or de- fining all the units for the same temperature of the standard substance, we have the following definitions. The British thermal unit is the quantity of heat required to raise the temperature of one pound of water 1° F. The calorie is the quan- tity of heat required to raise the temperature of one kilogramme of water 1° C. The therm is the quantity of heat required to raise the temperature of one gramme of water 1° C. Hence :— (i) To find the number of calories in one British thermal unit, we have ^— -45399 and ^= f ; .-. mO= -45399 X 5/9= -25 199- (2) To find the number of therms in one calorie, w=iooo and 6=1; .'. m6=z 1000. It follows at once that the number of therms in one British thermal unit is 1000 X •25199= 251.99. (i>) What is the relation between the foot grain second Fahrenheit-degree and the centimetre gramme second Centigrade-degree units of conductivity? The number of the latter units in one of the former is given by the for- * It will be noticed that when is given the dimension formula L^T-^ the formulas in thermal and dynamical units are always identical. The thermometric units practically suppress mass. INTRODUCTION. XXV mula ml~'^t~'^$°, where w= .064 799, /= 30.48, and i=-i, and is therefore= .064799/30.48 = 2.126 X io~*. {c) Find the relation between the units stated in {b) for emissivity. In this case the conversion formula is ml~H~^, where ml and / have the same value as before. Hence the number of the latter units in the former is 0.064 799/3o.48"-^= 6.975 X Io-^ id) Find the number of centimetre gramme second units in the inch grain hour unit of emissivity. Here the formula is 7nt~H~^, where w= 0.064 799, '^=2.54, and /= 36oo. Therefore the required number is 0.064 799/2.54^^ X 3600= 2.790 X io~®. {e) If Joule's equivalent be 776 foot pounds per pound of water per degree Fahrenheit, what will be its value in gravitation units when the metre, the kilogramme, and the degree Centigrade are units ? The conversion factor in this case is ,._; or /(?" , where / = .304.8 and ^^ = 1.8; .-. 776 X .3048 X 1.8 = 425.7. (/) If Joule's equivalent be ^4832 foot poundals when the degree Fahren- heit is unit of temperature, what will be its value when kilogramme metre second and degree-Centigrade units are used ? The conversion factor is Pf'^O''^ where I= .3048, t ^ i, and (9~' = 1.8 ; .-. 24832 X /=r^^-' = 24832 X .3048' X 1.8=4152.5. In gravitation units this would give 4152. 5/9. 81 =423.3. ELECTRIC AND MAGNETIC UNITS. There are two systems of these units, the electrostatic and the electromagnetic systems, which differ from each other because of the different fundamental suppo- sitions on which they are based. In the electrostatic system the repulsive force between two quantities of static electricity is made the basis. This connects force, quantity of electricity, and length by the equation/:= a ^,where / is force, a a quantity depending on the units employed and on the nature of the medium, g and g^ quantities of electricity, and / the distance between q and q^. The magnitude of the force / for any particular values of q, q^ and / depends on a property of the medium across which the force takes place called its inductive capacity. The in- ductive capacity of air has generally been assumed as unity, and the inductive capacity of other media expressed as a number representing the ratio of the induc- tive capacity of the medium to that of air. These numbers are known as the spe- cific inductive capacities of the media. According to the ordinary assumption, then, of air as the standard medium, we obtain unit quantity of electricity when in the above equation ^= ^^, and/, «, and / are each unity. A formal definition is given below. In the electromagnetic system the repulsion between two magnetic poles or XXVI INTRODUCTION. quantities of magnetism is taken as the basis. In this system the quantities force, quantity of magnetism, and length are connected by an equation of the form r mm, where m and m^ are in this case quantities of magnetism, and the other symbols have the same meaning as before. In this case it has been usual to assume the magnetic inductive capacity of air to be unity, and to express the magnetic induc- tive capacity of other media as a simple number representing the ratio of the in- ductive capacity of the medium to that of air. These numbers, by analogy with specific inductive capacity for electricity, might be called specific inductive capac- ities for magnetism. They are usually called permeabilities. {^Vide Thomson, " Papers on Electrostatics and Magnetism," p. 484.) In this case, also, like that for electricity, the unit quantity of magnetism is obtained by making m ^=^ m^, and /, a, and / each unity. In both these cases the intrinsic inductive capacity of the standard medium is suppressed, and hence also that of all other media. Whether this be done or not, direct experiment has to be resorted to for the determination of the absolute val- ues of the units and the relations of the units in the one system to those in the other. The character of this relation can be directly inferred from the dimen- sional formulae of the different quantities, but these can give no information as to the relative absolute values of the units in the two systems. Prof. Riicker has suggested (Phil. Mag. vol. 27) the advisability of at least indicating the exist- ence of the suppressed properties by putting symbols for them in the dimensional formulae. This has the advantage of showing how the magnitudes of the different units would be affected by a change in the standard medium, or by making the standard medium different for the two systems. In accordance with this idea, the symbols K and P have been introduced into the formulae given below to represent inductive capacity in the electrostatic and the electromagnetic systems respectively. In the conversion formulae k and/ are the ordinary specific inductive capacities and permeabilities of the media when air is taken as the standard, or generally those with reference to the first medium taken as standard. The ordinary for- mulae may be obtained by putting K and P equal to unity. ELECTROSTATIC UNITS. 1. Quantity of Electricity.— The unit quantity of electricity is defined as that quantity which if concentrated at a point and placed at unit distance from an equal and similarly concentrated quantity repels it, or is repelled by it, with unit force. The medium or dielectric is usually taken as air, and the other units in ac- cordance with the centimetre gramme second system. In this case we have the force of repulsion proportional directly to the square of the quantity of electricity and inversely to the square of the distance between the quantities and to the inductive capacity. The dimensional formula is there- fore the same as that for [force X length^ X inductive capacity]* or M*L'T~^K\ and the conversion factor is mHH~^k^, INTRODUCTION. XXVli 2. Electric Surface Density and Electric Displacement.— The density of an electric distribution at any point on a surface is measured by the quantity per unit of area, and the electric displacement at any point in a dielectric is mea- sured by the quantity displaced per unit of area. These quantities have therefore the same dimensional formula, namely, the ratio of the formulae for quantity of electricity and for area or M*L"^T~^K*, and the conversion factor w-/~-/~U'^. 3. Electric Force at a Point, or Intensity of Electric Field.— This is measured by the ratio of the magnitude of the force on a quantity of electricity at a point to the magnitude of the quantity of electricity. The dimensional formula is therefore the ratio of the formulas for force and electric quantity, or MLT-2 ^ M^L-^T-^K-i, M^L'T-^K^ which gives the conversion factor ni'-l~^t~'^k~^. 4. Electric Potential and Electromotive Force.— Change of potential is proportional to the work done per unit of electricity in producing the change. The dimensional formula is therefore the ratio of the formulae for work and elec- tric quantity, or ML^T-^ ^M^L^T-^K-*, M^L^T-^K* which gives the conversion factor m^l^t~^k~^. 5. Capacity of a Conductor. — The capacity of an insulated conductor is proportional to the ratio of the numbers representing the quantity of electricity in a charge and the potential of the charge. The dimensional formula is thus the ratio of the two formulae for electric quantity and potential, or M^UT-^K^ _ ., y MiL*T-^K-4 ' which gives ik for conversion factor. When K is taken as unity, as in the ordinary units, the capacity of an insulated conductor is simply a length. 6. Specific Inductive Capacity. — This is the ratio of the inductive cap?c- ity of the substance to that of a standard substance, and hence the dimensional formula is K/K or i.* 7. Electric Current.— Current is quantity flowing past a point per unit of time. The dimensional formula is thus the ratio of the formulae for electric quan- tity and for time, or M^L'T-^K* T and the conversion factor mrl't'^k^. = M^L^T-^'K*, * According to the ordinary definition referred to air as standard medium, the specific inductive capacity of a substance is K, or is identical in dimensions with what is here taken as inductive ca- pacity. Hence in that case the conversion factor must be taken as i on the electrostatic and as l~'^fi on the electromagnetic system. XXVlll INTRODUCTION. 8. Conductivity, or Specific * Conductance.— This, like the corresponding term for heat, is quantity per unit area per unit potential gradient per unit of time. The dimensional formula is therefore M^L'T-^K> _ ^1j^ electric quantity ^ ^M^UT~^K~^rY> ' area X potential gradient X time The conversion factor is /~*i. 9. Specific * Resistance.— This is the reciprocal of conductivity as above defined, and hence the dimensional formula and conversion factor are respec- tively TK-i and fk-\ 10. Conductance.— The conductance of any part of an electric circuit, not containing a source of electromotive force, is the ratio of the numbers represent- ing the current flowing through it and the difference of potential between its ends. The dimensional formula is thus the ratio of the formulae for current and poten- tial, or M^L^T-^K^ _ J ^_,^ MiL^T-^K-i ' from which we get the conversion factor U~^k. 11. Resistance.—This is the reciprocal of conductance, and therefore the dimensional formula and the conversion factor are respectively L<"~'TK~^ and EXAMPLES OF CONVERSION IN ELECTROSTATIC UNITS, (a) Pind the factor for converting quantity of electricity expressed in foot grain second units to the same expressed in c. g. s. units. By (i) the formula is m-Ih~^^-, in which in this case m= 0.0648, /= 30.48, /= I, and ^= 1 ; ,-. the factor is 0.0648^ X 30-48'= 4.2836. (^) Find the factor required to convert electric potential from millimetre milli- gramme second units to c. g. s. units. By (4) the formula is M^-/-f~'^k~\ and in this case m = 0.00 1, /= o.i, /= i, and k=i; .'. the factor= 0.001* X o- 1^= 0.01. (c) Find the factor required to convert from foot grain second and specific in- ductive capacity 6 units to c. g. s. units. By (5) the formula is /k, and in this case /= 30.48 and k= 6 ; .'. the factor = 30.48 X 6 = 182.88. * The term "specific," as used here and in 9, refers conductance and resistance to that between the ends of a bar of unit section and unit length, and hence is different from the same term in specific heat, specific inductivity, capacity, etc., which refer to a standard substance. INTRODUCTION. XXIX ELECTROMAGNETIC UNITS. As stated above, these units bear the same relation to unit quantity of magne- tism that the electric units do to quantity of electricity. Thus, when inductive capacity is suppressed, the dimensional formula for magnetic quantity on this sys- tem is the same as that for electric quantity on the electrostatic system. All quan- tities in this system which only differ from corresponding quantities defined above by the substitution of magnetic for electric quantity may have their dimensional formulas derived from those of the corresponding quantity by substituting P for K. 1. Magnetic Pole, or Quantity of Magnetism.— Two unit quantities of magnetism concentrated at points unit distance apart repel each other with unit force. The dimensional formula is thus the same as for [force X length^ X in- ductive capacity] or M*L'T~^P^, and the conversion factor is w?-/'/^*/*. 2. Density of Surface Distribution of Magnetism.— This is measured by quantity of magnetism per unit area, and the dimension formula is therefore the ratio of the expressions for magnetic quantity and for area, or M^L"^T~^P*, which gives the conversion factor m^t^t~^J>^. 3. Magnetic Force at a Point, or Intensity of Magnetic Field. — The number for this is the ratio of the numbers representing the magnitudes of the force on a magnetic pole placed at the point and the magnitude of the magnetic pole. The dimensional formula is therefore the ratio of the expressions for force and magnetic quantity, or MT T-'' MiL^T-ipi ' and the conversion factor fn^lr^t~'^p~^. 4. Magnetic Potential. — The magnetic potential at a point is measured by the work which is required to bring unit quantity of positive magnetism from zero potential to the point. The dimensional formula is thus the ratio of the formula for work and magnetic quantity, or which gives the conversion factor m^l^t~'^p~^. 5. Magnetic Moment. — This is the product of the numbers for pole strength and length of a magnet. The dimensional formula is therefore the pro- duct of the formulcE for magnetic quantity and length, or M-L*T~^P*, and the con- version factor w-/*/''/^ 6. Intensity of Magnetization.— The intensity of magnetization of any por- tion of a magnetized body is the ratio of the numbers representing the magni- XXX INTRODUCTION. tude of the magnetic moment of that portion and its volume. The dimensional formula is therefore the ratio of the formulae for magnetic moment and volume, or M.L. The conversion factor is therefore n^lr^-t~^p^. 7. Magnetic Permeability,* or Specific Magnetic Inductive Capacity. — This is the analogue in magnetism to specific inductive capacity in electricity. It is the ratio of the magnetic induction in the substance to the magnetic induc- tion in the field which produces the magnetization, and therefore its dimensional formula and conversion factor are unity. 8. Magnetic Susceptibility.— This is the ratio of the numbers which repre- sent the values of the intensity of magnetization produced and the intensity of the magnetic field producing it. The dimensional formula is therefore the ratio of the formulae for intensity of magnetization and magnetic field or or P. MJL-^T-ip-i The conversion factor is therefore/, and both the dimensional formula and con- version factor are unity in the ordinary system. 9. Current Strength.— A current of strength c flowing round a circle of radius r produces a magnetic field at the centre of intensity 2TTCJr. The dimen- sional formula is therefore the product of the formulae for magnetic field intensity and length, or M-L*T~^P~*, which gives the conversion factor mH^t~'^p~^. 10. Current Density, or Strength of Current at a Point.— This is the ratio of the numbers for current strength and area. The dimensional formula and the conversion factor are therefore M^L~*T~^P~* and m^l~H^^p~^. 11. Quantity of Electricity.— This is the product of the numbers for cur- rent and time. The dimensional formula is therefore M*L*T~^P~^ X T= M-L*P~*, and the conversion factor m^fip~^. 12. Electric Potential, or Electromotive Force.— As in the electrostatic system, this is the ratio of the numbers for work and quantity of electricity. The dimensional formula is therefore ^L T~ — ^jy s-T^api aPiTp^" ' and the conversion factor m^l^t~'^p^. * Permeability, as ordinarily taken with the standard medium as unity, has the same dimension formula and conversion factor as that which is here taken as magnetic inductive capacity. Hence for ordinary transformations the conversion factor should be taken as i in the electromagnetic and J~2/2 in the electrostatic systems. INTRODUCTION. XXxi 13. Electrostatic Capacity.— This is the ratio of the numbers for quantity of electricity and difference of potential. The dimensional formula is therefore ^^^ ^ ^ T —l'p2p— 1 and the conversion factor /~V^~^ 14. Resistance of a Conductor.— The resistance of a conductor or elec- trode is the ratio of the numbers for difference of potential between its ends and the constant current it is capable of producing. The dimensional formula is therefore the ratio of those for potential and current or MiL4T-^P-i~ The conversion factor thus becomes //~^/, and in the ordinary system resistance has the same conversion factor as velocity. 15. Conductance.— This is the reciprocal of resistance, and hence the dimen- sional formula and conversion factor are respectively L~^TP~^ and lr'^tp~'^. 16. Conductivity, or Specific Conductance.— This is quantity of electric- ity transmitted per unit of area per unit of potential gradient per unit of time. The dimensional formula is therefore derived from those of the quantities men- tioned as follows :— M^L^p-i LjM^L'T-^Pt = L-^TP- L The conversion factor is therefore l~'^tp~'^. 17. Specific Resistance. — This is the reciprocal of conductivity as defined in 16, and hence the dimensional formula and conversion factor are respectively L^'T-^P and Pr^p. 18, Coefficient of Self-induction, or Inductance, or Electro-kinetic In- ertia.— These are for any circuit the electromotive force produced in it by unit rate of variation of the current through it. The dimensional formula is therefore the product of the formulas for electromotive force and time divided by that for current or M^L^T-^pi MiL^T-^p-i X T = LP. The conversion factor is therefore Ip, and in the ordinary system is the same as that for length. 19. Coefficient of Mutual Induction.— The mutual induction of two cir- cuits is the electromotive force produced in one per unit rate of variation of the current in the other. The dimensional formula and the conversion factor are therefore the same as those for self-induction. XXXU INTRODUCTION. 20. Electro-kinetic Momentum.— The number for this is the product of the numbers for current and for electro-kinetic inertia. The dimensional formula is therefore the product of the formulae for these quantities, or M-L*T~^P~* X LP = M^L^T~^P^, and the conversion factor is mHH~'^p'^. 21. Electromotive Force at a Point.— The number for this quantity is the ratio of the numbers for electric potential or electromotive force as given in 12, and for length. The dimensional formula is therefore M^L^T~^P*, and the conversion factor m^lH~'^p^. 22. Vector Potential.— This is time integral of electromotive force at a point, or the electro-kinetic momentum at a point. The dimensional formula may therefore be derived from 21 by multiplying by T, or from 20 by dividing by L. It is therefore M*L^T~^P*, and the conversion factor w-7-/~^/-. 23. Thermoelectric Height. — This is measured by the ratio of the num- bers for electromotive force and for temperature. The dimensional formula is therefore the ratio of the formula for these two quantities, or M-L^T~'^P*0~^, and the conversion factor m^l^t~'^J>^6~^. 24. Specific Heat of Electricity. — This quantity is measured in the same way as 23, and hence has the same formulae. 25. Coefficient of Peltier Effect. — This is measured by the ratio of the numbers for quantity of heat and for quantity of electricity. The dimensional formula is therefore and the conversion factor m^l~^p^9. EXAMPLES OF CONVERSION IN ELECTROMAGNETIC UNITS. (a) Find the factor required to convert intensity of magnetic field from foot grain minute units to c. g. s. units. By (3) the formula is m^t^t~^p~^, and in this case m = 0.0648, /= 30.48, /= 60, and/ = I ; .". the factors = 0.0648* X 30.48^^ X 6o~^= 0.00076847. Similarly to convert from foot grain second units to c. g. s. units the factor is 0.0648* X 30-48"- = 0.046 108. (J)) How many c. g. s. units of magnetic moment make one foot grain second unit of the same quantity ? By (5) the formula is ;«/*/"'/-, and the values for this problem are m = 0.0648, /= 30.48, f= I, and/ = I ; .