Smithsonian

Contributions to Astrophysics

VOLUME 4, NUMBER 2

ORBITAL ELEMENTS

OF PHOTOGRAPHIC METEORS

by RICHARD E. MCCROSKY and ANNETTE POSEN

SMITHSONIAN INSTITUTION

Washington, D. C.

1961

Publications of the Astrophysical Observatory

This series, Smithsonian Contributions to Astrophysics, was inaugurated in 1956 to provide a proper communication for the results of research conducted at the Astrophysical Observatory of the Smithsonian Institution. Its purpose is the “increase and diffusion of knowledge” in the field of astrophysics, with particular emphasis on problems of the sun, the earth, and the solar system. Its pages are open to a limited number of papers by other investigators with whom we have common interests.

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Smithsonian Institution.

Cambridge, Mass.

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Contents

Publications of the Astrophysical Observatory

Orbital Elements of Photographic Meteors

The data

Reliability of the method

Distributions of orbital elements

The table of data

References

Orbital Elements of Photographic Meteors

By RICHARD E. MCCROSKY[1] and ANNETTE POSEN[2]

This paper presents an analysis of the trails and the distributions of the orbital and physical parameters for 2,529 meteors photographed simultaneously from two camera stations in New Mexico. The two Baker Super-Schmidt cameras of the Harvard Meteor Project were located at the Soledad Canyon and Doña Ana stations, separated by a distance of 28.6 kilometers. The sample reported here comprises 70.4 percent of all meteors photographed during 1,125 hours of exposure by two cameras, operating simultaneously, during the period February 1952 to July 1954.

The data

Of the meteors included in this analysis, 2,059 were analyzed by the method of graphical reduction (McCrosky, 1957). A partial graphical reduction has positively identified as shower members an additional 115 meteors comprising 108 Geminids, 5 Perseids, and 2 Taurids. We have also included 355 meteors reduced by Jacchia (Whipple and Jacchia, in press) that would have been accepted for a graphical reduction had they not already been treated by the more accurate technique.

The orbital elements for all the fully reduced meteors were computed by the method described by Whipple and Jacchia (1957). We have assigned the mean orbital elements of the appropriate shower to the 115 meteors identified by partial graphical reduction.

The graphical reduction method was used to obtain geocentric velocities and radiants. All meteors were accepted for graphical reduction except those excluded by limitations inherent in the method.

[1] Harvard College Observatory and Smithsonian Astrophysical Observatory.

[2] Harvard College Observatory.

Determination of the radiant by this method requires the superposition of the two films, and one image must be dense enough to be visible through the other film. Some very faint meteor trails (10.4 percent of the total) did not meet this requirement, and hence were not used.

The method also requires the selection of a common point on the two meteor trails—the same point in space as seen from the two stations. Finding a common point precisely enough on the two films is not always possible, particularly if the meteor begins or ends outside the field recorded by the camera, or if a part of the trajectory lies on the outer 12 percent of the field that is not occulted by the rotating shutter. This difficulty in finding a common point led us to reject 13.8 percent of the meteor trails. We also excluded 0.6 percent of the meteors because of an ambiguity of 180° in the position of the radiant. Other meteors (4.8 percent) could not be reduced by this method because the photographic records had been affected by instrumental faults, clouds, and other random factors.

Reliability of the method

The speed of the graphical method results, in part, from the use of a common point—which involves human judgement in its selection—instead of detailed measurements alone. The consequent possibility that systematic errors or selection effects were introduced by the human computer, affecting the reliability of the method, warrants investigation.

Effects of selection.—A random selection of 360 meteors reduced by the short trail method (Hawkins and Southworth, 1958) includes 254 meteors that were reduced independently by the graphical technique. The short trail reductions are more accurate than the graphical by an order of magnitude. Comparisons of the results of these two sets of reductions have been made to determine the errors and selection effects in the graphical reduction.

The velocity distributions of the meteors chosen for short trail and graphical reductions, shown in figure 1, indicate that the choice of meteors was essentially random with respect to velocity. The larger errors inherent in the graphical method result in a greater diffusion into the hyperbolic velocity range, but the percentages of high velocity meteors (V greater than 60 km/sec) are similar in the two sets of data. The elimination of the very faint meteors from our data does not represent a new selection factor but merely places a slightly lower limit on the limiting magnitude than is already imposed by the observing technique. The distributions of maximum and minimum magnitudes are given in table 1. The influence of selection in meteor brightness becomes effective at magnitudes fainter than Mpg=1, for discovery of the meteor on the film is no longer a certainty. The distributions given here therefore apply to meteors whose magnitudes have a median value of Mpg=0.8.

FIGURE 1.—Velocity distribution for meteors reduced by the graphical and short-trail methods.

TABLE 1.—Distribution of maximum and minimum magnitudes of 2,529 meteors

The rms errors in geocentric velocity and apparent radiant, as derived from comparisons of the short trail and graphical reductions, are 3 percent and 3°, respectively. These and the mean and median deviations determined for inclination (i), eccentricity (e), perihelion distance (q), and longitude of perihelion (π) are given in table 2. There is no systematic error in the geocentric velocity or the orbital elements.

The apparent degree of error in the elements is misleading, since most of the error was contributed by only 5 percent of the meteors, whose measurements show deviations of more than five times the mean. The median of the deviations is less than half their mean. Most of the extremely large errors are attributable to poorly determined radiants. It was not possible to discover any criteria for rejecting these cases.