*. the number = 0.0648* X 30-48*= 1305.6. (c) If the intensity of magnetization of a steel bar be 700 in c. g. s. units, what will it be in millimetre milligramme second units ? INTRODUCTION. XXXIU By (6) the formula is m^fir^J>^, and in this case m =. looo, /= lo, /= i, and / = I ; .•. the intensity = 700 X 1000* X 10* = 70000. (d) Find the factor required to convert current strength from c. g. s. units to earth quadrant io~" gramme and second units. By (9) the formula is /«W~^/~*, and the values of these quantities are here m = io^\ /= Io~^ /= I, and/ = i ; .-. the factor = lo^i X io~»= 10. (, and for this case /== io~®, / = i, and / = i ; .'. the factor = io~^. (/) Find the factor required to convert electromotive force from earth-quadrant io~" gramme and second units to c. g. s. units. By (12) the formula is m-P^~^J>^, and for this case m = io~", /= 10®, /= i, and/ = I ; .*. the factor = 10'. PRACTICAL UNITS. In practical electrical measurements the units adopted are either multiples or submultiples of the units founded on the centimetre, the gramme, and the second as fundamental units, and air is taken as the standard medium, for which K and P are assumed unity. The following, quoted from the report to the Honorable the Secretary of State, under date of November 6th, 1893, by the delegates repre- senting the United States, gives the ordinary units with their names and values as defined by the International Congress at Chicago in 1893 :— " Resolved, That the several governments represented by the delegates of this International Congress of Electricians be, and they are hereby, recommended to formally adopt as legal units of electrical measure the following : As a unit of re- sistance, the international ohm, which is based upon the ohm equal to 10^ units of resistance of the C. G. S. system of electro-magnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grammes in mass, of a constant cross- sectional area and of the length of 106.3 centimetres. " As a unit of current, the international ampere, which is one tenth of the unit of current of the C. G. S. system of electro-magnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with accom- panying specifications,* deposits silver at the rate of 0.001118 of a gramme per second. * " In the following specification the term ' silver voltameter' means the arrangement of appara- tus by means of which an electric current is passed through a solution of nitrate of silver in water. The silver voltameter measures the total electrical quantity which has passed during the time of the experiment, and by noting this time the time average of the current, or, if the current has been kept constant, the current itself can be deduced. " In employing the silver voltameter to measure currents of about one ampere, the following arrangements should be adopted :— XXXIV INTRODUCTION. " As a unit of electromotive force, the international volt, which is the electro- motive force that, steadily applied to a conductor whose resistance is one interna- tional ohm, will produce a current of one international ampere, and which is rep- resented sufficiently well for practical use by \%%% of the electromotive force between the poles or electrodes of the voltaic cell known as Clark's cell, at a tem- perature of 15° C, and prepared in the manner described in the accompanying specification.* " As a unit of quantity, the international coulomb, which is the quantity of elec- tricity transferred by a current of one international ampere in one second. "As a unit of capacity, the international farad, which is the capacity of a con- denser charged to a potential of one international volt by one international cou- lomb of electricity.t " As a unit of work, the joule, which is equal to 10^ units of work in the c. g. s. system, and which is represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm, "As a unit of power, the watt, which is equal to 10'' units of power in the c. g. s. system, and which is represented sufficiently well for practical use by the work done at the rate of one joule per second. " As the unit of induction, the henry, which is the induction in a circuit when the electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampbre per second. " The Chamber also voted that it was not wise to adopt or recommend a stand- ard of light at the present time." By an Act of Congress approved July 12th, 1894, the units recommended by the Chicago Congress were adopted in this country with only some unimportant verbal changes in the definitions. By an Order in Council of date August 23d, 1894, the British Board of Trade adopted the ohm, the ampere, and the volt, substantially as recommended by the Chicago Congress. The other units were not legalized in Great Britain. They are, however, in general use in that country and all over the world. " The kathode on which the silver is to be deposited should take the form of a platinum bowl not less than 10 centimetres in diameter and from 4 to 5 centimetres in depth. " The anode should be a plate of pure silver some 30 square centimetres in area and 2 or 3 millimetres in thickness. " This is supported horizontally in the liquid near the top of the solution by a platinum wire passed through holes in the plate at opposite corners. To prevent the disintegrated silver which is formed on the anode from falling on to the kathode, the anode should be wrapped round with pure filter paper, secured at the back with sealing wax. "The liquid should consist of a neutral solution of pure silver nitrate, containing about 15 parts by weight of the nitrate to 85 parts of water. " The resistance of the voltameter changes somewhat as the current passes. To prevent these changes having too great an effect on the current, some resistance besides that of the voltameter should be inserted in the circuit. The total metallic resistance of the circuit should not be less than 10 ohms." * A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, was appointed to pre- pare specifications for the Clark's cell, but no report was made, on account of Helmholtz's death. t The one millionth part of the farad is more commonly used in practical measurements, and is called the microfarad. PHYSICAL TABLES Table 1 . FUNDAMENTAL AND DERIVED UNITS. To change a quantity from one system of units to another : substitute in the correspond- Table 1 . FUNDAMENTAL AND DERIVED UNITS. IT. Heat Units. Table 1. FUNDAMENTAL AND DERIVED UNITS. ///. Magnetic and Electric Units. Table 2. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES.* (1) CUSTOMARY TO METRIC. LINEAR. Table 2. TABLES FOR CONVERTING U. S. WEIGHTS AND MEASURES. (2) METRIC TO CUSTOMARY. LINEAR. Table 3. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES.* (1) METRIC TO IMPERIAL. LINEAR MEASURE. I millimetre (mm.) I (.001 m.) I I centimetre (.01 m.) I decimetre (.1 m.) I METRE (m.) I dekametre (10 m.) I hectometre (100 m.) I kilometre (1,000 m.) \ I myriametre (10,000 m.) I micron . . [• = 0.03937 in. = 0.39370 " = 3-9370I " 39-370113 " 3.280S43 ft. 1.09361425 yds. 10.93614 109.361425 " 0.62137 mile. 6.21372 miles, o.ooi mm. SQUARE MEASURE. i = I sq. centimetre I sq. decimetre (100 sq. centm.) I sq. metre or centi- ) __ are (100 sq. dcm.) ) I ARE (100 sq. m.) = I hectare (100 ares ) _ or 10,000 sq. m.) j 0.1550 sq. in. 15.500 sq. in. ( 10.7639 sq. ft. ( 1. 1960 sq. yds. 119.60 sq. yds. 2.47 1 1 acres. CUBIC MEASURE. cub. centimetre | (c.c.) (1,000 cubic ^ = millimetres) cub. decimetre (c.d.) (t.ooo cubic j- = 61.024 centimetres) CUB. METRE or stere (1,000 c.d.) 0.0610 cub. in. _ j 35.3148 cub. ft. 1.307954 cub. yds. H 0.61024 " 0.070 gill. 0.176 pint. MEASURE OF CAPACITY. I millilitre (ml.) (.001 | ^ ^ ^gj^ ^^^ litre) ) I centilitre (.01 litre) I decilitre (.1 litre) . . I LITRE (1,000 cub. ) centimetres or i V = 1.75980 pints. cub. decimetre) ) I dekalitre (10 litres) . = 2.200 gallons. I hectolitre (100 " ) . = 2.75 bushels. I kilolitre (1,000 '* ) . = 3.437 quarters. APOTHECARIES' MEASURE. cubic centi- ) metre (i ? gramme w't) ) cub. millimetre 0.03520 fluid ounce. 0.28157 fluid drachm. 1 5.43236 grains weight. 0.01693 minim. AVOIRDUPOIS WEIGHT. I milligramme (mgr.) . . I centigramme (.oi gram.) I decigramme (.1 " ) I GRAMME ' I dekagramme (10 gram.) I hectogramme (100 " ) I KILOGRAMME (l,000" ) I myriagramme (lokilog.) I quintal (100 " ) I millier or tonne I (1,000 kilog.) j 0.01543 gram. 0.15432 « 1-54324 grains. 15.43236 " 5.64383 drams. 3.52739 oz. 2.2046223 lbs. 15432.3564 grains. 22.04622 lbs. = 1.96841 cwt. = 0.9842 ton. TROY WEIGHT. I GRAMME . . = 0.03215 OZ. Troy. 0.64301 pennyweight. 15.43236 grains. APOTHECARIES' WEIGHT. I GRAMME ( 0.25721 drachm. = ) 0.77162 scruple. (1 543236 grains. Note.—The Metre is the length, at the temperature of o° C, of the platinum-indium bar deposited at the International Bureau of Weights and Measures at Sevres, near Pans, France. The present legal equivalent of the metre is 39-:(70' '3 inches, as above stated. The Kilogramme is the mass of a platinum-iridiiim weight deposited at the same place. . v The Litre contains one kilogramme weight of distilled water at its maximum density (4^ C), the barometer being at 760 millimetres. *In accordance with the schedule adopted under the Weights and Measures (metric system) Act, 1897. Smithsonian Tablcs. Table 3. EQUIVALENTS OF METRIC AND BRITISH IMPERIAL WEIGHTS AND MEASURES. Table 3. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (3) IMPERIAL TO METRIC. LINEAR MEASURE. I inch I foot {i2 in.) . . I YARD (3 ft.) . . I pole (si yd.) . . I chain (22 yd. or ) 100 links) ) I furlong {220 yd.) I mile (1,760 yd.) . =^ j f 25.400 milli- = I metres. __ o. 30480 metre. = 0.914399 " =: 5.0292 metres. = 20.1168 " = 201.168 " ^ j 1.6093 kilo- metres. SQUARE MEASURE. f 6.4516 sq. cen- I square inch . . = | timetres. ( 9.2903 sq. deci- I sq.ft. (144 sq. in.) = | metres. , , f 0.836126 sq. I SQ. YARD (9 sq. ft.) = \ metres. I perch (30^ sq. yd.) = { ^^' tres^^* ™^' I rood (40 perches) = 10.I17 ares. I ACRE (4840 sq. yd.) = 0.40468 hectare. I sq. mile (640 acres) — <259.oo hectares. CUBIC MEASURE. I cub. inch^ 16.387 cub. centimetres. I cub. foot (1728 I f 0.02831 7 cub. me- cub. in.) J" i tre, or 28.317 cub. decimetres. CUB. cub YARD (27 ) 0.7645 s cub. metre APOTHECARIES' MEASURE. r gallon (8 pints or ) ^ 4.5459631 litres, 160 fluid ounces) j I fluid ounce, f 3 ) _ 428.4123 cubic (8 drachms) ) ] centimetres. I fluid drachm, f 3 I _ r3.55l5cubic (60 minims) ) \ centimetres. I minim, ITJ (0.91 146 I / 0.05919 cubic grain weight) J ~~ 1 centimetres. Note. — The Apothecaries' gallon is of the same capacity as the Imperial gallon. MEASURE OF CAPACITY. igni I pmt (4 gills) . . . I quart (2 pints) . . I GALLON (4 quarts) I peck (2 galls.) . . I bushel (8 galls.) . I quarter (8 bushels) : 1.42 decilitres. : 0.568 litre. : 1. 136 litres. 4.5459631 " 9.092 " 3.637 dekalitres. = 2.909 hectolitres. AVOIRDUPOIS WEIGHT. I gram .... I dram .... I ounce (16 dr.) . I POUND (16 oz. or 7,000 grains) I stone (14 lb.) . I quarter (28 lb.) I hundredweight } (112 lb.) J I ton (20 cwt.) . ={ 64.8 m i 11 i- grammes. 1.772 grammes. 28.350 o 45359243 l^ilogr- 6.350 12.70 " 550.80 I 0.5080 quintal. 1.0160 tonnes or 1016 kilo- grammes. TROY WEIGHT. 1-5552 I Troy OUNCE (480 ) ^31.1035 grammes. grams avoir.) ) ^ o I pennyweight (24 / grains) J "" Note. — The Troy grain is of the same weight as the Avoirdupois grain. APOTHECARIES' WEIGHT. I ounce (8 drachms) = 31.1035 grammes. I drachm, 51(3 scru- { __ ggg ,, pies) _ i •' I scruple, 3: (20 / grains) 1.296 Note.— The Apothecaries' ounce is of the same weight as the Troy ounce. The Apothecaries' grain is also of the same weight as the Avoirdupois grain. Note. —The Yard is the length at 62° Fahr., marked on a bronze bar deposited with the Board of Trade. The Pound is the weight of a piece of platinum weighed in vacuo at the temperature of 0° C, and which is also deposited with the Board of Trade. The Gallon contains 10 lb. weight of distilled water at the temperature of 62° Fahr., the barometer being at 30 inches. Smithsonian Tables. lO Table 3. EQUIVALENTS OF BRITISH IMPERIAL AND METRIC WEIGHTS AND MEASURES. (4) IMPERIAL TO METRIC. LINEAR MEASURE. Table 4. II VOLUME OF A CLASS VESSEL FROM THE WEIGHT OF ITS EQUIVALENT VOLUME OF MERCURY OR WATER. If a glass vessel contains at ^ C, /* grammes of mercury, weighted with brass weights in air at 760 mm. pressure, then its volume in c. cm. at the same temperature, i, : F'= PR = /^» at another temperature, tx, : F= PRx = Fp/d i i + 7 (4 - ^) ! / = the weight, reduced to vacuum, of the mass of mercury or water which, weighed with brass weights, equals i gramme ; d =^ the density of mercury or water at t°C, and 7 = 0.000 025, is the cubical expansion coefficient of glass. 12 Table 5. DIFFERENTIAL COEFFICIENTS. INTEGRALS. DIFFERENTIAL COEFFICIENTS. «=«" loge« sin. X COS. X tan. X cot. X sec. X cosec. X ax tan.—* X cot.- cosec.—' 3f covers.—* x a^ loge a a; COS. « —sin. X sec' :» —cosec' X sin. Jg COS.' ;c COS.* V(i-^') I I i+x"^ I I x\/{x'^—i) I 5C\/(»'— l) I v/lz x—x^) I v/(2 a;—*2) INTEGRALS. fx^dx fa^dx SeUx fdx *f X y*cos. ax • dx ysin. ax • dx /sec' ax • dx /cosec' ax- dx sin. 5c^/ / COS.* X cos, a; sin.' X dx dx dx \/{a^-x^) r dx Ja'+x' r dx J x^(x^-a^) A dx\/(2X—X^) n+i a' loge* loge» sin, ax a —cos. ax a tan, ax a —cot, ax a sec. X —cosec. X f • _i ^ ' sin. ' - a —COS.—'- a ' I . , a; - tan.-' - a a cot.-' - I , X - sec.—' - a a cosec ' — a a vers.—' X —covers.—' x Taylor's series : u=f{x+h)=f{x) +f'(x)h+r(x) ^ +f'"(x)—^ +• 2 I • 2 • 3 The remainder after the first n terms is expressed by X"/"+'(*+A-s)s"'<^z- I .2 -3 ...n Maclaurin's series : x' u=J(x)=J{o) +f'(o)x+J"(o) -^ +r'(o)-—-+ • I •2 I • 2 • 3 ^=3.14159265359 1=0.31830988618 7r'=9.8696o440i09 6=2.71828182846 v't=i.7724S38509I ^=0.88622692546 log,oir=o.497i4987269 logioe=o.43429448i90 loge 10=2.30258509299 loga(number) =loge (number) • log^ e __logp(number) log,B Smithsonian Tables^ Table 6. 13 VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, OF NATURAL NUMBERS. n 14 Table 6 (continued). VALUES OF RECIPROCALS, SQUARES, CUBES, SQUARE ROOTS, OF NATURAL NUMBERS. n Table 6 {continued). 15 VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS, OF NATURAL NUMBERS. n i6 Table 6 (continued). VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n Table 6 {continued). I J VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n i8 Table 6 {continued). ' 19 VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n 670 20 Table 6 {continued). VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. n Table 6 (continued). 21 VALUES OF RECIPROCALS, SQUARES, CUBES, AND SQUARE ROOTS OF NATURAL NUMBERS. « 22 Table 7 {continued). LOGARITHMS. 23 N. 24 Table 8. LOGARITHMS. N Table 8 {continued). LOGARITHMS. 25 26 Table 9. ANTILOGARITHMS. P.P. 12 3 4 5 .00 .oi .02 •03 .04 .05 .06 .07 .08 .09 .10 .11 .12 •13 .14 .15 .16 •17 .18 .19 .20 .21 .22 •23 .24 .25 .26 .27 .28 .29 .30 •31 •32 33 •34 .35 •36 37 •38 •39 .40 .41 .42 •43 •44 .45 .46 •47 .48 •49 000 023 047 072 096 122 148 175 202 230 259 288 318 349 3S0 413 445 479 514 549 58s 622 660 698 738 778 820 862 90s 950 199s 2042 2089 2138 2188 2239 2291 2344 2399 245s 2512 2570 2630 2692 2754 2818 28S4 2951 3020 3090 1002 1026 1050 1074 1099 1125 1151 1178 1205 1233 1262 1291 1321 1352 1384 1416 1449 1483 I5'7 1552 1589 1626 16G3 1702 1742 1782 1824 1866 1910 1954 2000 2046 2094 2143 2193 2244 2296 2350 2404 2460 2518 2576 2636 2698 2761 2S25 2891 2958 3027 3097 005 028 052 076 102 127 153 ISo 208 236 265 294 324 355 3^7 419 452 486 521 556 592 629 667 706 746 786 8 28 871 9'4 959 2004 2051 2099 2148 2198 2249 2301 2355 2410 2466 2523 2582 2642 2704 2767 2S31 2897 2965 3034 3105 007 030 054 079 104 130 156 183 211 239 268 297 327 358 390 422 455 489 524 560 596 633 671 710 750 791 832 875 919 963 2009 2056 2104 2153 2203 2254 2307 2360 2415 2472 2529 2588 2649 2710 2773 2838 2904 2972 3041 31 12 1009 1033 1057 108 1 1 107 1132 1159 1 186 1213 1242 1 27 1300 1330 1361 1393 1426 1459 1493 1528 1563 1600 1637 1675 1714 1754 1795 1837 1879 1923 1968 2014 2061 2109 2158 2208 2259 2312 2366 2421 2477 2535 2594 2655 2716 2780 2844 291 1 2979 3048 3119 012 035 059 084 109 135 161 189 216 245 274 303 334 365 396 429 462 496 531 567 603 641 679 718 758 799 841 884 928 972 2018 2065 2113 2163 2213 2265 2317 2371 2427 2483 2541 2600 2661 2723 2786 2851 2917 2985 3055 3126 014 038 062 086 112 138 164 191 219 247 276 306 337 368 400 432 466 500 535 570 607 644 683 722 762 803 845 888 932 977 2023 2070 2n8 2168 2218 2270 2323 2377 2432 2489 2547 2606 2667 2729 2793 2858 2924 2992 3062 3^33 1016 1040 1064 1089 1114 1140 1167 1 194 1222 1250 1279 1309 1340 1371 1403 1435 1469 1503 1538 1574 1611 1648 1687 1726 1766 1807 1849 1892 1936 1982 019 042 067 091 117 M3 169 197 225 253 282 3'2 343 374 406 439 472 507 542 578 614 690 730 770 811 854 897 941 986 021 045 069 094 119 146 172 199 227 256 285 315 346 377 409 442 476 510 545 581 618 656 694 734 774 816 858 901 945 991 2028 2032 2037 2075 20S0 20S4 2123 2128 2133 2173 2178 2183 2223 2228 2234 2275 2280 2286 2328 2333 2339 2382 2388 2393 2438 2443 2449 2495 2500 2506 2553 2559 2564 2612 2618 2624 2673 2679 2685 2735 2742 274S 2799 2805 2812 2864 2871 2877 2931 2938 2944 2999 3006 3013 3069 3076 30S3 3141 3148 3155 Smithsonian Tables. Table 9 {continued). ANTILOGARITHMS. 27 P.P. 1 2 I 3 4 5 3162 3-^36 33S8 3467 3548 3715 3S02 3S90 3981 4074 4169 4266 4365 4467 4571 4677 47S6 4898 5012 5129 5-48 5370 S49S 5623 5754 5888 6026 6166 6310 6457 6607 6761 6918 7079 7244 7413 75S6 7762 7943 S128 8318 8511 S710 8913 9120 9333 9550 9772 3170 3243 3319 3396 3475 7096 7261 7430 7603 7780 8933 9141 9354 9572 9795 3177 3251 3327 3404 34S3 7112 7278 7447 7621 7798 8954 9162 9376 9594 9817 3184 3258 3334 3412 3491 3556 3565 3573 3639 3648 3656 3724 3733 3741 3S11 3819 3828 3899 3908 3917 3990 3999 4009 4083 4093 4102 4178 418S 4198 4276 4285 4295 4375 4385 4395 4477 4487 4498 4581 4592 4603 46S8 4699 4710 4797 4808 4819 4909 4920 4932 5023 28 Table 10. ANTILOGARITHMS. Table 1 {continued). ANTILOGARITHMS. 29 30 Table 1 1 . CIRCULAR (TRIGONOMETRIC) FUNCTIONS. (Taken from B. O. Peirce's " Short Table of Integrals," Ginn & Co.) Table 1 1 {continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 31 32 Table 1 1 {continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 33 34 Table 1 1 {continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. RADI- ANS. Table 12. CIRCULAR (TRIGONOMETRIC) FUNCTIONS.* 35 m < Q < Pi z^ Table 1 2 {continued). CIRCULAR (TRIGONOMETRIC) FUNCTIONS. Table 1 2 {continued), CIRCULAR (TRIGONOMETRIC) FUNCTIONS. 37 C/3 12; < S < 05 38 Tables 1 2 {continued) and 1 2a. CIRCULAR FUNCTIONS AND FACTORIALS. TABLE 12 {continued). — ^^va^si (Trigonometric) Fnncttons. 'A < < Table 13. HYPERBOLIC FUNCTIONS.* Hyperbolic sines. Valnea ol 39 X 40 Table 14. HYPERBOLIC FUNCTIONS. Common logarltlims -|- 10 of \he hyperbolic sines. X Table 15. HYPERBOLIC FUNCTIONS. 41 HTperliollc cosines. Values of px _|. p-a X 42 Table 1 6. HYPERBOLIC FUNCTIONS. Common logarithms of the hyperbolic cosines. X Table 1 7. 43 EXPONENTIAL FUNCTIONS. Values of e* and e~* intermediate to those here given may be found by adding or subtracting the values of the hyperbolic cosine and sine given in Tables 15 and 13. X 44 Table 18. EXPONENTIAL FUNCTIONS, LOG e^. X Table 19. 45 EXPONENTIAL FUNCTIONS. Value of e*' and e-*' and theli logarithms. The equation to the probability curve isj' =: r—*^, where x may have any value, positive or negative, between zero and infinity. X 46 Tables 22 AND 23. EXPONENTIAL FUNCTIONS AND LEAST SQUARES. 47 TABLE 22. —Exponential Functions. Value of e' and e-" and their logarithms. X 48 Table 24. LEAST SQUARES. This table gives the values of the probability P, as defined in last table, corresponding to different values of j: I r where r is the " probable error." The probable error r is equal to 0.47694 / /*. r Table 26. ^ LEAST SQUARES. Valnes ol the factor 0.6745a/ ,^ ,, .\ w(»—1) This factor occurs in the equation e = 0.6745-%/ /"-^ for the probable error of the arithmetic 1\ «(«— i) 49 n 50 Table 29. DIFFUSION. 2 pi e-'fi dq. Inverse* values of vie =\ — tt I log X = log (2q) + \o%\/kt. t expressed in seconds. = log 5 + logV-^^- t expressed in days. = log 7 + log \/kt. " " years. (. ^= coefficient of diffusion.t c= initial concentration. V= concentration at distance x, time t. v/c Table 29 (continued). DIFFUSION. 51 vie 52 Table 30. GAMMA FUNCTION.* Value ollog I Jo e-'»"-^ is the latitude. Table 85. GRAVITY. 105 In this table the results of a number of the more recent gravity determinations are bought together. They serve to show the degree of accuracy which may be assumed for the numbers in Table 112. In general, gravity is a little lower than the calculated value for stations far inland and slightly higher on the coast line. Place. Latitude. N. +, S. - Elevation in metres. Gravity, Observed. Reduced to sea level. Refer- ence. Singapore Georgetown, Ascension . Green Mountain, Ascension Loanda, Angola . . . Caroline Islands . . . Bridgetown, Barbadoes Jamestown, St. Helena Longwood, " Pakaoao, Sandwich Islands Lahaina, " " Haiki, Honolulu, " " St. Georges, Bermuda Sidney, Australia . . Cape Town .... Tokio, Japan .... Auckland, New Zealand Mount Hamilton, Cal. (Lick Obs San Francisco, Cal. Washington, D. C* Denver, Colo. . . . York, Pa Ebensburgh, Pa. . . Allegheny, Pa. . . Hoboken, N. J. . . Salt Lake City, Utah Chicago, 111. . . . Pampaluna, Spain . Montreal, Canada . Geneva, Switzerland Berne, " Zurich, Paris, France .... Kew, England . . . Berlin, Germany . . . Port Simpson, B. C. . Burroughs Bay, Alaska Wrangell, " Sitka, St. Paul's Island, " Juneau, " Pyramid Harbor, " Yakutat Bay, " I" 17' — 7 56 — 7 57 -8 49 — 10 00 13 04 — 15 55 — 15 57 20 43 20 52 20 56 21 18 32 23 — 33 52 — 33 56 35 41 — 36 52 37 20 37 20 37 47 37 47 38 53 39 54 39 58 40 27 40 28 40 44 40 46 41 49 42 49 45 31 46 12 46 12 46 57 47 23 48 50 51 28 52 30 54 34 55 59 56 28 57 03 57 07 58 18 59 10 59 32 14 686 46 2 18 10 533 3001 3 117 3 2 43 II 6 43 1282 1282 114 114 10 1645 122 348 II 12S8 165 450 100 405 405 572 466 67 7 49 6 978.08 978.25 97S.10 978.15 978.37 978.18 978.67 978.53 978.28 978.S6 978.91 978.97 979-77 979.68 979.62 979-95 979.68 979.66 979.68 979.96 980.02 980. 1 1 979.68 980. 1 2 980.08 980.09 9S0.27 979.82 980.34 980.34 980.7^ 980.58 980.60 980.61 980.67 980.96 981.20 981.26 981.46 9S1.51 981.60 981.69 981.67 981.74 981.82 981.83 978.08 978.25 978.23 978.16 978.37 978.18 978.67 978.59 978.85 978.86 978.93 978.97 979-77 979.69 979.62 979-95 979.69 979-91 979-92 979.98 980.04 980.11 979.98 980.14 980.20 980.15 9S0.27 980.05 980.37 980.42 980.75 980.64 980.66 980.69 980.74 980.97 981.20 981.27 98 1 .46 981.51 98 1 .60 981.69 981.67 981.74 981.82 981.83 1 Smith : " United States Coast and Geodetic Survey Report for 1884," App. 14. 2 Preston : " United States Coast and Geodetic Survey Report for 1890," App. 12. 3 Pre-ston : Ibid. 1888, App. 14. 4 Mendenhall : Ibid. 1891, App. 15. 5 Defforges : " Comptes Rendus," vol. 118, p. 231. 6 Pierce : " U. S. C. and G. S. Rep. 1883," App. 19. 7 Cebrian and Los Arcos : " Comptes Rendus des Seances de la Commission Perma- nente de I'Association Geodesique International," 1893. 8 Pierce: « U. S. C. and G. S. Report 1876, App. 15, and 1881, App. 17." 9 Messerschmidt : Same reference as 7. • For references 1-4, values are derived by comparative experiments with invariable pendulums, the value for Washington taken as 980.111. For the latter see Appendix 5 of the Coast and Geodetic Survey Report for 1901. Smithsonian Tables. io6 Table 86. SUMMARY OF RESULTS OF THE VALUE OF GRAVITY {g) AT STATIONS IN THE UNITED STATES AND ALASKA.* Station. Tables 87-88. LENGTH OF THE SECONDS PENDULUM. TABLE 87. — Length of Seconds Pendulum at Sea Level for Different Latitudes.* 107 Lati- tude. lOS Table 89. MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS.* Length of the seconds pendulum at sea level =/=39.oi2540+c.2o8268 sin'^ (finches. =3.251045+0.017356 sin^ (pieet. =^0.9909910+0.005290 sin^ metres. Acceleration produced by gravity per second per second mean solar time . . . ^^=32.086528+0.17 1293 sin^0 feet. =977.9886+ 5.2210 sin^0 centimetres. Equatorial radius =^^6378206 metres ; 3963.225 miles. Polar semi-diameter =^=6356584 metres ; 3949.790 miles. Reciprocal of flattening= =295.0 Square of eccentricity =^^=—j— =0.006768658 6378388+18 metres; " ^ 3963-339 miles. ^ 6356909 metres; ? 3949-992 miles. ;s, 297.0+ 0.5 S^ 0.0067237+0.0000120. Difference between geographical and geocentric latitude=0—0'= 688.2242" sin 2 0—1. 1482" sin40+o.oo26"sin60. Mean density of the Earth= 5.5247 + 0.0013 (Burgess Phys. Rev. 1902). Continental surface density of the Earth= 2.67 "l „ . Mean density outer ten miles of earth's crust= 2.40 j ^^ 'ness. Moments of inertia of the Earth; the principal moments being taken as A, B, and C, and C the greater: C-A . I —7;— =0.00526521=—7 ;C ^ •' 306.259 C—.,4=0.001064767 Ea^; A—B—o.22i,02g£a^; C =0.326094 j5'a' ; where E is the mass of the Earth and a its equatorial semidiameter. Length of sidereal year=365.2563578 mean solar days; =365 days 6 hours 9 minutes 9.314 seconds. Length of tropical year=365.242i99870—0.0000062124-^^—^mean solar days; 100 ' =365 days 5 hours 48 minutes { 46.069—0.53675-^—^ ) seconds. ^ 100 J Length of sidereal month _ - /c^ /: ^ /— 1800 , — 27.32 1 661 162—0.00000026240 days: 100 •' =27 days 7 hours 43 minutes ( 1 1.524—0.022671-^ j seconds. Length of synodical month = 29.53058843 5 —0.00000030696 days ; 100 =:29days i2hours44 minutes (2.841—0.0261522 j seconds. \ -' 100 / Length of sidereal day = 86164.09965 mean solar seconds. N- B.—The factor containing t in the above equations (the epoch at which the values of the quantities are required) may in all ordinary cases be neglected. • Mostly from Harkness, " Solar Parallax and Allied Constants." Smithsonian Tables. Table 89 {continued). 109 MISCELLANEOUS DATA WITH REGARD TO THE EARTH AND PLANETS. Masses of the Planets. Reciprocals of the masses of the planets relative to the sun and the mass of the moon relative to the Earth. Mercury = 6000000 Venus = no Table 90. TERRESTRIAL MAGNETISM. Secular Change ol Declination. Changes in the magnetic declination between iSio, the date of the earliest available observa- tions, and 1910, for one or more places in each state and territory. State. Table 90 (continued). TERRESTRIAL MAGNETISM {continued). Secular Cbange of Declination (continued). Ill State. 112 Tables 91-92. TERRESTRIAL MAGNETISM {continued). TABLE 91.— Dip or Inclination. This table gives for the epoch January i, 1905, the values of the magnetic dip, I, corresponding to the longitudes west of Greenwich in the heading and the north latitudes in the first column. Tables 93-94. TERRESTRIAL MAGNETISM (continued). TABLE 93. — Horizontal Intensity. 113 This table gives for the epoch January i, 1905, the horizontal intensity, H, expressed in CG. S. units, corresponding to the longitudes in the heading and the latitudes in the first column. 114 Tables 95-96. TERRESTRIAL MAGNETISM (continued). TABLE 95.— Total Intensity. This table gives for the epoch January i, 1905, the values of total intensity, F, expressed in C. G. S. units corresponding to the longitudes in the heading and the latitudes in the first column. Table 97. AGONIC LINE. IIS The line of no declination appears to be still mov> ing westward in the United States, but the line of no annual change is only a short distance to the west of it, so that it is probable that the extreme westerly position will soon be reached. Lat. N. Ii6 Table 98. PRESSURE OF COLUMNS OF MERCURY AND WATER. British and metric measures. Correct at o° C. for mercury and at 4° C. for water. Metric Measure. Table 99. II7 REDUCTION OF BAROMETRIC HEIGHT TO STANDARD TEMPERATURE.* Corrections for brass scale and lis Table 100. CORRECTrON OF BAROMETER TO STANDARD GRAVITY. Height Table 101. 119 REDUCTION OF BAROMETER TO STANDARD GRAVITY.* Redaction to Latitude 46^. — Engllsb Scale. N. B. From latitude o° to 44° the correction is to be subtracted. From latitude 90° to 46° the correction is to be added. 120 Table 102. REDUCTION OF BAROMETER TO STANDARD GRAVITY.* Reduction to Latitude 46°. —Metric Scale. N. B. — From latitude o° to 44° the correction is to be subtracted. From latitude 90° to 46° the correction is to be added. Table 103. 121 CORRECTION OF THE BAROMETER FOR CAPILLARITY.* I. Metric Measure. 122 Table 104. AERODYNAMICS. The pressure on a plane surface normal to the wind is for ordinary wind velocities expressed by P=^ kwav"^ where k\%2. constant depending on the units employed, w the mass of unit volume of the air, a the area of the surface and v the velocity of the wind.* Engineers generally use the table of values of /"given by Smeaton in 1759. This table was calculated from the formula />=.00492 z/2 and gives the pressure in pounds per square foot when v is expressed in miles per hour. The corresponding formula when v is expressed in feet per second is /'=.00228z^^. Later determinations do not agree well together, but give on the average somewhat lower values for the coefficient. The value of w depends, of course, on the temperature and the baro- metric pressure. Langley's experiments give /^w=:.ooi66 at ordinary barometric pressure and 10° C. temperature. For planes inclined at an angle a less than 90° to the direction of the wind the pressure may be expressed as jfo= -'^oAo- Table 104, founded on the experiments of Langley, gives the value of Fa. for different values of a. The word aspect, in the headings, is used by him to define the position of the plane relative to the direction of motion. The numerical value of the aspect is the ratio of the linear dimension transverse to the direction of motion to the linear dimension, a vertical plane through which is parallel to the direction of motion. TABLE 104.— Values of Fa In Equation Pa= FaP!!o- Plane 30 in. X 4.8 in. Aspect 6 (nearly). Table 105. 123 AERODYNAMICS. On the basis of the results given in Table 104 Langley states the following condition for the soaring of an aeroplane 76.2 centimetres long and 12.2 centimetres broad, weighing 500 grammes. — that is, a plane one square foot in area, weighing i.i pounds. It is supposed to soar in a horizontal direction, with aspect 6. TABLE 106. — Data for the Soaring of Planes 76.2 X 12.2 cms. welgUng 600 Grammes, Aspect 6. Inclination to the hori- zontal a. 124 Table 106. FRICTION. The following table of coefficients of frictionf and its reciprocal 1 1/, together with the angle of friction or angle of repose <^, is quoted from Rankine's "Applied Mechanics.'" It was compiled by Rankine from the results of General Morin and other authorities, and is sufficient for all ordinary purposes. Material. Table 107. VISCOSITY. 125 The coefficient of viscosity is the tangential force per unit area of one face of a plate of the fluid which is required to keep up unit distortion between the faces. Viscosity is thus measured in terms of the temporary rigidity which it gives to the fluid. Solids may be included in this definition when only that part of the rigidity which is due to varying distortion is considered. One of the most satisfactory methods of measuring the viscosity of fluids is by the observation of the rate of flow of the fluid through a capillary tube, the length of which is great in comparison with its diameter. Poiseuille* gave the following formula for calculating the viscosity coefiicient in this case : n ^= -0-7-1 where h is the pressure height, r the radius of the tube, s the density of the fluid, V the quantity flowing per unit time, and / the length of the capillary part of the tube. The liquid is supposed to flow from an upper to a lower reservoir joined by the tube, hence h and / are different. The product hs is the pressure under which the flow takes place. Hagen- bach t pointed out that this formula is in error if the velocity of flow is sensible, and suggested a correction which was used in the calculation of his results. The amount to be subtracted from h, according to Hagenbach, is -f=— , where g is the acceleration due to gravity. Gartenmeister JS2 . g points out an error in this to which his attention had been called by Finkener, and states that the quantity to be subtracted from h should be simply — ; and this formula is used in the reduction of his observations. Gartenmeister's formula is the most accurate, but all of them nearly agree if the tube be long enough to make the rate of flow very small. None of the formulae take into account irregularities in the distortion of the fluid near the ends of the tube, but this is probably negligible in all cases here quoted from, although it probably renders the results obtained by the " viscosimeter " commonly used for testing oils useless for our purpose. The term "specific viscosity" is sometimes used in the headings of the tables; it means the ratio of the viscosity of the fluid under consideration to the viscosity of water at a specified tem- perature. The friction of a fluid is proportional to the size of the rubbing surface, to -^, where v is the velocity of motion in a direction perpendicular to the rubbing surface, and to a constant known as the viscosity. Variation of Viscosity of Water, wltli Temperature. Dynes per sq. cm. Temp. 126 Tables 1 08-1 1 0. VISCOSITY. TABLE 108. -Solution of Alcohol in Water.* Coefficients of viscosity, in C. G. S. units, for solution of alcohol in water. Table 1 1 1. 1:27 VISCOSITY. This table gives some miscellaneous data as to the viscosity of liquids, mostly referring to oils and paraffins. viscosities are in C. G. S. units. The I2S Table 112. VISCOSITY. This table gives the viscosity of a number of liquids together with their temperature variation. The headings are temperatures in Centigrade degrees, and the numbers under them the coeffi- cients of viscosity in C. G. S. units.* Table 113. VISCOSITY OF SOLUTIONS. 129 This table is intended to show the effect of change of concentration and change of temperature on the viscosity o£ solutions of salts in water. The specific viscosity X loo is given for two or more densities and for several tem- peratures in the case of each solution, fx stands for specific viscosity, and / for temperature Centigrade. Salt. 130 Table 113 {continued). VISCOSITY OF SOLUTIONS. Table 113 {continued). VISCOSITY OF SOLUTIONS. 131 132 Table 113 {continued). VISCOSITY OF SOLUTIONS. Salt. Table 114. SPECIFIC VISCOSITY.* 133 Dissolved salt. Acids : CIbOs HCl . HCIO3 HNO3 H2SO4 Aluminium sulphate Barium chloride . " nitrate Calcium chloride " nitrate . Cadmium chloride " nitrate " sulphate Cobalt chloride . " nitrate " sulphate . Copper chloride . " nitrate . " sulphate Lead nitrate . . Lithium chloride " sulphate Magnesium chloride " nitrate . " sulphate Manganese chloride " nitrate . " sulphate Nickel chloride . . " nitrate . . . " sulphate . . Potassium chloride . " chromate " nitrate . " sulphate Sodium chloride . " bromide . " chlorate " nitrate . Silver nitrate . . Strontium chloride " nitrate Zinc chloride . . " nitrate . . " sulphate . . Normal solution. 1.0562 I.0177 1.0485 1-0332 1-0303 1-0550 1.0884 1 .0446 1.0596 1.0779 1.0954 1-0973 1.057 1 1.07 28 1.0750 1.0624 I-075S 1.0790 1 . 1 380 1.0243 I -0453 I-I375 1.0512 1.0584 1.0513 1 .0690 1.0728 1.0591 I-0755 I -0773 1.0466 1-0935 1.0605 1 .0664 1.040 1.0786 1.0710 1.0554 1.13S6 1.0676 1.0822 1.0590 1.0758 1.0792 012 067 052 027 090 406 123 117 134 165 34S 204 166 354 205 179 358 lOI 142 290 201 171 367 209 183 364 205 180 361 987 "3 975 105 097 064 090 065 058 141 115 189 164 367 J normal. .02S3 .0092 .0244 .0168 .0154 .0278 .0441 .0518 .0218 .0300 0394 .0479 .0487 .0286 .0369 •0383 •0313 .0372 .0402 0.0699 .0129 .0234 .0188 .0259 .0297 .0259 -0349 .0365 .0308 .0381 .0391 .0235 0475 •0305 0338 .0208 .0396 •0359 .0281 .0692 •0336 .0419 .0302 .0404 .0402 Cfj- .003 •034 .025 .Oil •043 .178 .057 .044 .076 053 .063 ,074 157 097 075 160 098 080 .160 042 066 ^37 .094 ,082 164 098 .0S7 169 097 084 161 987 053 982 049 047 030 042 026 020 067 049 096 086 173 i normal. .0143 .0045 .0126 .0086 .0074 .0138 .0226 .0259 .0105 .0151 .0197 .0249 .0244 .0144 .0184 .0193 ,0158 .0185 .0205 •0351 .0062 ,0115 ,0091 .0130 .0152 .0125 .0174 0179 .0144 .0192 .0198 .0117 ,0241 .0161 .0170 .0107 .0190 .0180 .0141 ,0348 0171 0208 0152 0191 0198 1.000 I.0I7 I.OI4 1.005 1.022 1.082 1.026 1.02 1 1.036 1.022 1.03 1.038 1.078 1.048 1.032 1.077 1.047 1.040 i.oSo 1.017 1.03 1 1.065 1.044 1.040 1.07S 1.048 1.043 1.076 1.044 1.042 1-075 0.990 1.022 0.987 1.021 1.024 1.015 1.022 1.012 1.006 1.034 1.024 1-053 1.039 1.0S2 I normal. .0074 .0025 .0064 .0044 .0035 .0068 .0114 .0130 .0050 .0076 .0098 .0119 .0120 .0058 .0094 .0110 .0077 .0092 .0103 0175 .0030 .0057 •0043 .0066 .0076 .0063 ,0093 .0087 .0067 .0096 .0017 .0059 .0121 .0075 .0084 ,0056 .0100 .0092 ,0071 •0173 .0084 ,0104 ,0077 ,0096 ,0094 0.999 .009 .006 •003 .008 .038 .013 .008 .017 .008 .020 .018 •033 .023 .018 .040 .027 .018 -038 .007 .012 .032 .021 .020 .032 -023 -023 •037 .021 .019 .032 0-993 012 0.992 .008 -01 3 .008 .012 .007 .000 .014 .011 .024 .019 .036 Authority. Reyher. Wagner. Reyher. «( Wagner. * In the case of solutions of salts it has been found (v, the specific viscosity can, in many cases, be nearly expressed '(fe Arrhennius, Zeits. fiir Phys. Chem. vol. i, p. 285) that by the equation ;ii^/iij", where /u.^ is the specific viscosity for a normal solution referred to the solvent at the same temperature, and « the number of gramme molecules in the solution under consideration. The same rule may of cou gramme molecules. The table here given has been compil p. 749) and of Wagner (Zeits. fiir Phys, Chem. vol. 5, p. 3 Smithsonian Tables. se be applied to solutions stated in percentages instead of d from the results of Reyher (Zeits. fiir Phys. Chem. vol. 2, ) and illustrates this rule. The numbers are all for 2$'-' C. 134 Table 115. VISCOSITY OF GASES AND VAPORS. The values of /t given in the table are lo* times the coefificients of viscosity in C. G. S. units. Substance. Table 116. COEFFICIENT OF VISCOSITY OF GASES. Temperature Coefllolents. 135 If /tt=the viscosity at f C, /Uo= the vicosity at 0°, 0= the coefficient of expansion, &, 7, and «= coefficients independent of /, then (I) /j(=:/xo(i+o/)'». (Meyer, Obermayer, Puluj, Breitenbach.) (II) =/to(i+j3/). (Meyer, Obermayer.) (Ill) =/io(i+«^)*(i+70^. (Schumann.) (IV) = Mo- 1+ 'i-l—— . (Sutherland.) 273 Gas. 136 Table 117. DIFFUSION OF AN AQUEOUS SOLUTION INTO PURE WATER. If k is the coefficient of diffusion, dS the amount of the substance which passes in the time dt, at the place x, through q sq. cm. of a diffusion cylinder under the influence of a drop of concen- tration dcI dx, then , dS = —kq ^ dt.dx k depends on the temperature and the concentration, c gives the gram-molecules per litre. The unit of time is a day. Substance. Table 118. DIFFUSION OF VAPORS. 137 CoefiScients of diffusion of vapors in C. G. S. units. The coefficients are for the temperatures given in the table and a pressure of 76 centimetres of mercury.* Vapor. 138 Tables 1 1 9-1 1 9a. DIFFUSION OF GASES, VAPORS, AND METALS. TABLE 119. — Coefllclents ol Diffusion for Various Qases and Vapors.* Gas or Vapor difiusing. Air .... Carbon dioxide Carbon disulphide Carbon monoxide Ether Hydrogen Nitrogen Oxygen . Sulphur dioxid Water . , Gas or Vapor diffused into. Hydrogen . . . Oxygen . . . , Air Carbon monoxide Hydrogen . . . Methane . . . . Nitrous oxide . . Oxygen . . . . Air Carbon dioxide Ethylene . . . . Hydrogen . . . Oxygen . . . . Air ..'.!! ! Hydrogen . . . Air Carbon dioxide " monoxide Ethane . . . . Ethylene . . . . Methane . . . . Nitrous oxide . . Oxygen . . . . Carbon dioxide Hydrogen . . . Nitrogen . . . . Hydrogen . • . Air Hydrogen . . . Temp. °C. i8 Coefficient of Diffusion. 0.661 0.1775 0.1423 0.1360 0.1405 0-1314 0.5437 0.1465 0.0983 C.I802 0.0995 O.I314 O.IOI 0.6422 o. 1 802 0.1872 0.0827 0.3054 0.6340 o.53''^4 0.6488 0-4593 0.4863 0.6254 0-5347 0.6788 0.1787 0.1357 0.7217 0.1710 0.4828 0.2390 0.2475 0.8710 Authority. Schulze. Obermayer. Loschmidt. Waltz. Loschmidt. Obermayer. Loschmidt. Stefan. Obermayer. Loschmidt. Obermayer. Stefan. Obermayer. Loschmidt. Obermayer. Loschmidt. Guglilemo. * Compiled for the most part from a similar table in Landolt & Bornstein's Phys. Chem. Tab. TABLE 119 A. — Diffusion of Metals Into Metals. dv i,4-2L. where x is the distance in direction of diffusion; v, the degree of concentration of fjH dx^ ' t^^ diffusing metal ; /, the time ; k, the diffusion constant = the quantity of metal in grammes diffusing through a sq. cm. in a day when unit difference of concentra- tion (gr. per cu. cm.) is maintained between two sides of a layer one cm. thick. Diffusing Metal. Table 120. 139 SOLUBILITY OF INORGANIC SALTS IN WATER; VARIATION WITH THE TEMPERATURE. The numbers give the number of grammes of the anhydrous salt soluble in 1000 grammes of water at the given temperatures. <;Qlf 140 TABL.E.S i 20 (.continued) -i 22. SOLUBILITY OF SALTS AND GASES IN WATER. TABLE 120 (coHimued).— Solxi\ii]ity of Inorganic Salts In Water; Variation with the Temperature. The numbers give the number of grammes of the anhydrous salt soluble in 1000 grammes of water at the given temperatures. Salt. Temperature Centigrade. 60° NaOH NaiPaO, NasSOg Na2S04 . . (loaq) • • (7aq) NaaSaOa NiCla NiS04 PbBr2 Pb(N03)2 . . . . RbCl RbNOg RboS04 SrCla Snl2 Sr{N03)2 . . . . Th(S04)3 . .(9aq) " • . (4aq) TlCl TINO3 T].>S04 Ybo(S04)3 . . . . Zn(N03)2 . . . . ZnS04 420 32 141 196 5_25 272 5 365 770 195 364 442 395 7 2 39 27 442 39 90 305 610 600 6 444 844 330 426 483 549 10 2 62 37 1090 62 287 194 447 700 640 523 911 533 482 539 10 70S 14 3 96 49 1 190 99 400 847 680 425 12 607 976 813 535 600 12 876 20 5 143 62 1290 135 495 [482 1026 720 15 694 1035 1 167 58s 667 14 913 30 40 6 209 76 2069 700 1450 174 1697 760 502 20 787 1093 1556 631 744 17 926 51 25 8 304 92 768 1740 220 455 2067 810 548 24 880 "55 2000 674 831 21 940 16 10 462 109 104 255 445 594 28 977 1214 2510 714 896 25 956 13 695 127 72 3130 300 437 2488 632 33 1076 1272 3090 750 924 30 972 16 mo 146 69 860 429 2542 1174 1331 3750 787 962 34 990 20 2000 165 _58 920 330 427 2660 776 48 1270 1389 5420 818 1019 40 lOII 4140 47 785 TABLE 121. - Solubility of a Table 1 23. ABSORPTION OF CASES BY LIQUIDS.* 141 Temperature 142 Tables 124-126. CAPILLARITY.-SURFACE TENSION OF LIQUIDS.* TABLE 124. — Water and Alcobol in Contact with Air. TABLE 126. — Solutions of Salts In Water, t Temp. Tables 127-129. TENSION OF LIQUIDS. TABLE 127. —Surface Tension of Liquids. 143 Liqtiid. Water Mercury .... Bisulphide of carbon . . Chloroform .... Ethyl alcohol Olive oil ... . Turpentine .... Petroleum .... Hydrochloric acid Hyposulphite of soda solution Specific gravity. 13-543 1.2687 1.4878 0.7906 0.9136 0.8867 9-7977 1. 10 1. 1248 Surface tension in dynes per cen- timetre of liquid in contact with — 7S-0 513-0 30-5 (3I-S) (24.1) 34-6 28.8 29.7 (72.9) 69.9 Water. Mercury. 0.0 392.0 41.7 26.8 18.6 II.S {28.9) (392) (3S7) (415) 364 317 241 271 (392) 429 144 Table 130. VAPOR PRESSURES. The vapor pressures here tabulated have been taken, with one exception, from Regnault's results. The vapor pressure of Pictet's fluid is given on his own authority. The pressures are in centimetres oi mercury. Tem- pera- ture Cent. Table 1 30 {continued). VAPOR PRESSURES. 145 Tem- 146 Tables 131-132. VAPOR PRESSURE. TABLE 131. —Vapor Pressure of Ethyl Alcohol.* d I H 0° 10 20 30 40 70 Table 1 33. VAPOR PRESSURE.* Carbon DlsnlpMde, Chlorobenzene, Bromolsenzene, and Aniline. 147 Temp. 148 Table 1 33 {continued). VAPOR PRESSURE. Metliyl Salicylate, Bromonaphthalliie, and Mercnry. Temp. C. Table 134. 149 VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER.* The first column gives the chemical formula of the salt. The headings of the other columns give the number of gramme-molecules of the salt in a litre of water. The numbers in these columns give the lowering of the vapor pressure produced by the salt at the temperature of boiling water under 76 centimetres barometric pressure. Substance. 1 50 Table i 3A {continued). VAPOR PRESSURE OF SOLUTIONS OF SALTS IN WATER. Substance. Table 135. 151 PRESSURE OF AQUEOUS VAPOR AT LOW TEMPERATURE.* Pressures are given in inches and millimetres of mercury, temperatures in degrees Fahrenheit and degrees Centigrade. (a) Pressures in inches of mercury; temperatures in degrees Fahrenheit. 152 Table 136. PRESSURE OF AQUEOUS VAPOR, 0° C TO 100° C. According to Broch.* Temp. Table 137. PRESSURE OF AQUEOUS VAPOR, 100° C. TO 230° C. According to Regnault. 153 154 Tables 1 37 (.coniiKued)-i 39. PRESSURE AND WEIGHT OF AQUEOUS VAPOR. TABLE 137 {continuecf).— PiBssuie ot Aqueous Vapor, 100° 0-230° 0. According to Regnault. g Table 140. PRESSURE OF AQUEOUS VAPOR IN THE ATMOSPHERE. 155 This table gives the vapor pressure corresponding to various values of the difference t— t-^ between the readings of dry and wet bulb thermometers and the temperature /j of the wet bulb thermometer. The differences t— /j are given by two-degree steps in the top line, and t-^ by degrees in the first column. Temperatures in Centigrade degrees and Rcgnault's vapor pressures in millimetres of mercury are used throughout the table. The table was calculated for barometric pressure B equal to 76 centimetres, and a correction is given for each centimetre at the top of the columns.* ^1 156 Table 1 41 . DEW- The first column of this table gives the temperatures of the wet-bulb thermometer, and the top line the difference the table. The dew-points were computed for a barometric pressure of 76 centimetres. When the barometer differs and the resulting number added to or subtracted from the tabular number according as the barometer is below or h Table 141 {conttntud). 157 POINTS. between the dry and the wet bulb, when the dew-point has the values given at corresponding points in the body of from 76 centimetres the corresponding numbers in the lines marked ST/ SB are to be multiplied by the difierencej or above 76. See examples. ST/SB-- 3 4 ST/SB = 5 6 7 8 9 ST/SB = 10 II 12 13 14 ST/SB = 15 16 17 18 19 sr/sB = 20 21 22 23 24 IT/IB-- 25 26 27 28 29 ZT/IB-- 30 31 32 33 34 ZT/IB- 35 36 37 38 39 t— n(inue the temperature of the substances before mixture, £ the temperature of the mixture, /^the lowering of temperature, G the temperature when all snow is melted, when snow is used, and // the amount of heat absorbed in heat units (small calories wheu A is grammes). Temperatures are in Centigrade degrees. Substance. Table 218. 221 CRITICAL TEMPERATURES, PRESSURES, VOLUMES, AND DENSITIES OF GASES.* == Critical temperature. J'= Pressure in atmospheres. = Volume referred to air at o° and 76 centimetres pressure. ^ = Density in grammes per cubic centimetre. Substance. 222 Table 219. COEFFICIENTS OF THERMAL EXPANSION. Coefficients of Linear Expansion of the Cliemloal Elements. In the heading of the columns T is the temperature or range of temperature ; C is the coefficient of linear expansion ; A\ is the authority for C\ M\s the mean coefficient of expansion between o° and 100° C. ; o and 3 are the coefficients in the equation /e= /o (i + o/ + /S/-), where /q is the length at o° C. and /jthe length at /* C. ; Ai is the authority for a, yS, and m. Substance. Table 220. COEFFICIENTS OF THERMAL EXPANSION. Coefficients of Linear Expansion for Miscellaneous Substances. 223 The coefficient of cubical expansion may be taken as three times the linear coefEcient. T is the temperature or range of temperature, C the coefficient of expansion, and A the authority. Substance. 224 Table 221 . COEFFICIENTS OF THERMAL EXPANSION. Coefllclents o2 Cubical Expansion of some CTystalllne and other Solids.* 7"= temperature or range of temperature, C::= coefficient of cubical expansion, A ^authority. Substance. Table 222. COEFFICIENTS OF THERMAL EXPANSION. 22$ Coetflclents ol Cnlilcal Expansion ol Llaolds. This table contains the coefficients of expansion of some liquids and solutions of salts. When not otherwise stated atmospheric pressure is to be understood. T gives the temperature range, C the mean coefficient of expansion for range T in degrees C, and A-i the authority for C. a, p, and y are the coefficients in the volume equation v, =: z/fl (i + a^ + /8/= + yfi), and m the mean coefficient for range o"-ioo° C, and Wj is the authority for these. Liquid. Acetic acid .... Acetone Alcohol : Amyl Ethyl, sp. gr. .8095 . " 50 % by volume " 30% " 500 atmo. press. " 3000 " " Methyl Benzene Bromine Calcium chloride : CaCl2, 5.8 % solution CaClo, 40.9 % " . Carbon disulphide . . 500 atmos. pressure . 3000 " " Chloroform . . . . Ether Glycerine Hydrochloric acid : HCI4-6.25H2O . . HCl + 50H2O . . Mercury Olive oil Potassium chloride : KCl, 2.5% solution . KCl. 24.3 % " Potassium nitrate : KNO3, 5-3 % sol'n KNO3, 21.9% " Phenol, CeHeO . . . Petroleum Sp. gr. 0.8467 . . . Sodium chloride : NaCl, 1.6 % solution . Sodium sulphate : Na2S04, 24 % sol'n . Sodium nitrate : NaNOs, 36.2% sol'n. Sulphuric acid : H0SO4 H2SO4 + 50H2O . Turpentine . . . . Water i6°-io7° 0-54 -15 to +80 0-80 0-39 18-39 0-40 0-40 -38 to +70 11-81 -7 to +60 18-25 17-24 -34 to +60 0-50 0-50 0-63 -15 to +38 0-30 0-30 s^4-299 36-157 7-38 24-120 10-40 20-78 0-30 0-30 -9 to 4-106 0-33 c X 1000 .866 •524 .940 .581 .992 /3Xio« •1433 .1616 •1433 •1385 .1168 .0506 .0510 .1468 1399 2150 0534 0489 0933 0742 0572 0477 0539 0577 0899 1039 1067 061 1 0627 0489 0799 105I 1 .0630 1.3240 0.8900 1.0414 0.7450 0.2928 1. 1856 1. 1763 1.0382 0.0788 0.4238 1-1398 I.I07I 1-5132 0.4853 0.4460 0.0625 O.18182 C.6821 0.8340 0.8994 0.0213 0-3599 0.5408 0.5758 0.2835 0.9003 —.0643 o. 1 264 3.8090 0.6573 0.7836 1.850 17.900 1.5649 1.2775 1.7114 4.2742 0.8571 1.3706 4.6647 2-3592 0.4895 0.430 8.710 0.00078 1.1405 0.1073 1.396 10.462 2.516 1.075 0.864 5,160 1-959 8.50s y X 108 1.0876 O.S ' 1. 1846 I.7168 0.730 11.87 0.91 1 1 0.8065 0.5447 I.9122 1-7433 4.0051 —539 0.4446 6.790 1 Amagat. 2 Barrett. 3 Zander. 4 Pierre. 5 Kopp. 6 Recknagel. Authorities. 7 Decker. 8 Emo. 9 Marignac. 10 Broch. 11 Spring. 12 Nicol. 13 Pinette. 14 Frankenheitn. 15 Scheel. Smithsonian Tables. 226 Table 223. COEFFICIENTS OF THERMAL EXPANSION. Ooefflclents of Expansion of Oases. Pressures are given in centimetres of mercury. Coefficient at Constant Volume. Tables 224-226. MECHANICAL EQUIVALENT OF HEAT. 227 TABLE 224. — Summary. Taken from J. S. Ames, L'equivalent mecanique de la chaleur, Rapports presentes au congres international du physique, Paris, 1900. Name. Joule . Rowland Reynolds-Morby . Griffiths Schaster-Gannon Callendar-Barnes Method. Mechanical Mechanical Mechanical Electrical E^t . R Scale. Latimer-Clark= 1.4342V at 15° C. International Ohm Latimer-Clark = 1.4340V. at 15° ) Electrical Eit. I C, Elec. Chem. Equiv. Silver? = 0.001 1 i8g ) Electrical Eit. ( Latimer-Clark = i.4342V. at 15° C. Result. 4-173 4-195 4.187 4.181 4.176 4.1832 4.198 4.192 4.187 4.1905 4.179 Temp. °C. 16.S 10. IS- 20. 25. Mean- calory. 15- 19.1 40. TABLE 225. — Reduced to Gramme-calory at 20° C. (Nitrogen thenuometer). Joule . 228 Table 227. SPECIFIC HEAT OF THE CHEMICAL ELEMENTS. Element. Tables 227 {ca>ii!nu£j)-223 SPECIFIC HEAT. TABLE 227. —Specific Heat of the Chemical ZlemenXa {coniinued). 229 Element. 230 Tables 229-230. TABLE 229. — Speclllc Heat of Various Solids.* Solid. Alloys : Bell metal Brass, red " yellow 8o Cu-j-20 Sn 88.7 Cu+i 1.3 Al German silver Lipowitz alloy: 24.97 Pb + 10.13 Cd + 50.66 Bi +14.24 Sn . . . . Rose's alloy : 27.5 Pb+48.9 Bi+23.6 Sn Wood's alloy : 25.85 Pb + 6.99 Cd + 52.43 Bi + 1473 Sn " " (fluid) Miscellaneous alloys : 17.5 Sb+29.g Bi4-i8.7 Zn+33.9 Sn . . . 37.1 Sb+62.9 Pb 39.9 Pb-j-6o.i Bi " (fluid) 63.7 Pb+36.3 Sn 46.7 Pb+53.3 Sn 63.8 Bi+36.2 Sn 46.9 Bi+53.1 Sn Gas coal Glass, normal thermometer 16°^ " French hard thermometer .... crown flint . Ice India rubber (Para) Paraffin " fluid . Vulcanite Temperature 15-98 O o 14-98 20-100 O-IOO s-50 100-150 —77-20 20-89 5-50 100-150 20-99 10-98 16-99 144-358 12-99 10-99 20-99 20-99 20-1040 19-100 10-50 10-50 -188 252 —78 188 _i8 78 .'-lOO —20- +3 —19-4-20 0-20 35-40 60-63 Specific Heat. .08831 .0862 .10432 .09464 •0345 .0426 •0356 .0552 •0352 .0426 .05657 .03880 .03165 .03500 .04073 .04507 .04001 .04504 •3145 .161 .117 .146 .285 •463 .481 .3768 •5251 •6939 .622 .712 •3312 Authority, t R L (i R Ln T M (( S u M R it P (( R W Z H M D G-T R W B A M TABLE 230. — Specific Heat of Various Liquids.* Liquid. Tables 230 {coniinued)-23i . TABLE 230. — Specific Heat of Varlooa Llnnlds. 231 Liquid. 232 Table 232. SPECIFIC HEATS OF GASES AND VAPORS. Tables 233-236. THERMOMETERS. TABLE 233. — Gas and Mercury Thermometers. 233 If /h, ^n, ^co2) ^16. '69. ^T, are temperatures measured with the hydrogen, nitrogen, carbonic acid, 16"^, 59"', and " verre dur " (Tonnelot), respectively, then (100—/)/ /h — ^T=—^^^2— [— 0.61859+ 0.0047351./— o.ooooi 1 577-^^]* (100— /)/r it,— ii= —i^o2~ [—0-55541+ 0.0048240./— 0.000024S07./2]* ^002— ^T= °~^^^ [—0-33386+ 0.0039910./— 0.000016678./2]* /h— /i6= ^^°°~/^^ [— 0.67039+ 0.0047351./— o.ooooi 1 577./2]t /"u—49= ^^°°~2 [—0.310S9+ 0.0047351./— o.ooooi 1 577./2]t • Chappuis ; Trav. et Mdm. du Bur. internat. des Poids et Mes. 6, i88S. t Thiesen, Scheel, Sell; Wiss. Abh. d. Phys. Techn.Reichanstalt, 2, 1895; Scheel; Wied. Ann. 58, 1896 • D. Mech. Ztg. 1897. TABLE 234. ta — 1,8 (Hydrogen— 16™). 234 Tables 237, 238. AIR AND MERCURY THERMOMETERS. TABLE 237. tiOB-tig. (Air -161".) °c. o Tables 239-241 . 235 GAS, MERCURY, ALCOHOL, TOLUOL, PETROLETHER, PENTANE, AND PLATINUM-RESISTANCE THERMOMETERS. TABLE 239. tH— tji (Hydrogen-Mercury). Temper- ature, C. 236 Table 242. CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM. The Stem Correction is proportional to nfi[T—l) : where « is the number of degrees in the exposed stem; ^ is the apparent coefficient of expansion of mercury in the glass ; 7" is the measured temperature ; and i is the mean temperature of the exposed stem determined by another ther- mometer, exposed some 10 cm. from, and at about half the height of, the exposed stem of the first. For temperatures up to ioo°C, the value of ^ is for : Jena glass XVI''^ or Greiner and Friedrich resistance glass, -^ or 0.000159; 6300 Jena glass 59™, -,— or 0.000164. ^ *• ^^ 6100 ^ At 100° the correction is in round numbers 0.01° for each degree of the exposed stem ; at 200° 0.02° ; and for higher temperatures proportionately greater. At 500° it may amount to 0.07° for each exposed degree. Tables 242-244 are taken from Rimbach, Zeitschrift fiir Instrumentenkunde, 10, 153, 1890, and apply to thermometers of Jena or of resistance glass. TABLE 242. — Stem Gorrectlon for Theimometer of Jena Glass (0°-360°C). Degree length 0.9 to i.i mm; ^= the observed temperature; /'=that of the surrounding air I dm. away; «= the length of the exposed thread. Correction to be added to the Reading *. Tables 243, 244. 237 CORRECTION FOR TEMPERATURE OF MERCURY IN THERMOMETER STEM {continued). TABLE 243. — Stem Correction for Thermometer of Jena Qlass (0°-360° 0). Degree length i to 1.6 mm.; /=the observed temperature; ^= that of the surrounding air one dm. away ; ?i= the length of the exposed thread. 238 Tables 245-247. RADIATION CONSTANTS. TABLE 246. — Radiation Formula and Oonstants 2or Perfect Radiator. The radiation per sq. cm. from a " black body " (exclusive of convection losses) at the temper- ature T° (absolute, C) to one at f is equal to /= 0- ( r4_ /4) (Stefan-Boltzmann) ; where (r= i.277X10-12 gramme-calories per second per sq. centimetre. = 7.66 X 10-" " " " minute " " " = 5.32 X 10-12 Tjvatts per sq. centimetre. The distribution of this energy in the spectrum is represented by Planck's formula : where /;^ is the intensity of the energy at the wave-length X (X expressed in microns, /u) and e is the base of the Napierian logarithms. From Kurlbaum's value of the difference of the total energy radiated from black bodies at 100° C and 0° C,/ioo — /o= 0.0731 watts per square cen- timetre (whence the above value of lutely Cold Space (-273° C). Computed from the Stefan-Boltzmann formula ( Ekholm, Met. Z 1902). fiQ Tables 248, 249. COOLING BY RADIATION AND CONVECTION. 239 TABLE 248. — At Ordinary Pressures. According to McFarlane* the rate of loss of heat by a sphere placed in the centre of a spherical enclosure which has a blackened surface, and is kept at a constant temperature of about 14° C, can be expressed by the equations t r= .000238 + 3.06 X 10 — ^t — 2.6 X 10—'/', when the surface of the sphere is blackened, or e = .000168 + 1. 98 X io-«< — 1.7 X io-«/2, when the surface is that of polished copper. In these equa- tions, e is the amount of heat lost in c. g. s. units, that is, the quantity of heat, small calories, radiated per second per square centimetre of surface of the sphere, per degree differ- ence of temperature t, and t is the difference of temperature between the sphere and the enclosure. The medium through which the heat passed was moist air. The following table gives the results. Differ- ence of tempera- ture t 240 Tables 250, 251. COOLING BY RADIATION AND CONVECTION. TABLE 250. — Cooling of Platinum Wire In Copper Envelope. Bottomley gives for the radiation of a bright platinum wire to a copper envelope when the space between is at the highest vacuum attainable the following numbers : — ^:=4o8° C, *^= 378.8 X 10—*, temperature of enclosure 16° C. /= 505° C, et= 726.1 X io-«, " " 17° C. It was found at this degree of exhaustion that considerable relative change of the vacuum produced very small change of the radiating power. The curve of relation between degree of vacuum and radiation becomes asymp- totic for high exiiaustions. The following table illustrates the variation of radiation with pressure of air in enclosure. Temp, of enclosure 16° C, ^= 408° C. Table 252. PROPERTIES OF STEAM. HetrlQ Measure. 241 The temperature Centigrade and the absolute temperature in degrees Centigrade, together with other data for steam or water vapor stated in the headings of the columns, are here given. The quantities of heat are in therms or calo- ries according as the gramme or the kilogramme is taken as the unit of mass. 242 Table 253. PROPERTIES OF STEAM. British Ueasore. The quantities given in the different columns of this table are sufficiently explained by the headings. The abbrevia- tion B. T. U. stands for British thermal units. With the exception of column 3, which was calculated for this table, the data are taken from a table given by Dwelshauvers-Dery (Trans. Am. Soc. Mech. Eng. vol. xi.). Table 253 {continued). PROPERTIES OF STEAM. Brltlsb OSeasnie. 243 •st-g = -S t i" <= rt 2 3 = 244 Table 253 {continued). PROPERTIES OF STEAM. British Measure. Table 253 {continued), PROPERTIES OF STEAM. British Measnie. 245 .Sfc-g lis 4) = 3 246 Table 253 (.continued). PROPERTIES OF STEAM. British Measure. 5 u'u Table 254. 247 RATIO OF THE ELECTROSTATIC TO THE ELECTROMAGNETIC UNIT OF ELECTRICITY = F Date. 248 Tables 255, 256. DIELECTRIC STRENGTH. TABLE 256. — Steady Potential DUference in Volts leqniied to produce a Spark in Air with Ball Electrodes. Spark length. cm. Tables 257, 258. 249 DIELECTRIC STRENGTH. TABLE 257. — Potential Necessary to produce a Spark In Air between more widely Separated Electrodes. £ 250 Tables 259, 260. DIELECTRIC STRENGTH. TABLE 259.— Dielectric Strength 0! Materials. Potential necessary for puncture expressed in kilovolts per centimetre thickness of the dielectric. Substance. Table 261. 251 ABSOLUTE MEASUREMENTS OF CURRENT AND OF THE ELECTROMO- TIVE FORCE OF STANDARD CELLS. Date. 1896 1898 1899 1903 1904 1906 1907 1907 1908 1 90S 1908 Observer, F. and W. Kohlrausch j Rayleigh & Sidgwick . | Potier and Pellat . Kahle Patterson and Guthe Carhart and Guthe Pellat and Leduc . Van Dijk and Kunst Guthe ..... Ayrton, Mather and Smith Smith and Lowry . . Janet, Laporte and j Jouaust j Pellat Guillet Method. Tangent galvanometer . Filter paper voltameter Current balance . . . Filter paper voltameter Current balance . . . Filter paper voltameter Current balance . . . Electrodynamometer . Silver oxide voltameter Electrodynamometer . Current balance . . . Leduc voltameter . . Tangent galvanometer. Filter paper voltameter Electrodynamometer . Current balance . . . Filter paper voltameter Filter paper voltameter Current balance . . . Current balance . . . Current balance . . . Electromotive Force of Clark Cell at 15°. volts. } 14345 \- 1.4328 I- 1-4333 i- }- 1-4330 1-4323 1- Weston Cell at 20°. volts. I.01S6 I.0185 I.01819 I.0187 1.0184 I.0182 Klectrochemical Equivalent found with Voltameter of Rayleigh Form. mg. I.I 183 I.II79 I.II92 I.I182 I.II95 1. 1182 I.I1827 I.I182 Porous Cup Form. I.II92 I.II77 The most probable value of the Weston cell at 20° is 1.0182 volts, assuming the International ohm to be 10^ c. g. s. units and the volt to be 10* c. g. s. units. The corresponding value of the Clark cell, as prepared at present, at 15°, is 1.4324 volts. The legal values of the Weston cell, however, are different in different countries, as follows : United States (Bureau of Standards) 1.019125* v. at 20° Germany (Physikalisch-Technische Reichsanstalt) i.0186 volts at 20° England (National Physical Laboratory) i.01 84 volts at 20° The value of the Weston standard cell, used in the United States, is based upon the value adopted by the Chicago Electrical Congress (1893) for the Clark cell. The value used by Ger- many was adopted in 1896, and is based on Kahle's work at the Reichsanstalt. The value used in England was adopted January i, 1909, and is based on the recommendation of the London Electrical Conference of 1908. It is expected that a new value will soon be agreied upon by the International Committee on Electrical Units and Standards, which will be adopted generally in all countries. The value of the electrochemical equivalent of silver is different when filter paper (Rayleigh form), silk, or other textile is used to separate the anode from the cathode from what it is when a porous cup is employed. The value found is also affected by the addition of silver oxide to the silver nitrate solution. The legal value in all countries is 1.118 mg. of silver per coulomb, and this is nearly the value found when using a porous cup voltameter, and the best determinations of the current that have been made by absolute current balances. Some corrections have been made to the figures given in the above table for the excess due to filter paper, but such corrections are very uncertain. • Based on 1.0189 at 25° C. Smithsonian Tables. 252 Table 262. COMPOSITION AND ELECTROMOTIVE FORCE OF VOLTAIC CELLS. The electromotive forces given in this table approximately represent what may be expected from a cell in good work- ing order, but with the exception of the standard cells all of them are subject to considerable variatiou. (a) Double Fluid Cells. Name of cell. Negative pole. Solution. Positive pole. Solution. Bunsen . Chromate Daniell* Grove Amalgamated zinc Marie Davy Partz . . I part H2SO4 to ) 12 parts H2O . ) [12 parts KaCrsOT] I to 25 parts of I j H.2SO4 and 100 [ [ parts H2O . . J I part H2SO4 to I 12 parts H2O . ) I part H2SO4 to I 4 parts H2O . ) I part H2SO4 to 12 parts H2O . 5% solution of ZnS04 + 6H2O I part NaCl to 4 parts H2O . I part H2SO4 to 12 parts H2O . Solution of ZnS04 H2SO4 solution, ) density 1.136 . ) ( H2SO4 solution, I ( density 1.136 .J {H2SO4 solution, 1 density 1.06 . ) ( H2SO4 solution, ) ( density 1.14 . ) H2SO4 solution, density 1.06 . NaCI solution . . ( I part H2SO4 to ) I 12 parts H2O ) Solution of MgS04 Carbon Fuming H2NO3 HNO3, density 1.38 ( I part H2SO4 to ) I 12 parts H2O . 5 Copper 12 parts K2Cr207 ( to 100 parts HoO J Saturated solution ) ofCuS04+5H20 j Platinum Carbon Fuming HNO3 . . HNO3, density 1.33 Concentrated HNO3 PINO3, density 1.33 HNO3, density 1.19 " density 1.33 ! Paste of protosul- ) phate of mercury > and water . . . ) Solution of K2Cr207 1.94 1.86 2.00 2.03 .06 .09 .08 •05 •93 .66 •93 •79 •71 .66 .61 .88 .50 2.06 * The Minotto or Sawdust, the Meidinger, the Callaud, and the Lockwood cells are modifications of the Daniell, and hence have about the same electromotive force. Smithsonian Tables. Table 262 {continued). 253 COMPOSITION AND ELECTROMOTIVE FORCE OF VOLTAIC CELLS. Name of cell. Negativepole. Positive pole. E. M. F. in volts. (b) Single Fluid Cells. Leclanche . . . Chaperon . . . Edison-Lelande . Chloride of silver Law Dry cell (Gassner) Poggendorff . . J. Regnault . . Volta couple . Amal. zinc (< ICO parts HoO . . ) I part H2SO4 + 12 parts H2O -J- V I part CaS04 . . ) H2O f Carbon. Depolari- 1 zer : manganese I peroxide with f [ powdered carbon J I Copper. Depolar- \ \ izer : CuO ... J ({ ( Silver. Depolari ( zer : silver chl'ride Carbon , Cadmium Copper . 146 0.98 0.70 1.02 1-37 1-3 1.08 2.01 0-34 o.q8 (0) Standard Cells. Weston normal Clark standard jCadmi'ml \ am'lgamj ( Zinc I ( am'lgaml Saturated solution of CdS04 Saturated solution of ZnS04 Mercury. "| Depolarizer: paste I of Hg2S04 and ( CdS04 ... .J Mercury. \ Depolarizer; paste 1 of Hg2S04 and [ ZnSOi ... .J 1.0191 at 20° C 1-434* at 15° C (d) Secondary Cells. Lead accumulator Regnier (i) . . . (2). . . Main . Edison Lead Copper . Amal. zinc Amal. zinc Iron . . ( H2SO4 solution of ) I density i.i . . . ( CUSO4+H2SO4 . . ZnS04 solution . . . H2SO4 density ab't i.i KOH 20 % solution . PbOo " in H2SO4 A nickel oxide - * E. M. F. hitherto used at Bureau of Standards. See p. 251. The temperature formula is E, = E^o — 0.0000406 (t—20)— o.oooooog; (t— 20)2 + 0,00000001 (t— 20)^. The value given is that adopted by the Chicago International Electrical Congress in 1893. The temperature formula is E,= E,b — 0.00119 (t~'5) — 0.000007 (1—15)2. t F. Streinti gives the following value of the temperature variation —- at different stages of charge : dt E. M. F. 254 Table 263. CONTACT DIFFERENCE OF Solids wltb Liquids and Temperature of substances Distilled water Alum solution : saturated at i6°.5 C Copper sulphate solution : sp. gr. 1.087 at i6°.6 C. Copper sulphate solution : saturated at 15° C. . . Sea salt solution : sp. gr. 1.18 at 2o°.5 C. . . . Sal-ammoniac solution saturated at 15°. 5 C. . Zinc sulphate solution : sp. gr. 1. 125 at i6°.9 C. . . Zinc sulphate solution saturated at I5°.3 C. One part distilled water + 3 parts saturated zinc sulphate solution . . . Strong sulphuric acid i distilled water : I to 20 by weight . . I to 10 by volume . . I to 5 by weight . . . 5 to I by weight • . . Concentrated sulphuric acid Concentrated nitric acid Mercurous sulphate paste . Distilled water containing / trace of sulphuric acid ) 269 to 100 127 103 070 475 396 —•653 •.605 -.652 .171 •139 —.189 •.856 .059 .177 .225 ••334 .364 C —.105 ] to ^+•156 —•536 —565 —•637 —.238 —•430 —•444 — 344 —.25 1. 113 .241 * Everett's " Units and Physical Constants: " Table ol Smithsonian Tables. Table 263 ^continued). 25s POTENTIAL IN VOLTS. Lianlds wltb Liquids In Air.* during experiment about 16'-' C. 2^6 Table 264. CONTACT DIFFERENCE OF POTENTIAL IN VOLTS. SoUds with SoUds in Air.* The following results are the " Volta differences of potential," as measured by an electrometer. They represent the difference of the potentials of the air near each of two metals placed in con- tact. This should not be confused with the junction electromotive force at the junction of two metals in metallic contact, which has a definite value, proportional to the coefficient of Peltier effect. The Volta difference of potential has been found to vary with the condition of the me- tallic surfaces and with the nature of the surrounding gas. No great reliance, therefore, can be placed on the tabulated values. The temperature of the substances during the experiment was about i8° C. Table 265. 257 DIFFERENCE OF POTENTIAL BETWEEN METALS IN SOLUTIONS OF SALTS. The following numbers are given by G. Magnanini * for the difference of potential in hundredths of a volt between zinc in a normal solution of sulphuric acid and the metals named at the head of the different columns when placed in the solution named in the first column. The solutions were contained in a U-tube, and the sign of the differ- ence of potential is such that the current will flow from the more positive to the less positive through the ex- ternal circuit. Strength of the solution in 2S8 Table 266. THERMOELECTRIC POWER. The thermoelectric power of a circuit of two metals is the electromotive force produced by one degree C. difference of temperature between the junctions. The thermoelectric power varies with the temperature, thus : thermoelectric powers Q^=dE /dt= A -\- Bt, where A is the thermoelec- tric power at o° C, B is a. constant, and / is the mean temperature of the junctions. The neutral point is the temperature at which dE /dt^=o, and its value is— A /B. When a current is caused to flow in a circuit of two metals originally at a uniform temperature, heat is liberated at one of the junctions and absorbed at the other. The rate of production or liberation of heat at each junction, or Peltier effect, is given in calories per second, by multiplying the current by the co- efficient of the Peltier effect. This coefficient in calories per coulomb= QT/J, in which Q is in volts, T'is the absolute temperature of the junction, and ^= 4.19. Heat is also liberated or ab- sorbed in each of the metals as the current flows through portions of varying temperature. The rate of production or liberation of heat in each metal, or the Thomson effect, is given in calories per second by multiplying the current by the coefficient of the Thomson effect. This coefficient, in calories per coulomb,= ^ 7^0 /y, in which B is in volts per degree C, T'is the mean absolute temperature of the junctions, and is the difference of temperature of the junctions. (BT) is Sir W. Thomson's " Specific Heat of electricity." The algebraic signs are so chosen in the following table that when A is positive, the current flows in the m.etal considered from the cold junction to the hot. When B is positive, Q increases (algebraically) with the temperature. The values of A, B, and thermoelectric power, in the following table are with respect to lead as the other metal of the thermoelectric circuit. The thermoelectric power of a couple composed of two metals, i and 2, is given by subtracting the value for 2 from that for i ; when this difference is positive, the current flows from the cold junction to the hot in i. In the following table, A is given in micro- volts, B in microvolts per degree C, and the neutral point in degrees C. The table has been compiled from the results of Becquerel, Matthiessen and Tait ; in reducing the results, the electromotive force of the Grove and Daniell cells has been taken as 1.95 and 1.07 volts. The value for constantin was reduced from results given in Landolt-Bornstein's tables. The thermoelectric powers of antimony and bismuth alloys are given by Becquerel in the reference given below. Substance. Aluminum Antimony, comm'l pressed wire " axial " equatorial . . . . " ordinary . . . . Argentan Arsenic Bismuth, comm'l pressed wire . " pure " " " crystal, axial. . . . " " equatorial . . " commercial . . . . Cadmium " fused Cobalt Constantin Copper " commercial . . . . " galvanoplastic . . . . Gold Iron " pianoforte wire , . . . " commercial Lead Magnesium Mercury Nickel " (—18® to 175°) . . . . " (25o°-3oo°) " (above 340°) A Microvolts. 0.76 11.94 -2.63 -1-34 —2.80 —17-15 21.8 83-57 3-04 B Microvolts. 1.0039 0.0506 1.0424 1.0094 —O.OIOI 0.0482 0.0000 0.0094 0.0506 -0.2384 0.0506 Thermoelectric power at mean temp. o£ junctions (microvolts). 20° C. 0.68 —6.0 22.6 26.4 17.0 12.95 13-56 97.0 89.0 65.0 45.0 -3-48 22. —1.52 O.IO -3-8 — 1.2 —3-0 —16.2 —17-5 0.00 —2.03 0.413 22.8 50° C. 0.56 14.47 12.7 39-9 —4-75 —2-45 + 19-3 —1.81 —3-30 —14.74 —12.10 —9.10 0.00 -1-75 3-3° 15-50 24-33 Neutral point _A_ B 19s —236 —62 —143 [—277] 356 236 [-431] Author- ity, T M B T B M B T B M T M M B T M B Smithsonian Tablcsi Tables 266 {,conitnued)-2Q7 , THERMOELECTRIC POWER. TABLE 266. — Thermoelectilo Power {continued). 259 Substance. A Microvolts. B Microvolts. Thermoelectric power at mean temp, of junctions (microvolts). 20° C. 50° C. Neutral point _A B Author- ity- Palladium Phosphorus (red) . • . Platinum " (hardened) . . (malleable) . . " wire .... " another specimen Platinum-iridium alloys : 85%Pt+iS%Ir . . 90%Pt+io%Ir . . 95%l^t+s%Ir . . Selenium Silver " (pure hard) . . . " wire Steel Tellurium Tin (commercial) . . . II Zinc " pure pressed . . . 6.18 —2.57 0.60 —7.90 —5.90 —6.15 — 11.27 0.43 0-0355 0.0074 0.0109 —0.0062 0.0133 —0.0055 —0.0147 0.0325 -0.0055 -0.0238 6.9 —29.9 —0.9 —2.42 8.82 —8.03 —5-63 —6.26 —807. —2.4T —3.00 —10.62 —502. —0.1 0-33 —2.79 —3-7 7.96 6.9 —2.20 1-15 —0.94 2.14 —8.21 -6.42 —2.86 —2.18 —9.65 -429-3 —0-33 0.16 —3-51 -174 347 —55 -1274] 444 1118][- -144 347 7'8 T B M T (( B M T M B T M B M T M B Ed. Becquerel, "Ann. de Chim. et de Phys." [4] vol. 8, M Matthiesen, " Pogg. Ann." vol. 103, reduced by Fleming Jenkin. T Tait, " Trans. R. S. E." vol. 27, reduced by Mascart. TABLE 267.— TbermoelectrlG Power against Platinum. One junction is supposed to be at 0° C ; -f indicates that the current flows from the 0° junction into the platinum. The rhodium and iridium were rolled, the other metals drawn.* Tempera- 26o Table 268. PELTIER EFFECT. The coefficient of Peltier effect may be calculated from the con- stants A and B of Table 255, as there shown. Experimental re- sults, expressed in slightly different units, are here given. The figures are for the heat production at a junction of copper and the metal named, in calories per ampere-hour. The current flowing from copper to the metal named, a positive sign indicates a warm- ing of the junction. The temperature not being stated by cither author, and Le Roux not giving the algebraic signs, these results are not of great value. Metals. Table 269. 261 VARIOUS DETERMINATIONS OF THE VALUE OF THE OHM. 262 Table 270. SPECIFIC RESISTANCE OF METALLIC WIRES. This table is modified from the table compiled by Jenkin (1862) from Matthiessen's results by taking the resistance of silver, gold, and copper from the observed metre gramme value aod assuming the densities found by Matthiessen, namely, 10.468, 19.265, and 8.95. Substance. Table 271. SPECIFIC RESISTANCE OF METALS. 263 The specific resistance is here given as the resistance, in microhms, per centimetre of a bar one square centimetre in cross section. Substance. 264 Table 272. RESISTANCE OF METALS AND The electrical resistance of some pure metals and of some alloys have been determined by Dewar and Fleming and increases as the temperature is lowered. The resistance seems to approach zero for the pure metals, but not for temperature tried. The following table gives the results of Dewar and Fleming.* When the temperature is raised above o° C. the coefficient decreases for the pure metals, as is shown by the experi- experiments to be approximately true, namely, that the resistance of any pure metal is proportional to its absolute is greater the lower the temperature, because the total resistance is smaller. This rule, however, does not even zero Centigrade, as is shown in the tables of resistance of alloys. (Cf. Table 262.) Temperature = -80° Metal or alloy. Specific resistance in c. g. s. units. Aluminium, pure hard-drawn wire . Copper, pure electrolytic and annealed . Gold, soft wire Iron, pure soft wire .... Nickel, pure (prepared by Mond's process from compound of nickel and carbon ^ monoxide) Platinum, annealed . . Silver, pure wire Tin, pure wire German silver, commercial wire Palladium-silver, 20 Pd + 80 Ag Phosphor-bronze, commercial wire Platinoid, Martino's platinoid with i to 2% ) tungsten ) Platinum-iridium, 80 Pt -+- 20 Ir Platinum-rhodium, 90 Pt -f 10 Rh . Platinum-silver, 66.7 Ag + 33.3 Pt . Carbon, from Edison-Swan incandescent ) lamp ) Carbon, from Edison-Swan incandescent lamp ) Carbon, adamantine, from Woodhouse and ) Rawson incandescent lamp ) 4745 1920 2665 I3970t 19300 10907 2139 13867 35720 15410 9071 44590 31848 18417 27404 3834X103 6i68Xio3 3505 1457 2081 9521 13494 8752 1647 10473 34707 14984 43823 29902 14586 26915 4046X io3 3908 Xio* 6300X lo^ 3161 1349 1948 8613 12266 8221 1559 9575 34524 14961 8479 43601 29374 13755 26818 4092X10' 3955X108 6363X10' 1400 7470 6133 1138 6681 33664 14482 8054 43022 27504 10778 263 II 4189X108 4054X108 6495X108 • " Phil. Mag." vol. 34, 1892. t This is given by Dewar and Fleming as 13777 for 96°.4, which appears from the other measurements too high. Smithsonian Tables. Table 272 {continued). ALLOYS AT LOW TEMPERATURES. 265 by Cailletet and Bouty at very low temperatures. The results show that the coefEcient of change with temperature the alloys. The resistance of carbon was found by Dewar and Fleming to increase continuously to the lowest ments or Miiller, Benoit, and others. Probably the simplest rule is that suggested by Clausius, and shown by these temperature. This gives the actual change of resistance per degree, a constant ; and hence the percentage of change approximately hold for alloys, some of which have a negative temperature coefficient at temperatures not far from Temperature =: 266 Table 273. CONDUCTIVITY OF THREE-METAL AND MISCELLANEOUS ALLOYS. Conductivity !n mhos or ohms per cm. cube =Ci=C^{i-at+bfi). Metals and alloys. Gold-copper-silver « it <( Nickel-copper-zinc Brass .... " hard drawn " annealed . German silver Aluminum bronze . . . Phosphor bronze . . . Silicium bronze . . . . Manganese-copper . . . Nickel-manganese-copper Nickelin Patent nickel Rheotan Copper-manganese-iron Manganin . Constantan Composition by weight. 58.3 Au -f 26.5 Cu + 1 5.2 Ag 66.5 Au -j- 15.4 Cu -f 18.1 Ag 7.4 Au 4- 78.3 Cu + 14,3 Ag I 12.84 Ni + 30.59 Cu + ) \ 6.57 Zn by volume . . . ) Various 70.2 Cu-f 29.8 Zn .... Various ! 60.16 Cu + 25.37 Zn + 1 4.03 Ni+ .30 Fe with trace \ of cobalt and manganese . 30 Mn + 70 Cu 3 Ni + 24 Mn -f- 73 Cu . . ^i8.46Ni + 61.63 Cu-f ? 19.67 Zn -\- 0.24 Fe -)- ( 0.19 Co + 0.18 Mn . . . ( 25.1 Ni-f- 74.41 Cu + l 0.42 Fe -f 0.23 Zn + (0.13 Mn -j- trace of cobalt ( 53.28 Cu -f 25.31 Ni -f- ] 16.89 Zn -1-4.46 Fe4- ( 0.37 Mn 91 Cu -1- 7.1 Mn -}- i.9Fe . 70.6 Cu -|- 23.2 Mn -|- 6.2 Fe 69.7 Cu -}- 29.9 Ni -\- 0.3 Fe 84CU-I- i2Mn-}-4Ni. . 60 Cu -f- 40 Ni 7.58 6.83 28.06 4.92 I2.2-I5.6 Table 274. 267 CONDUCTING POWER OF ALLOYS. This table shows the conducting power of alloys and the variation of the conducting power with temperature.* The ,06 values of C„ were obtained from the original results by assuming silver = —^ mhos. The coDductivity is taken as C,= C„ {i—ai+ifl), and the range of temperature was from o° to ioo° C. The table is arranged in three groups to show (i) that certain metals when melted together produce a solution which has a conductivity equal to the mean of the conductivities of the components, (2) the behavior of those metals alloyed with others, and (3) the behavior of the other metals alloyed together. It is pointed out that, with a few exceptions, the percentage variation between o^ and loo*^ can be calculated from the formula P-^P^ -^ where/ is the observed and /' the calculated conducting power of the mixture at 100° C., and Pc is the calculated mean variation of the metals mixed. Alloys. Weight% Vo lume % of first named. Co aXio" 5Xio9 Variation per 100° C. Observed. Calculated Group i. SnePb Sn4Cd SnZn PbSn ZnCd2 SnCd4 CdPbe 77.04 82.41 78.06 64.13 24.76 23.05 7-37 83.96 83.10 77.71 53-41 26.06 23.50 IO-57 7-57 9.18 10.56 6.40 16.16 13-67 5-78 3890 4080 3880 3780 3780 3850 3500 8670 1 1870 8720 8420 8000 9410 7270 30.18 28.89 30.12 29.41 29.86 29.08 27.74 29.67 30-03 30.16 29.10 29.67 30.25 27.60 Group 2. Lead-silver (Pb2oAg) Lead-silver (PbAg) Lead-silver (PbAga) Tin-gold (Snt2Au) " " (SnsAu) Tin-copper Tin-silver Zinc-copper t " t " t " t " " t 95-05 48.97 32-44 77-94 59-54 92.24 80.58 12.49 10.30 9.67 4.96 I-I5 91.30 53-85 36.70 25.00 16.53 8.89 4.06 94.64 46.90 30.64 90.32 79-54 93-57 83.60 14.91 12.35 1 1.61 6.02 1.41 96.52 75-51 42.06 29-45 23.61 10.88 503 5.60 8.03 13.8b 5.20 3-03 7-59 8.05 5-57 6.41 7.64 12.44 39-41 7.81 8.65 13-75 13-70 13-44 29.61 38.09 3630 i960 1990 3080 2920 3680 3330 547 666 691 995 2670 3820 3770 1370 1270 1880 2040 2470 7960 3100 2600 6640 6300 8130 6840 294 1 185 304 705 5070 8190 8550 1340 1240 1800 3030 4100 28.24 16.53 17-36 24.20 22.90 28.71 26.24 5.18 5-48 6.60 9.25 21.74 30.00 29.18 12.40 11.49 12.80 17.41 20.61 19.96 7-73 10.42 14.83 5-95 19.76 14-57 3-99 4.46 5.22 7-83 20.53 23-31 11.8Q 11.29 10.08 12.30 17.42 20.62 NoTB. — Barus, in the " Am. Jour, of Sci." vol. 36, has pointed out that the temperature variation of platinum alloys containing less than 10% of the other metal can be nearly expressed by an equation j/ =:—— m, where y is the temperature coefficient and x the specific resistance, m and « being constants. If o be the temperature coefficient at 0° C. and s the corresponding specific resistance, i (a -f- m) =: «. For platinum alloys Barus's experiments gave >« =:— .000194 and n =: .0378. For steel m =: —.000303 and « ^ .0620. Matthiessen's experiments reduced by Barus gave for Gold alloys w =: — .000045, «= .00721. Silver »» =— .000112, « ^ .00538. Copper " m^— .000386, n= .00055. • From the experiments of Matthiessen and Vogt, "Phil. Trans. R. S." y. 154. t Hard-drawn. Smithsonian Tables. 268 Table 274 {continuti). CONDUCTING POWER OF ALLOYS. Group 3. Alloys. Weight% Volume% of first named. Co Table 275. 269 ELECTRICAL RESISTANCE OF STRAIGHT WIRES WITH ALTERNATING CURRENTS OF DIFFERENT FREQUENCIES. This table gives the ratio of the resistance of straight copper wires with alternating currents of different frequencies to the value of the resistance with direct currents. Diameter of wire in millimeters. 2/0 Table 276. INTERNATIONAL ATOMIC WEIGHTS AND ELECTROCHEMICAL EQUIVA- LENTS. The International Atomic Weiglits are quoted from the report of the International Committee on Atomic Weights ("Jour. Am. Chem. Soc.," vol. 32, p. 3, 1910). With the exception of the value given for silver and that corresponding to valence 2 for copper, the electrochemical equivalents given in this table have been calculated from the atomic weights and one or two of the more common apparent valences of the substance. The value given for silver is that which was adopted by the International Congress of Electricians at Chicago in 1894. Substance. Aluminum Antimony . Argon . . Arsenic Barium Bismuth . Boron . . Bromine . Cadmium . Caesium . Calcium . Carbon Cerium Chlorine . Chromium « Cobalt . . « Columbium Copper Dysprosium Erbium Europium . Fluorine . Gadolinium Gallium Germanium Glucinum . Gold , . Helium Hydrogen Indium . . Iodine . . Iridium Iron . . . Krypton . Lanthanum Lead . . Lithium Lutecium . Magnesium Manganese Symbol. Al Sb A As Ba Bi B Br Cd Cs Ca C Ce CI Cr u Co Cb Cu Dy Er Eu F Gd Ga Ge Gl Au He H In I Ir Fe Kr La Pb Li Lu Mg Mn Relative atomic wt. Oxygen = i6. 27.1 120.2 39-9 74.96 137-37 208.0 II.O 79.92 1 1 2.40 132.81 40.09 12.00 140.25 3546 52.0 (( 58-97 93-5 63;57 162.S 167.4 152.0 19.0 157-3 69.9 72.5 9.1 197.2 4.0 1.008 114.8 126.92 1 93- 1 S5;85 83.0 139.0 207.10 7.00 174.0 24.32 54-93 Relative atomic wt. Hydrogen =: i. 26.9 1 19-3 39-6 74-4 136.27 206.3 10.9 79.28 III. 51 131.76 39-77 11.99 139-14 35-19 51.6 58.50 92.8 63.07 t( 161. 2 166.1 150.8 18.9 156.1 69-3 71.9 9-03 195-7 4.0 1.000 113-9 125.91 191.6 5541 82.4 137-9 205.46 6.94 172.6 24-13 54-49 Valence. Electrochemical equivalent in grammes per coulomb X looo. .0936 .4152 .2491 .2590 •1554 .7118 .7185 43" .0380 .8283 0.5824 1-3764 0.2077 •0313 .7267 •3675 .1797 .0900 .3061 .2041 •1937 .6588 .3290 .8624 .1968 .2414 .0471 .68 1 8 .0104 0.3966 1-3153 0.5003 .2894 .1929 0.7202 1.0731 0.0725 .1260 .2846 .1423 Smithsonian Tables. Table 276 {continued). 271 INTERNATIONAL ATOMIC WEIGHTS AND ELECTROCHEMICAL EQUIVA- LENTS. Substance. Symbol. Relative atomic wt. Oxygen= i6. Relative atomic wt. Hydrogen =: i. Valence. Electrochemical equivalent in grammes per coulomb X looo. Mercury . . Molybdenum Neodymium . Neon . . . Nickel . . . Nitrogen . . Osmium . . O.xygen . . Palladium Phosphorus u Platinum . . Potassium . Praesodymium Radium . . Rhodium . . Rubidium Ruthenium . Samarium . Scandium Selenium • . Silicon . . . Silver . . . Sodium . . Strontium Sulphur . . Tantalum Tellurium Terbium . . Thallium . . Thorium . . Thulium . . Tin. . . . Titanium . Tungsten . . Uranium . . i< Vanadium . (( Xenon . . . Ytterbium . Yttrium . . Zinc . . . Zirconium Hg Mo Nd Ne Ni N Os O Pd Pt K Pr Rd Rh Rb Ru Sa Sc Se Si Ag Na Sr S Ta Te Tb Tl Th Tm Sn Ti W U 200.0 96.0 1443 20.0 5S.68 14.01 a 190.9 16.00 106.7 31.0 ti 195.0 39.10 140.6 226.4 102.9 8545 IOI.7 150.4 44.1 79.2 28.3 107.88 23.00 87.62 32.07 181.O 127.5 159.2 204.0 232.42 168.5 1 19.0 48.1 184. 238;S 51.2 Xe 272 Tables 277, 278. CONDUCTIVITY OF ELECTROLYTIC SOLUTIONS. This subject has occupied the attention of a considerable number of eminent workers in molecular physics, and a few results are here tabulated. It has seemed better to confine the examples to the work of one experimenter, and the tables are quoted from a paper by F. Kohl- rausch,* who has been one of the most reliable and successful workers in this field. The study of electrolytic conductivity, especially in the case of very dilute solutions, has fur- nished material for generalizations, which may to some extent help in the formation of a sound theory of the mechanism of such conduction. If the solutions are made such that per unit volume of the solvent medium there are contained amounts of the salt proportional to its electro- chemical equivalent, some simple relations become apparent. The solutions used by Kohlrausch were therefore made by taking numbers of grammes of the pure salts proportional to their elec- trochemical equivalent, and using a litre of water as the standard quantity of the solvent. Tak- ing the electrochemical equivalent number as the chemical equivalent or atomic weight divided by the valence, and using this number of grammes to the litre of water, we get what is called the normal or gramme molecule per litre solution. In the table, m is used to represent the number of gramme molecules to the litre of water in the solution for which the conductivities are tabulated. The conductivities were obtained by measuring the resistance of a cell filled with the solution by means of a Wheatstone bridge alternating current and telephone arrangement. The results are for i8° C, and relative to mercury at o° C, the cell having been standardized by filling with mercury and measuring the resistance. They are supposed to be accurate to within one per cent of the true value. The tabular numbers were obtained from the measurements in the following manner :— Let A',8= conductivity of the solution at i8° C. relative to mercury at o° C. A'J", = conductivity of the solvent water at iS° C. relative to mercury at o° C. i Then K^^—JC^g = k^^= conductivity of the electrolyte in the solution measured. -iS.= fi= conductivity of the electrolyte in the solution per molecule, or the " specific tn molecular conductivity." TABLE 277.—Value of ku lor a lew Electrolytes. This short table illustrates the apparent law that the conductivity in very dilute solutions is proportional to the amount of salt dissolved. m Table 279. 273 SPECIFIC MOLECULAR CONDUCTIVITY/*: MERCURY = 10'. 274 Tables 280, 281 . LIMITING VALUES OF fl. TEMPERATURE COEFFICIENTS. TABLE 280.— Llfflltlsg Valnea of )i. This table shows limiting values of fi = — . io» for infinite dilution for neutral salts, calculated from Table 271. Salt. Table 282. 275 THE EQUIVALENT CONDUCTIVITY OF SALTS, ACIDS AND BASES IN AQUEOUS SOLUTIONS. In the following table the equivalent conductance is expressed in reciprocal ohms. The con- centration is expressed in milli-equivalents of solute per litre of solution at the temperature to which the conductance refers. (In the cases of potassium hydrogen sulphate and phosphoric acid the concentration is expressed in milli-formula-weights of solute, KHSO4 or H3PO4, per litre of solu- tion, and the values are correspondingly the modal, or " formal," conductances.) Except in the cases of the strong acids the conductance of the water was subtracted, and for sodium acetate, ammonium acetate and ammonium chloride the values have been corrected for the hydrolysis of the salts. The atomic weights used were those of the International Commission for 1905, referred to oxygen as 16.00. Temperatures are on the hydrogen gas scale. r- * ..• • gramme equivalents Concentration m 2 \1000 litre Equivalent conductance in reciprocal ohms per centimetre cube gramme equivalents per cubic centimetre* 276 Table 282 (ctmiinued). THE EQUIVALENT CONDUCTIVITY OF SALTS, AQUEOUS SOLUTIONS. ACIDS AND BASES IN Table 283/ 277 THE EQUIVALENT CONDUCTIVITY OF SOME ADDITIONAL SALTS IN AQUEOUS SOLUTION. Conditions similar to those of the preceding table except that the atomic weights for 1908 were used. Substance. 2/8 Tables 284, 285. CONDUCTANCE OF IONS. - HYDROLYSIS OF AMMONIUM ACETATE. TABLE 284. —The Eaoivalent Conductance of the Separate Ions. Ion. Tables 286, 287. 279 DIELECTRIC CONSTANTS* TABLE 286.— Dielectric Constant (Specific IndnctlTO Oapaolty) Of Gasos. Atmospheric Pressure. Wave-lengths of the measuring current greater than loooo cm. Gas. Temp. °C Dielectric constant referred to Vacuum= i Air=i Authority. Air Ammonia Carbon bisulphide . . . Carbon dioxide .... (< << Carbon monoxide .... Ethylene Hydrochloric acid . . . Hydrogen Methane Nitrous oxide (N2O) . . If « a Sulphur dioxide .... i< 9= the dielectric constant at the temperature 6° C, Dt at the tempera- ture t° C, and a and )8 are quantities given in the following table, then Dq= Dt\\— a{i— e) + i3(/— 0)2]. The temperature coefficients are due to Badeker. Gas. 280 Tables 288, 289. DIELECTRIC CONSTANTS {.continued). TABLE 288.— Ohange of tbe Dielectric Constant of Qases with tlia Presinre, Gas. Air Carbon dioxide . , « i( Nitrous oxide, N2O Temper- ature,° C. 19 15 15 Pressure atmos. 20 40 60 80 100 20 40 60 80 ICO 120 140 160 180 10 20 40 10 20 40 Dielectric constant. I.OI08 I.0218 1.0330 1.0439 1.0548 I.OIOI 1.0196 1.0294 1.0387 1.0482 1.0579 1.0674 1.0760 1.0845 1.008 1.020 1.060 I.OIO 1.025 1.070 Authority. Tangl, 1907. Occhialini, 1905. Linde, 1895. TABLE 289.— Dielectric Constants of LUnlds. A wave-length greater than loooo centimetres is denoted by 00. Substance. Table 289 {continued). DIELECTRIC CONSTANTS OF LIQUIDS. A wave-length greater than loooo centimetres is desiguated by oo. 281 Substance. 282 Tables 290-291. DIELECTRIC CONSTANTS OF LIQUIDS {continued). TABLE 290.— Temperature Coetflclents of tbe FormnlA: Z><,= A[i-o(/— e)+/3(/- 0)2]. Substance. Tables 292, 293. -DIELECTRIC CONSTANTS {continwd). 283 TABLE 292. — Standard Solutions for the Calibration ol Apparatus for the Measuring of Dlelectrlo Constants. Turner. Substance. Benzol . . . Meta-xylol . Ethyl ether . Aniline . . Ethyl chloride O-nitro toluol Nitrobenzol . Water (conduct, io-«) Diel. const. at iS""". A= 00. 2.288 2.376 4-36^ 7.298 10.90 27.71 3645 81.07 Drude. Acetone in benzol at 19°. A= 75 cm. Per cent by weight. O 20 40 60 80 100 Density 16°. 0.885 0.866 0.847 0.830 0.813 0.797 Dielectric constant. 2.26 5.10 8.43 I2.I 16.2 20.5 Temp. coeflScient. 0.1% 0-3 0.4 0-5 0.5 0.6 Water in acetone at 19°. A = 75 era. O 20 40 60 80 100 0.797 0.856 0.903 0.940 0-973 0.999 20.5 31-5 43-5 57 -o 70.6 80.9 0.6% 0.5 0.5 0.5 o. 0.4 Nemst. Ethyl alcohol in water at 19.5°. A= 00. Per cent by weight. 90 80 70 60 Dielectric constant. 26.0 29-3 33- S 38.0 43-1 284 Tables 293, 294. DIELECTRIC CONSTANTS {contmuel). TABLE 293. — Dlelectrlo Oonstants of SoUds {continued). Substance. Table 295. 285 VARIATION OF ELECTRICAL RESISTANCE OF CLASS AND PORCELAIN WITH TEMPERATURE. The following table gives the values of a, i, and c in the equation log Ji z= a + it + cfl, where Jt is the specific resistance expressed in ohms, that is, the resistance in ohms per centiffletre of a rod one square centimetre in cross section.* No. 286 Tables 296, 297. PERMEABILITY OF IRON. TABLE 296.— Permeability of lion Rings and Wire. This table gives, for a few specimens of iron, the magnetic induction B, and permeability ft, corresponding to th» magneto-motive forces H recorded in the first column. The first specimen is taken from a paper by Rowland,* and refers to a welded and annealed ring of " Burden's Best " wrought iron. The ring was 6.77 cms. in mean diameter, and the bar had a cross sectional area of 0.916 sq. cms. Specimens 2-4 are taken from a paper by Bosanquet.t and also refers to soft iron rings. The mean diameters were 21.5, 22.1, and 22.725 cms., and the thickness of the bars 2.535, 1.295, and .7544 cms. respectively. These experiments were intended to illustrate the effect of thickness of bar on the induction. Specimen 5 is from Ewing's book,t and refers to one of his own experiments on a soft iron wire .077 cms. diameter and 30.5 cms. long. H Table 297 {continued). PERMEABILITY OF TRANSFORMER IRON. 287 (b) Westinghousk No 288 Tables 298-300. MAGNETIC PROPERTIES OF IRON. TABLE 298.— Magnetic Properties of Iron and SteeL Tables 301, 302. DEMAGNETIZING FACTORS FOR RODS. TABLE 301. 289 H^ true intensity o» magnetizing field, H'= intensity of applied field, /= in- tensity of magnetization, H^H'—NI. Shuddemagen says : The demagnetizing factor is not a constant, falling for highest values of /to about 1/7 the value when unsaturated; for values of B {=//-i-4-ir /) less than loooo, A' is approximately constant; using a solenoid wound on an insulating tube, or a tube of split brass, the reversal method gives values for yV^ which are considerably lower than those given by the step-by-step method ; if the solenoid is wound on a thick brass tube, the two methods prac- tically agree. Ratio of Length to Diameter. 290 Table 303. COMPOSITION AND MAGNETIC This table and Table 289 below are taken from a paper by Dr. Hopkinson * on the magnetic properties of iron and steel, which is stated in the paper to have been 240. The maximum magnetization is not tabulated ; but as stated in the by 4ir. " Coercive force" is the magnetizing force required to reduce the magnetization to zero. The '"demag- previous magnetization in the opposite direction to the " maximum induction " stated in the table. The "energy which, however, was only found to agree roughly with the results of experiment. No Table 303 {continued). PROPERTIES OF IRON AND STEEL. 291 The numbers in the columns headed "magnetic properties" give the results for the highest magnetizing force used, paper, it may be obtained by subtracting the magnetizing force (240) from the maximum induction and then dividing netizing force " is the magnetizing force which had to be applied in order to leave no residual magnetization after dissipated" was calculated from the formula:— Energy dissipated = coercive force X maximum induction ~ ir 292 Tables 304-306. PERMEABILITY OF SOME OF THE SPECIMENS IN TABLE 303. This table gives the induction and the permeability for different values of the magnetizing force of some of the speci- mens in Table 303. The specimen numbers refer to the same table. The numbers in this table have been taken from the curves given by Dr. Hopkinson, and may therefore be slightly in error ; they are the mean values for rising and falling magnetizations. Tables 307-31 3. MAGNETIC PROPERTIES OF METALS. TABLE 307. - Cobalt at 100° 0. TABLE 308. —Nickel at 100° 0. 293 H 294 Tables 314-316. Table 314.-MAGNETIC PROPERTIES OF IRON IN VERY WEAK FIELDS. The effect of very small magnetizing forces has been studied by C. Baur* and by Lord Rayleigh.t The following short table is taken from Baur's paper, and is taken by him to indicate that the susceptibiluy is finite for zero values of H and for a finite range increases in simple proportion to H. He gives the formula /4^= 15 + 100 //, or /= ^ 1_ ,00 //2. The experiments were made on an annealed ring of round bar 1.013 cms. radius, the ring having a radius of 9.432 cms. Lord Rayleigh's results for an iron wire not annealed give ,4 = 6.4+ 5.1 H,or 1=:(>.^H J.. , ff2^ xhe forces were reduced as low as 0.00004 c. g. s., the relation of ^ to jY remaining constant. First experiment. Table 31 7. 295 DISSIPATION OF ENERGY IN THE CYCLIC MAGNETIZATION OF VARIOUS SUBSTANCES. C. P. Steinmetz concludes from his experiments* that the dissipation of energy due to hysteresis in magnetic metals can be expressed by the formula e=^aB^-^, where e is the energy dissipated and a a constant. He also concludes that the dissipation is the same for the same range of induction, no matter what the absolute value of the terminal inductions may be. His experiments show this to be nearly true when the induction does not exceed -|- 15000 c. g. s. units per sq. cm. It is possible that, if metallic induction only be taken, this may be true up to saturation ; but it is not likely to be found to hold for total inductions much above the satura- tion value of the metal. The law of variation of dissipation with induction range in the cycle, stated in the above formula, is also subject to verification.f Values of Constant a. The following table gives the values of the constant a as found by Steinmetz for a number of different specimens. The data are taken from his second paper. Number of specimen. Kind of material. Description of specimen. Value of 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 22 23 24 25 26 Iron Steel Cast iron it i< Magnetite Nickel « Cobalt Iron filings Norway iron ........ Wrought bar ........ Commercial ferrotype plate Annealed " " Thin tin plate Medium thickness tin plate Soft galvanized wire ...... Annealed cast steel Soft annealed cast steel Very soft annealed cast steel Same as 8 tempered in cold water .... Tool steel glass hard tempered in water " " tempered in oil " " annealed....... ( Same as 12, 13, and 14, after having been subjected ) } to an alternating m. m. f. of from 4000 to 6000 [ ( ampere turns for demagnetization . . . . ) Gray cast iron " " " containing J % aluminium " " " " i% " . . ( A square rod 6 sq. cms. section and 6.5 cms. long, ) < from the Tilly Foster mines, Brewsters, Putnam > ( County, New York, stated to be a very pure sample ) Soft wire ( Annealed wire, calculated by Steinmetz from I Swing's experiments Hardened, also from Ewing's experiments ( Rod containing about 2 % of iron, also calculated ) j from Ewing's experiments by Steinmetz . . ) ' Consisted of thin needle-like chips obtained by milling grooves about 8 mm. wide across a pile of thin sheets clamped together. About 30 % by vol- ume of the specimen was iron. 1st experiment, continuous cyclic variation of m. m. ) f. I So cycles per second j 2d experiment, 114 cycles per second [ 3d " 79-91 cycles per second . . . .00227 .00326 .00548 .00458 .00286 .00425 .00349 .00457 .00318 .02792 .07476 .02670 .01899 .06130 .02700 .01445 .01300 .01365 .01459 .02348 .0122 .0156 .0385 .0120 •0457 .0396 •0373 * " Trans. Am. Inst. Elect. Enp." January and September, 1892. t See T. Gray, " Proc. Roy. Soc." vol. Ivi. Smithsonian Tables. 296 Table 318. ENERGY LOSSES IN TRANSFORMER STEELS. Determined by the wattmeter method. Loss per cycle per cc= AB'-^-bnBv, where ^= flux density in gausses and « = frequency in cycles per second, x shows the variation of hysteresis with B between 5000 and loooo gausses, and y the same for eddy currents. Table 31 9. 297 MACNETO-OPTIC ROTATION. Faraday discovered that, when a piece of heavy glass is placed in magnetic field and a beam of plane polarized light passed through it in a direction parallel to the lines of magnetic force, the plane of polarization of the beam is rotated. This was subsequently found to be the case with a large number of substances, but the amount of the rotation was found to depend on the kind of matter and its physical condition, and on the strength of the magnetic field and the wave-length of the polarized light. Verdet's experiments agree fairly well with the formula— '-^'H-^T.n- where r is a constant depending on the substance used, / the length of the path through the substance, // the intensity of the component of the magnetic field in the direction of the path of the beam, r the index of refraction, and \ the wave-length of the light in air. If // be dif- ferent, at different parts of the path, /// is to be taken as the integral of the variation of mag- netic potential between the two ends of the medium. Calling this difference of potential z', we may write 6=^ Av, where A is constant for the same substance, kept under the same physical conditions, when the one kind of light is used. The constant A has been called " Verdet's con- stant," * and a number of values of it are given in Tables 303-310. For variation with tempera- ture the following formula is given by Bichat : — Ji =1 /^(,(i — 0.00104;? — 0.000014/2), which has been used to reduce some of the results given in the table to the temperature corre- sponding to a given measured density. For change of wave-length the following approximate formula, given by Verdet and Becquerel, may be used :— where fi is index of refraction and A wave-length of light. A large number of measurements of what has been called molecular rotation have been made, particularly for organic substances. These numbers are not given in the table, but numbers proportional to molecular rotation may be derived from Verdet's constant by multiplying in the ratio of the molecular weight to the density. The densities and chemical formulae are given in the table. In the case of solutions, it has been usual to assume that the total rotation is simply the algebraic sum of the rotations which would be given by the solvent and dissolved substance, or substances, separately; and hence that determinations of the rotary power of the solvent medium and of the solution enable the rotary power of the dissolved substance to be calculated. Experiments by Quincke and others do not support this view, as very different results are obtained from different degrees of saturation and from different solvent media. No results thus calculated have been given in the table, but the qualitative result, as to the sign of the rotation produced by a salt, may be inferred from the table. For example, if a solution of a salt in water gives Verdet's constant less than 0.0130 at 20° C, Verdet's constant for the salt is negative. The table has been for the most part compiled from the experiments of Verdet,t H. Becque- rel,}: Quincke, § Koepsel,|| Arons,1[ Kundt,** Jahn.tt Schbnrock.JJ Gordon, §§ Rayleigh and Sidgewick,|||| Perkin,iri[ Bichat.*** As a basis for calculation, Verdet's constant for carbon disulphide and the sodium line D has been taken as 0.0420 and for water as 0.0130 at 20° C. * The constancy of this quantity has been verified through a wide range of variation of magnetic field by H. £ J. G. Du Bois (Wied. Ann. vol. 35). t "Ann. de Chim. et de Phys." [3] vol. 52. t " Ann. de Chim. et de Phys." [5] vol. 12 ; " C. R." vols. 90 and 100. § " Wied. Ann." vol. 24. II " Wied. Ann." vol. 26. • IT "Wied. Ann." vol. 24. * " Wied. Ann." vols. 23 and 27. tt "Wied. Ann." vol. 43. tX " Zeits. fiir Phys. Chem." vol. 11. §§ " Proc. Roy. Soc." 1883. nil " Phil. Trans. R. S." 1885. IFli " Jour. Chem. Soc." vols. 8 and 12. *** "Jour, de Phys." vols. 8 and 9. Smithsonian Tables. 298 Table 320. MACNETO-OPTIC ROTATION. SoUds. Substance. Table 321. MACNETO-OPTIC ROTATION. Liquids. 299 30O Table 321 {continued). MACNETO-OPTIC ROTATION. LUulds. Table 322. MAGNETO-OPTIC ROTATION. Solutions of Acids and Salts in Water. 301 302 Table 322 {continued). MACNETO-OPTIC ROTATION. Solntlons of Acids and Salts In Water. Substance. Tables 322 (cat!i!nuecf)-32A, MACNETO-OPTIC ROTATION. TABLE 322. — Solutions of Acids and Salts in Water. 303 Substance. .304 Tables 325, 326. TABLE 326. — Magneto-Optlo Rotation. Gases. Tables 327, 328. TABLE 327.— Magnetic Susceptibility of Liquids and Oases. 305 The following table gives a comparison by Du Bois • of his own and some other determinations of the magnetic sua. ceptibility of a few standard substances. Verdet's and Kundt's constants are in radians for the sodium line D. Substance. 306 Tables 329-331 . RESISTANCE OF METALS. TABLE 329. —Variation of Resistance of Blsmutli, with Temperature, in a Transverse Hagnetlo Field. TABLE 332. Tables 332, 333. -Transverse Galvanomagnetic and Thermomagnetlc Effects. 307 Effects are considered positive when, the magnetic field being directed away from the observer, and the primary current of heat or electricity directed from left to right, the upper edge of the Specimen has the higher potential or higher temperature. .£;= difference of potential produced; 7"= difference of temperature produced; /= primary dt current; ^ = primary temperature gradient; .5= breadth, and Z?= thickness, of specimen; .^= intensity of field. C. G. S. units. Trr Hall effect (Galvanomagnetic difference of Potential), E= ^-f^ Ettingshauscn effect ( " Nemst effect (Thermomagnetic Leduc effect ( " TTT " Temperature), T=P-^ " Potential), E=QHB^ " Temperature), T=S//B dt_dx Tellurium Antimony Steel . . . Hensler alloy Iron . . . Cobalt . . Zinc . . . Cadmium Iridium . . Lead . . . Tin. . . . Platinum . . Copper . . German silver Gold . . . Constantine. Manganese . Palladium . Silver . . . Sodium . . Magnesium . Aluminum . Nickel . . Carbon . . Bismuth . . Values of R. +400 to Soo 4- 0.9 " 0.22 +.012 " 0.033 4- .010 " 0.026 +•007 " 0.0 1 1 +.0016 " 0.0046 + .00055 + .00040 +.00009 — .00003 — .0002 — .00052 — .00054 — .00057 to .00071 — .0009 — .00093 0007 to .0012 .0008 " .0015 —.0023 — .00094 to .0035 — .00036 " .0037 — .0045 " .024 — .017 — up to 16. P X 108. + 200 + 2 —0.07 0.06 +0.01 +0.04 to 0.19 + 5- +3 to 40 Q X 106. —360000 +9000 to 18000 —700 " 1700 + 1600 " 7000 — 1000 " 1500 + 1800 " 2240 —54 " 240 up to —5.0 —5.0 {>) -4.0 (.?) —90 to 270 + 50 to 130 —46 " 430 + 2000 " 9000 + 100 — up to 132000 .S- X io«, +400 + 200 +69 +39 + 13 + 13 + 5 —3 —41 —45 TABLE 333. —Variation of Hall Constant with the Temperature. Bismuth.* APPENDIX I. Tables 334, 335. THE SPECIFIC HEAT OF IRON AT HIGH TEM- PERATURES. Analysis of iron— (o.oi C, .02 Si, .03 S, .04 P, trace Mn). TABLE 334. — nean Specific Heat between 0° and T° Centigrade, S?. APPENDIX II. DEFINITIONS OF UNITS. ACTIVITY. Power or rate of doing work; unit, the watt. AMPERE. Unit of electrical current. The international ampere, "which is one tenth of the unit of current of the C. G. S. system of electro-magnetic units, and which is represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with accompanying specifica- tions" (5ee pages xxxiv and 251), "deposits silver at the rate of o.ooi 118 of a gramme per second." The ampere = I coulomb per second = 1 volt through i ohm; Amperes = volts/ ohms= watts/ volts = (watts /ohms)*. AmperesX volts = amperes ^ Xohms = watts. ANGSTROM. Unit of wave-length = io-i» metre. ATMOSPHERE. Unit of pressure. English normal = 14.7 pounds per sq. in. =29.929 in. =760.18 mm. Hg. 32° F. French " =760 mm. of Hg. 0° C. =29.922 in. = 14.70 lbs. per sq. in. BARAD. C. G. S. unit of pressure = 1 dyne per sq. cm. BOUGIE DECIMALE. Photometric standard; see page 177. BRITISH THERMAL UNIT. Heat required to raise one pound of water at its temper- ature of maximum density, 1° F. = 252 gramme-calories. CALORY. Small calory = gramme-calory = therm = quantity of heat required to raise one gramme of water at its maximum density, one degree Centigrade. Large calory = kilogramme-calory = 1000 small calories = one kilogramme of water raised one degree Centigrade at the temperature of maximum density. For conversion factors see page 227. CANDLE. Photometric standard, see page 177. CARAT. The diamond carat =3.168 grains = 0.2053 grammes. The gold carat: pure gold is 24 carats; a carat is 1/24 part. CARCEL. Photometric standard; see page 177. CIRCULAR AREA. The square of the diameter = 1.2733 X true area. True area = 0.785398 X circular area. COULOMB. Unit of quantity. The international coulomb is the quantity of electricity transferred by a current of one international ampere in one second. Coulombs = (volts-seconds) /ohms = amperesX seconds. CUBIT = 18 inches. DAY. Mean solar day = 1440 minutes = 86400 seconds = 1.0027379 sidereal day. Sidereal day = 86164.10 mean solar seconds. DIGIT. 3/4 inch; r/12 the diameter of the sun or moon. DYNE. C. G. S. unit of force = that force which acting for one second on one gramme pro- duces a velocity of one centimetre per second. = weight in grammes divided by the acceleration of gravity in cm. per sec. ENERGY. See Erg. ERG. C. G. S. unit of work and energy =one dyne acting through one centimetre. For conversion factors see page 227. FARAD. Unit of electrical capacity. The international farad is the capacity of a con- denser charged to a potential of one international volt by one international coulomb of electricity. The one- millionth part of a farad (microfarad) is more commonly used. Farads = coulombs/ volts. FOOT-POUND. The work which will raise one pound one foot high. For conversion factors see page 227. FOOT-POUNDALS. The English unit of work = foot-pounds /g. For conversion factors see page 227. g. The acceleration produced by gravity. GAUSS. A unit of intensity of magnetic field = lO^ C. G. S. units. GRAMME. See page 6. 3IO APPENDIX. GRAMME-CENTIMETRE. The gravitation unit of work=g. ergs. For further conversion factors see page 227. HEAT UNIT. See Calory. HEAT OF THE ELECTRIC CURRENT generated in a metalhc circuit without self- induction is proportional to the quantity of electricity which has passed in coulombs multiplied by the fall of potential in volts, or is equal to (coulombsXvolts)/4.i8i in small calories. The heat in small or gramme-calories per second = (amperes ^ X ohms) /4.i8i= volts ^7 (ohms X4.i8i)=(voltsX amperes) /4.i8i = watts/4.181. HEAT. Absolute zero of heat = -273° Centigrade, -4594° Fahrenheit, -218.4° Reaumur. HEFNER UNIT. Photometric standard; see page 177. HENRY. Unit of induction. It is "the induction in a circuit when the electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second." HORSE-POWER. The practical unit of power = 33,000 pounds raised one foot per min- ute. JOULE. Unit of work = 10' ergs. Joules = (volts^X seconds) /ohms = wattsX seconds = amperes^XohmsX sec. For conversion factors see page 227. JOULE'S EQUIVALENT. The mechanical equivalent of heat = 4.i8i Xio^ ergs. See page 227. KILODYNE. 1000 dynes. About i gramme. LITRE. See page 6. MEGABAR. Unit of pressure = 0.987 atmospheres. MEGADYNE. One million dynes. About one kilogramme. METRE. See page 6. METRE CANDLE. The intensity lumination due to standard candle distant one metre. METRET. An exponential subdivision of the metre. The ordinal number before the word metre denotes the power of ten serving as the divisor; e. g., a tenth-metret = 10-^" = 1/10'° metre. The first metret is the decimetre, the second, the centimetre, etc. MHO. The unit of electrical conductivity. It is the reciprocal of the ohm. MICRO. A prefix indicating the millionth part. MICROFARAD. One millionth of a farad, the ordinary measure of electrostatic capacity. MICRON, (m) =one millionth of a metre. MIL. One thousandth of an inch. MILE. See pages 5, 6. MILE, NAUTICAL or GEOGRAPHICAL = 6080.204 feet. MILLI-. A prefix denoting the thousandth part. MONTH. The anomaUstic month = time of revolution of the moon from one perigee to another = 27.55460 days. The nodical month = draconitic month = time of revolution from a node to the same node again = 27.21222 days. The sidereal month = the time of revolution referred to the stars = 27.32166 days (mean value), but varies by about three hours on account of the eccentricity of the orbit and "perturbations." The synodic month = the revolution from one new moon to another = 29.5306 days (mean value) =the ordinary month. It varies by about 13 hours. OHM. Unit of electrical resistance. The international ohm is based upon the ohm equal to 10' units of resistance of the C. G. S. system of electromagnetic units, and "is repre- sented by the resistance offered to an unvarying electric current by a column of mer- cury, at the temperature of melting ice, 14.4521 grammes in mass, of a constant cross section and of the length of 106.3 centimetres." International ohm = 1.01367 B. A. ohms = 1.06292 Siemens* ohms. B. A. ohm =0.98651 international ohms. Siemens' ohm =0.94080 international ohms. See page 261. PENTANE CANDLE. Photometric standard. See page 177. PI=7r = ratio of the circumference of a circle to the diameter =3.14159265359. POUNDAL. The British unit of force. The force which will in one second impart a veloc- ity of one foot per second to a mass of one pound. RADIAN = 1 80° /t = 57.29578° = 57° 17' 45" = 206625". SECOHM. A unit of self-induction = i second X i ohm. THERM = small calory = quantity of heat required to warm one gramme of water at its temperature of maximum density one degree Centigrade. THERMAL UNIT, BRITISH = the quantity of heat required to warm one pound of water at its temperature of maximum density one degree Fahrenheit = 252 gramme-calories. VOLT. The unit of electromotive force (E. M. F.). The international volt is "the electromotive force that, steadily applied to a conductor whose resistance is one inter- national ohm, will produce a current of one international ampere, and which is repre- sented sufficiently well for practical use by 1000/1434 of the electromotive force be- APPENDIX. 311 ' tween the poles or electrodes of the voltaic cell known as Clark's cell, at a temperature of 15° C and prepared in the manner described in the accompanying specification." See pages xxxiv and 251. VOLT-AMPERE. Equivalent to Watt. WATT. The unit of electrical power = 10^ units of power in the C. G. S. system. It is re- presented sufficiently well for practical use by the work done at the rate of one Joule per second. Watts = volts Xamperes = amperes^ Xohms = volts''/ohms. For conversion factors see page 227. Watts Xseconds = Joules. WEBER. A name formerly given to the coulomb. YEAR. See page 108. Anomalistic year = 365 days, 6 hours, 13 minutes, 48 seconds. Sidereal " =365 " 6 " 9 " 9.314 seconds. Ordinary " =365 " 5 " 48 " 46+ TropicaJ " same as the ordinary year. INDEX. For the definitions of units, see Appendix. PAGE. Aberration constant 109 Absorption of gases by liquids 141 Absorption of Ught: atmosptieric 179 color screens 195 Jena glasses 193 various crystals . . . .194 Acceleration of gravity 104-107 Aerodynamic data: soaring data 123 wind pressures 122 Agonic line nS Air: density 160 Air thermometer, comparisons 234 Air: transmissibility of, for radiation . . . .179 Alcohol: density 98-100 vapor pressure 146 viscosity 126 Alloys: densities 89 electrical conductivity of ... . 266-268 resistance of .... 262-268 low temp. . . . 264 melting-points 214 specific heats 230 thermal conductivity 199 thermoelectric powers 258-259 Alternating currents, resistance of wires for . . 269 Aluminum wire, weights of 64 Alums: indices of refraction 181 Antilogarithms 26-28 Aqueous solutions : boiling-points 219 densities 92 alcohols 98 alcohol, temperature var'n 100 diffusion of 136 electrolytic conductivities 272-278 Aqueous vapor: vapor pressure, low temp . . .151 0° to 100° C . 152 100° to 230° C . 153 pressure of, in atmosphere . .155 (saturated) weight of .... 154 Astronomical data 108-109 Atmosphere, aqueous vapor in 155 transmissibility for radiation . . .179 Atomic weights 270 Barometer: boiling temperature of water for va- rious heights 168-169 correction for capillarity . . . .121 latitude, inch . . .119 metric . .120 sea level 118 temperature. . . .117 heights, determination of, by . . .167 Batteries: composition, electromotive forces . . 252 Beaume scale: conversion to densities .... 84 Birmingham wire gauge 59 Bismuth, resistance of, in magnetic field . . . 306 "Black-body" radiation 238 Boiling-points: chemical elements 210 inorganic compounds . . . .213 organic compounds 215 Boiling-point, raising of, by salts in solution . .219 of water and barometric pressure . 168 Brass wire, weights of, common measure ... 60 metric measure ... 62 Brick, crushing strength of 71 British wire gauge 59 British weights and measures 7-10 Cadmium line, wave-length red 170 Candle power, standard 177 Capacity, specific inductive: crystals .... 284 gases 279 liquids .... 280 liquid gases . . . 283 PAGE. Capacity, specific inductive: solids 283 Capillarity, correction to barometer for . . .121 liquids 142-143 liquids near solidifying point . . . 143 salt solutions in water 142 thickness of soap films 143 Carcel unit 177 Cells, voltaic: composition, E. M. F. . . 252-253 double-fluid 253 secondary 253 single-fluid 252 standard 251, 253 storage 253 Chemical, electro-, equivalents 270 equivalent of silver . . . .251 Chemical elements: atomic weights 270 boiling-points 210 compressibility 76 conductivity, thermal . . . 199 densities 8s, 91 electro-chemical equivalents 270 hardness 76 melting-points 209 resistance, electrical . 262-263 specific heats 228 thermal conductivities . . 199 expansion, linear . 222 Circular functions: argument (°') 30 (radians) .... 35 Coals, heat of combustion of 202 Cobalt, magnetic properties of 293 Color screens 195-196 Combination, heat of 204 Combustion, heat of: coals 202 explosives 203 fuels (liquid) 202 peats 202 Compressibility: chemical elements .... 76 gases 79-^1 liquids 82 solids 83 Concretes: resistance to crushing 71 Conductivity, electrical: see Resistance. alloys 266-268 alternating currents, effect of . 269 magnetic field, effect of . . . 306 electrolytic 272-278 equivalent . . . 275-278 ionic (separate ions) . . 278 specific molecular . . . 273 limiting values 274 temp 'tare coef. 274 glass and porc'l'n, temp'ture coef. 285 Conductivity, thermal: gases 200 liquids 200 salt solutions .... 200 solids 199 water 200 Contact differences of potential .... 254-256 Convection, cooling by ...... . 239-240 Conversion: Beaume to specific gravities ... 84 factors for work units 227 Cooling by radiation, perfect radiator .... 238 and convection . . 239-240 Cosines, hyperbolic natural 41 logarithmic 42 Critical data for gases 221 Crushing, resistance to: bricks 71 concretes 71 stones 71 timber, wood .... 72 Cubical thennal expansion: gases 226 liquids 225 solids 224 314 INDEX. Crystals: dielectric constant 284 elasticity 77-78 expansion, cubical thermal .... 224 transmissibility for radiation . . . .194 Current, absolute, measures 251 Cyclic magnetization, energy losses in . . 294-296 Declination, secular change of magnetic . . .110 Demagnetizing factors for rods 289 Density : air : values of h/Tto 160 alcohol : aqueous ethyl 98 methyl 98 temperature variation . . .100 alloys 89 aqueous alcohol 98 salt, acid, basic solutions . . 92 chemical elements 8s, 91 earth 108 gases 91 liquids 90 mercury 97 metals 8s organic compounds 21s water 95-96 woods 87 Dew points 156 Dielectric constant: (specific inductive capacity) calibration, standards for . 283 gases, atm. pressure . . 279 pressure coef. . . 279 temperature coef. . 280 liquids 280 temperature coef. . 282 solids 283 Dielectric strength: air: alternating potential . 248 steady potential . . . 248 kerosene 250 large spark-gaps . . . 249 pressure effect . . . 249 various materials . .250 Difference of potential: cells: double fluid 2S3 secondary 2S3 single fluid 2S3 standard 2Si, 233 storage 253 contact: liquids-liquids in air . 254 metals in salt solutions 2S7 salts with liquids . . 2S4 solids-solids in air . . 256 thermo-electric 258 platinum couples 259 Differential formulae 12 Diffusion: aqueous solutions, water 136 gases and vapors : coefficients . . . 138 metals into metals 138 vapors 137 Dmusion integral 50 Dip, magnetic 112 secular change 112 Dynamical equivalent of thermal unit .... 327 e, value of 13 e*. «"" and their logarithms 43, 47 log. e*, * from 10 to 30 44 «*'• «~* . and their logarithms 45 £ , £ *' , and their logarithms 46 € ' , C * '. and their logarithms .... 46 " — r — , and their logarithms 41.42 e'-t" .. .. i — 39. 40 Earth: densities 108 miscellaneous data 1 08 Elasticity: crystals 77, 78 moduli of rigidity 74 modulus, Young's 75 Electrical conductivity: alloys .... 266-268 alternating current, effect of 269 magnetic field, effect of . . 306 Electrical resistance: see Conductivity. metals and alloys, low temp. 264 ohm, various determinations 261 specific: metallic wires . . 262 metals 263 temperature effect, glass . 285 Electricity, specific heat of 238 Electric units, dimensional formula xxvi Electrochemical equivalents 270, 272 silver 251 Electrolytic conductivity: 272-278 dilute solutions 272 equivalent % . . . . 275-278 ionic 278 specific molecular .... 373 limiting values 274 temp. coef. . 274 Electromagnetic system of units xxix Electromagnetic/electrostatic units = v ... 247 Electromotive force: cells: double fluid • . . 253 secondary .... 253 single fluid . . . .252 standard . . . 251, 253 storage 253 liquids-liquids in air . . 254 metals in salt solutions . . 257 salts with liquids .... 254 solids-solids in air . . . 256 thermo-electric .... 258 (platinum) . 259 Elements: atomic weights 270 boiling-points 210 compressibility 76 conductivity, thermal 199 densities 85, 91 electrochemical equivalents .... 270 hardness 76 melting-points 209 resistance, electrical 263 specific heats 228 spectra (prominent lines) .... 170 thermal conductivities 199 expansion, linear .... 223 cubical, gases . . 226 Elliptic integrals 57 Emission of perfect radiator 238 Equivalent, electro-chemical: elements . . . 270 ionic 272 silver 251 Equivalent, mechanical, of heat 227 Energy, data relating to solar 179 Ethyl alcohol, specific gravity of aqueous ... 98 Ettinghausen effect 307 Expansion, thermal: cubical, crystals .... 224 gases 226 liquids .... 225 solids 224 linear, elements .... 222 various 223 perfect gas 162 Explosives, composition, etc 203 Exponential functions: e", e~*, their logs. . . 43, 47 log. e*. «= 10 to 30 . . 44 «*", e"" , their logs ... 45 e^'.e-^'" "... 46 C * ',€ ~* '• their logs. 46 e'+x~' , their logs. . . 41, 42 diffusion integral . . hyperbolic sines . . cosines logs, hyperbolic sines cosines 39. 40 . SO . 39 . 41 . 40 42 probability integral . 47, 48 Eye, sensitiveness of, to radiation 178 Fabry-Buisson, standard arc Fe wave-lengths . 170 Factorials, n ! 38 Fechner's law 178 Field: earth's magnetic field, components of 110-115 magnetic, behavior of metals in . . 286-296 resistance of metals in 306 rotation of plane of polarization 297-304 thermo-, galvanometric effects . . 307 Films, thin: thickness, colors, tension of . 142, 143 ~ Fluorite: index of refraction 184 Formulse, conversion: dynamic units electric " . fundamental . geometric . , INDEX. 315 Formulm, conversion: heat 3 magnetic 3 see Introduction. Fraunhofer lines, wave-lengths of 176 Freezing mixtures 220 Freezing-points, lowering of, by salts in solution 217 Friction, coefficients of 124 Fuels, heats of combustion of 202 Functions: circular arguments (° ') . . ... . 30 (radians) . ' . . 35 exponential 39-47 gamma 52, 38 hyperbolic 39-42 Fundamental units 2 Fusion, latent heat of 208 Gcdvanometric effects of magnetic field . , . 307 Gamma function 52, 38 Gases: absorption of, by liquids .... 140, 141 atomic weights 270 compressibility of 7 9-81 conductivity, thermal 200 critical data for 221 densities 91 dielectric constants 279, 280 diffusion 138 expansion of perfect 162 expansion, thermal 226 heat, conductivity for 200 indices of refraction 190 magnetic susceptibility 305 magneto-optic rotation 304 refractive indices of 190 sound, velocity of, in 102 solubility of 140, 141 specific heats ?32 thermal conductivity 200 thermal expansion 226 viscosity of 134 volume of perfect (1+0.003760 . . 162-165 Gas thermometry 233-235 Gauges, wire: Birmingham 59 British standard 59 Brown and Sharp 66 Geodetic data 108 Geometric units, conversion factors for ... 2 Glass: indices of refraction 180 transraissibility of Jena 193 various . . . 195-196 electric resistance, temp, variation . . 285 Glass vessels, volumes of 11 Gravity, force of 104-106 correction to barometer 118 Gyration, radii of 58 Hall effect 307 Hardness 76 Harmonics, zonal 54 Heat: combination, heat of 204 combustion: coals 202 explosives 203 fuels liquid 202 peats 202 conductivity for: gases 200 liquids 200 salt solutions .... 200 solids 199 water 200 latent heat of fusion 208 vaporization. . . . 206, 241 mechanical equivalent of 227 specific: elements 228 gases 232 liquids 230 mercury 229 minerals 231 rocks 231 solids 230 vapors 232 water 229 " Heat, specific," of electricity 258 Hefner photometric unit I77 Heights determinations of by barometer . . . 167 Horizontal intensity of earth's field . . . .114 secular change 114 Humidity, relative 158 Humidity term, o.378e 1S9 Hydrogen thermometer 233 Hyperbolic cosines, natural 41 logarithmic ..... 42 Hyperbolic sines, natural 39 logarithmic 40 Hysteresis: soft iron cable transformer .... 294 wire 294 steel, transformer 296 various substances 295 Iceland spar, refractive index of 184 Inclination (dip) of magnetic needle , . . .112 secular change of 112 Index of refraction: alums 181 crystals 187 fiuorite 184 gases and vapors .... 190 glass 180 Iceland spar 184 liquids 189 metals, metallic oxides . . 182 monorefringent solids . . 186 nitroso-dimethyl-aniline . 184 quartz 185 rocli-salt 183 salt solutions 188 silvine 186 solids, isotropic . . . .186 Inductance, table for computing mutual . . . s6 Inductive capacity, specific: calibration st'ds . 283 gases, atm. pressure 279 pressure coef. 279 temp. coef. . 280 liquids 280 temp. coef. . 282 solids 283 Inertia, table of moments of 58 Inorganic compounds: boiling-points .... 213 melting-points . . .211 Integral, diffusion so elliptic 57 gamma function 52 probability 45, 47-48 Integrals, elementary 12 Intensity, horizontal, of earth's field .... 113 secular variation 113 total, of earth's field 114 secular variation 114 Ionization of water 278 Ions: equivalent conductivity of 278 Iron: hysteresis in soft 294 magnetic properties of, weak fields . . . 294 saturated . . . 293 permeabilities 286-292 specific heat at high temperatures . . . 308 standard arc lines, Fabry-Buisson . . . 170 Kayser 174 Joule's (mechanical) equivalent of heat . . . 227 Kayser's standard iron arc spectrum .... 174 Kerosene, dielectric strength 250 Kerr's constant 30S Kundt's constant 304 definition of 304 Latent heat of fusion 208 vaporization 206, 241 Latitude correction to barometer .... 119-120 Least squares 47-49 Legal electrical units xxxiv Leduc thermomagnetic effect 307 Light: indices of refraction 181-190 reflection of; function of "n" . . . . 191 metals 192 sensitiveness of eye to 178 transmissibility to, of substances . 193-196 polarized: rotation of plane by solutions 197 rotation, magneto . . . 297-304 wave-lengths: cadmium st'd line . . . 170 elements, brighter lines . 170 Fraunhofer, lines . . . 176 st'd iron arc, Fabry . .170 Kayser . . 174 solar, Rowland . .171 velocity of 109 Linear thermsd expansion coef. of elements , . 22a various . . . 223 Liquids: absorption of gases by 141 capillarity of 142-143 compressibility of 82-83 conductivity, thermal 200 densities 85, 90, 95-96 dielectric constants 280-282 dielectric strength 2S0 diffusion, aqueous solutions .... 136 expeinsion, thermal 225 3i6 INDEX. Liquids : fuels, heat of combustion 202 magnetic susceptibility 30S magneto-optic rotation 304 potential differences with liquids . . 254 metals . . 257 salts . . . 254 specific heats 230 surface tensions 142-143 thermal conductivity 200 expansion 225 vapor pressures 144-153 velocity of sound 102 viscosity 127-128 Logarithms 24 1000-2000 22 anti- 26 .9000-1.0000 28 Lowering of freezing-points by salts 217 Maclaurin's theorem 12 Magnetic field: bismuth, resistance in ... . 306 Ettingshausen effect .... 307 galvanomagnetic effects . . . 307 Hall effect 307 Leduc effect 307 Nemst effect 307 nickel, resistance in .... 306 optical rotation .... 297-304 resistance of metals in ... 306 thermo-magnetic effects . . . 307 Magnetic properties: of cobalt at 100° C . . . 293 iron: hysteresis . 294-296 permeability 286-288. 292-293 saturated . . . 293 weak fields . . 294 magnetite 293 nickel at 100° C . . . 293 Magnetic susceptibility, liquids, gases .... 30s Magnetic units, conversion formulae .... 3 Magnetism, terrestrial: agonic line lis declination no dip 112 horizontal intensity . .113 inclination 112 intensity, horizontal . .113 total . . . .114 Magneto-optic rotation 297-304 Masses of the earth and planets 109 alloys 89 elements, liquid and solid 85 sohds 88 woods 87 Materials, strength of: bricks 71 concrete 71 metals 71 stones 71 timber 72-73 woods 72-73 Mechanical equivalent of heat 227 Melting-points: chemical elements 209 inorganic compounds . . . .211 mixtures (alloys) 214 (low melting-points) . 214 organic compounds . . . .215 Mercury: density of 97 electric resistance of ... . 262-263 pressure of columns of 116 specific heat 229 vapor pressure 148 Metals: diffusion of , into metals 138 indices of refraction 182 potential differences with solids . . . 256 solutions . . 257 reflection of light by 192 refractive indices 182 resistance, electrical 262-263 specific 263 sheet, weight of 70 Metallic oxides, refractive indices 182 Methyl alcohol, density of aqueous 98 Metric weights and measures: British equiv . 7-10 U. S. equivalents 5-6 Minerals, specific heats of 231 Mixtures, freezing 220 Moduli of elasticity: rigidity 74 Young's 75 Molecular conductivities: equivalent . . 275-278 specific . . . 271-274 Moments of inertia 58 Musical scales 103 Mutual inductance, table for computing ... 56 Nemst thermo-magnetic difference of potential . 307 Neutral points, thermo-electric .... 258-259 Newton's rings and scale of colors 198 Nickel: Kerr's constants for 305 magnetic properties of, at 100° C . . . 293 resistance in magnetic field .... 306 Nitroso-dimethyl-aniline, refractive index • . 184 Ohm, various determinations of 261 legal value 261 Oils, viscosity of 126 Orgcmic compounds, boiling-po'nts 215 densities 2 is melting-points . . . .211 Parallax: solar; lunar 109 Peltier effect 258, 260 Pendulum, length of seconds 107 Perfect gas, expansion of 162 volume of 162 Permeabilities, magnetic . . . 286-288, 292-293 Photometric standards 177 Pi, 77, value of 12 Planck's radiation formula 238 Plane, data for the soaring of a 123 Planets, miscellaneous data 109 Poisson's ratio 76 Polarized light: by reflection 191 rotation by magnetic field 297-304 solutions .... 197 Potential difference: cells: double fluid .... 253 secondary .... 253 single fluid .... 252 standard . . .251, 253 storage 253 contact: liquid-liquid . . 254 liquid-salt . . . 254 metal-liquid . . 257 solid-solid . . . 256 sparking: air . . . 248-249 kerosene . . . 250 various . . . 250 thermoelectric . . . 258-259 Precession 109 Pressure: barometric measures .... 117-121 barometric and boiling water . . 168-169 heights 167 mercury columns, due to 116 water columns, " " 116 wind 122 Pressure, vapor: alcohol, ethyl and methyl . . 146 aqueous: low temperature . . 151 0° to 100° C . . . 152 100° to 230° C . . 153 in atmosphere . .155 mercury 148 salt solutions 149 various 144-148 Probability tables 47-48 Purkinje's phenomenon 178 Quartz fibres, strength of 71 refractive index of 185 Radiation: black-body 238 constants of 238 cooling by, and convection . . 239-240 eye, sensitiveness of, to 178 Planck's formula 238 sensitiveness of the eye to ... . 178 "solar constant " of 179 Stefan's formula 238 transmissibility of atmosphere to . 179 Radii of gyration 58 Refraction, indices of : alums 181 crystals 187 fluorite 184 gases and vapors . . .190 glass 180 Iceland spar 184 liquids 189 metals, metallic oxides . 182 monorefringent solids . 186 nitroso-dimethyl-aniline . 184 quartz 1 85 rock-salt 183 salt solutions . . . .188 silvine 183 solids, isotropic . . . 186 Reflection of light: by metals 192 terms of "n" and "«" . 191 Relative humidity IS8 INDEX. 317 Resistance: see also Conductivity. alloys, low temperature .... 264 alternating current, effect of . . . 269 electrolytic, see Conductivity, glass and porcelain 285 legal unit of 261 magnetic field, of bismuth in . . . 306 metals in ... 306 nickel in ... . 306 metals at low temperatures . . . 264 ohm, various determinations of . .261 specific: metals 263 wires 262 temperature variation . . 262-266, 285 wire (copper) table, common units . 66 metric units . . 68 Rigidity, modulus of 74 temperature variation . . 74 Ring correction (magnetization) 288 Rock-salt, indices of refraction 183 Rods, demagnetizing factors for 289 Rotation of polarized light: by solutions . . . 197 Rotation, magneto-optic: formulae 297 gases 304 Kerr's constant . . 305 liquids 299 solids 298 solutions . . . 301-303 Verdet's constant 297-304 Rowland's standard wave-lengths 171 Salts, lowering of freezing-point by 217 raising " boiling- " " 219 Saturation, magnetic, for steel 293 Scales, musical 103 Screens, color 195-196 Seconds pendulum 107 Secondary batteries 253 Sections of wires 59-66 Shearing tests of timber 72-73 Sheet metal, weights of 70 Silver, electro-chemical equivalent . . . 251, 270 Silvine, indices of refraction 183 Sines, natural and logarithmic, circular . . 30-38 hyperbolic . 39-40 Sky-light, comparison with sunlight 179 Soaring of planes, data for 123 Solar constant of radiation 179 energy, data of 179 wave-lengths, Rowland's 171 Solids: compressibility 76, 83 densities 85-89 dielectric constant 283 electrical resistance 261-269 hardness 76 indices of refraction 183-187 magneto-optic rotation by 298 thermal conductivity 199 expansion 222-224 Solutions: boiling-point, raising by sjilts in . . 219 boiling-points of aqueous .... 219 conductivity, thermal 200 electrolytic . . 272-278 densities of aqueous 92-93 diffusion of aqueous 136 freezing-points, lowering by salt . .217 of aqueous .... 217 indices of refraction 188 magneto-optic rotation of . . 301-303 potential (contact) differences . 254-257 specific heats 230-231 surface tensions 142 viscosities 129-133 Sound, velocity of, in solids loi liquids and gases . . . 102 Sparking potentials 248-250 Specific gravity, see Density. heat of air 232 elements 228 gases 232 iron at high temperatures . . 308 liquids 230 mercury 229 minerals and rocks 231 solids 230 ^ vapors 232 water 229 " Specific heat of electricity " 258 Specific inductive capacity: gases . . . 279-280 liquids . . . 280-282 solids 283 Specific molecular conductivities .... 373-274 Specific resistance 262-263 viscosity: gases and vapors . . . i34-i3S liquids and oils . . . 126-128 solutions 129-133 Spectra: elements, brighter lines 170 iron, Fabry-Buisson 170 Kayser 174 solar, Fraunhofer lines 176 Rowland's measures . . . .171 Squares, least, tables 47-49 Standard cells 251-253 wave-lengths: Fabry-Buisson . . . 170 Kayser 174 Rowland 171 Standards, photometric 177 Steam tables: metric units 241 common " 242 .Steel: magnetic properties: hysteresis 291, 294-296 permeabilities 286-294 Stefan- Boltzmann radiation formula .... 238 Stone: strength of 71 thermal conductivity 199 Storage batteries 253 Strength of materials: bricks 71 concrete 71 metals 71 stones 71 timber, woods . . . 72-73 Sun: constant of radiation 179 disk; distribution of intensity . . . .179 light; ratio to sky-light I79 parallax 109 radiation 179 spectrum 171, 179 temperature I79 Surface tension 142-143 Susceptibility, magnetic, liquids and gases . . 30S Sylvine. refractive indices 183 Taylor's series . . la Temperature, critical, for gases 221 resistances for low 264 sun's 179 Tensile strengths 71-73 Tension, surface 142-143 vapor, see Vapor pressure. Terrestrisd magnetism: agonic line us declination, secular change no dip 112 secular change . . .112 horizontal intensity . . .113 secular change 1 13 inclination 112 secular change . 112 total intensity 114 secular change 114 Thermal conductivities : gases 200 liquids 200 salt solutions .... 200 solids 199 water 200 Thermal expansion: cubical: crystsils .... 224 gases .... 226 liquids .... 225 solids .... 224 linear: elements .... 222 various .... 223 Thermal unit, dynamical equivalent .... 227 Thermo-electricity 258-260 Peltier effect .... 258, 260 Thermo-magnetic effects 307 Thermometer: air-i6, o* to 300° C 234 59, 100° to 200° C . . . . 234 high-temperature-S9 . . . 235 hydrogen- 1 6, 0° to 100° C . . . 233 16, 59. -5° to -35° C . 233 59. 0° to 100° C . . . 233 various 235 Thermometer stem correction 236-237 Thomson thermo-electric effect 258 Timber, strength of 72-73 Time, sidereal, solar 108 Transformer-iron, permeability of . . . 286-287 steels, energy losses in . . , 294, 296 Transmissibility to radiation: atmospheric . . 179 crystals . . . .194 glass 193 Trigonometric functions: arguments (° ') • • • 30 (radians) . 35 United States weights and measures, conversion to metric units 5-^ 3i8 INDEX. Units of measurement: definitions, see Appendix. conversion factors .... 2-3 discussion, see Introduction. photometric I77 ratio of electro-magnetic to static . . . 247 V, ratio of electro-magnetic to -static units . . 247 Vapor, aqueous: vapor pressure, low temp. . . isi o'^-ioo" C . . 152 100^-230° C . IS3 pressure of, in atmosphere . . 155 relative humidity . . . . .158 (saturated) weight of . . . . iS4 Vaporization, latent heat of 206 for steam . . 241,242 Vapors: densities 91 diffusion of I37, 138 indices of refraction 190 pressures: alcohol, ethyl, methyl . . . 146 aqueous: low temp. . . .151 o°-ioo^ C . . . 152 ioo°-23o'' C . . .153 mercury 148 salt solutions 149 various 144-148 specific heats 232 viscosity, specific 134 Velocity of light 109 sound; in gases and liquids . . .102 solids loi Verdet's constants: Verdet and Kundt's . . . 304 gasew 304, 305 liquids 299, 305 solids 298 solutions, alcoholic .... 303 aqueous . . . .301 hydrochloric . . 303 Viscosity: alcohol in water 126 gases 13s liquids 127 vapors 13s water: temperature variation . . .125 specific: gases 134 oils 126 solutions 129-133 vapors 134 water: temp, var 125 Voltaic cells: composition, E. M. F. . . 232-253 double-fluid 253 secondary 253 single-fluid 252 standard 251, 253 storage 253 Volts, legal (international) xxxiv, 251 Volumes; critical, for gases 221 Volumes: gases, perfect 162 glass vessels, determinations of . . . 11 Water: boiling-points for various pressures: common measures 168 metric measures . 169 densities, temperature variation . . 95, 96 ionization of 278 solutions in: boiling-points , . . .219 densities 92 diffusion 136 electrolytic conduction 272-278 solutions of alcohol, densities . . . 98-100 thermal conductivity , 200 vapor pressure: low temperatures . .151 0° to 100° C . , . . 152 100'' to 230° C . . . 153 vapor, pressure of, in atmosphere . . 155 (saturated) weights of . . . .154 viscosity: absolute, temp. var. . . , 125 specific, temp, var 125 Wave-lengths: cadmium red line 170 elements, brighter lines . , . 170 Fabry-Buisson iron arc lines . . 170 Fraunhofer lines 176 iron lines, Fabry-Buisson . . . 170 Kayser 174 Kayser's iron arc lines .... 174 Rowland's solar lines . . . .171 solar lines (Rowland) .... 171 Weights and measures: British to metric . . 9-10 metric to British . . . 7-8 metric to U. S. . . . 6 U. S. to metric ... 5 Weights of bodies 58 Weights of sheet metal 70 wire: copper, iron, brass: common units 60 metric units . 62 aluminum, common and metric . . 64 copper wire, electrical constants common units 66 metric units . 68 Wind pressures 122 Wire gauges: Birmingham 59 British standard 59 Brown and Sharp 66 Wire, weights of: brass, copper, iron . . . 60, 62 aluminum 64 copper 66, 68 Woods: densities of 87 strength of ........ . 72-73 Young's modulus of elasticity 75 Zonal harmonica 54