TABLE 2.—Errors in elements of graphically reduced meteors

The error in 1/a—the reciprocal of the semi-major axis—is a function of geocentric velocity and elongation λ, the angle between the heliocentric velocities of the earth and the meteor. For an error of 3 percent in geocentric velocity, the computed rms error in 1/a varies from 0.10 to 0.18 (a.u.)−1. However, for most of the meteors in our sample, the computed error in 1/a due to the velocity error lies between 0.13 and 0.15 (a.u.)−1. Errors in the radiant generally contribute smaller errors to 1/a except in the extreme cases mentioned above.

The error in q', the aphelion distance, will be similar to that in a.

Cosmic weights.—The orbital data can be weighted to remove some of the effects of physical and observational selection which prejudice our view of matter in space. These effects include (1) the dependence of mass on velocity for meteors of a given luminosity; (2) the law governing the increase in meteor numbers with increasing magnitude; (3) the velocity dependence of the photographic technique; and (4) the probability that meteors of a given orbit will collide with the earth. When the data are weighted for the first three factors, the resultant distributions refer to meteors of uniform mass. For these effects we have adopted Whipple’s (1954) weighting factor of 1/V^2∞, where V∞ is the velocity of the meteor outside the earth’s atmosphere. The uncertainties in the velocity-mass law and in the number-luminosity law are such that attempted corrections for these effects will probably be in error by at least 1 in the velocity exponent. In Whipple’s earlier work a weight of 1/3 V^2∞ was applied for meteors with V<19 km/sec, to compensate for the greater length of the trails, and for a possible decrease in the luminous efficiency in low velocity meteors. The low velocity meteors in our data are not characterized by exceptional length and, consequently, the 1/V^2∞ factor has been used for meteors of all velocities.

Öpik (1951) has investigated selection effect “(4)”, above. On the basis of his analysis we will write the probability of collision as follows:

where i is the inclination, a the semi-major axis, p the parameter of the orbit, and VG the geocentric velocity of the meteor. When the data are weighted by the factor 1/P the resultant distributions of orbital elements are proportional to the number of meteoroids with such orbits that pass perihelion per unit time. The product of these two weighting factors, 1/PV^2∞, has been called the “cosmic weight” and is used here to weight the observed numbers of meteors.

Distributions of orbital elements

Figure 2a, b presents the distribution of the reciprocal of the semi-major axis of the orbits of our meteors. Figures 3 through 6 present distributions—based on numbers of meteors (solid lines) and on numbers weighted by the cosmic weight (dotted lines)—for the orbital elements i, e; for perihelion distance q, and for aphelion distance q'. In each case the weighted distribution has been normalized to the observed distribution. Various two-dimensional distributions of these parameters appear in figures 9 to 14. Shower meteors include members of all major streams, as well as the seven new showers revealed by these data (McCrosky and Posen, 1959).

Inclination.—The distributions demonstrate the existence of a large number of direct, small meteor orbits of low inclination. The median inclination of the observed distribution is 18°, that of the weighted distribution 21°. The steady decrease in weighted numbers of orbits below i=5° is due, in part, to an obvious inexactness in the weighting function at very low inclinations. Öpik showed, however, that the weighting function is accurate within 10 percent for orbits with inclinations greater than 0.3°; hence the decrease must be attributed to the fact that these orbits have been eliminated by planetary collision and perturbations.

FIGURE 2.—Distribution of meteor orbits in reciprocal semi-major axis: a, the 2,529 meteors compared with Whipple’s bright photographic meteors; b, the sporadic component of the 2,529 meteors compared with Davies’ radar data weighted for observational selection.

FIGURE 3.—Distribution of meteor orbits in inclination, i°.

Figure 9, which gives the observed distribution of meteors in inclination and aphelion distance, shows that the ecliptic concentration is limited primarily to small orbits with q'<8 a.u.

The paucity of orbits at i≈90° was also noted in the data on brighter meteors (Whipple, 1954) and radar meteors (Davies, 1957). Orbits of both large and small aphelion distance exhibit this gap, although the latter group shows it more markedly. Of our 2,529 meteors, the number of short orbits (q'<10 a.u.) with 80°<i<100° is 12 as opposed to 41 with 70°<i<80°, 100°<i<110°. For long orbits (q'≥10 a.u.) the corresponding numbers are 39 and 61. An inspection of the weighted numbers of meteors at various inclinations shows that the decrease in numbers at i≈90° is primarily a result of observational selection.

In the radar meteors, which are observed at magnitudes of about Mpg=6, and have an average maximum brightness of somewhat more, possibly Mpg=5, Davies observed a bimodal distribution of inclination for q'<3 a. u. and e<0.3. The maxima occur at 60° and 140°; there are almost no meteors with i<30°. The reverse situation occurs in our faint photographic meteors; the smaller and less eccentric the orbit, the more pronounced the ecliptic concentration. Our data include 146 meteors whose aphelion and eccentricity lie within the limits specified by Davies. Only 8 of these have inclinations greater than 30°. The medians of the observed and weighted distributions are respectively 11° and 14°, both substantially lower than those found for the sample as a whole.

Semi-major axis.—Figure 2a shows the distribution of the reciprocal semi-major axis 1/a for our sample, compared with that for the brighter photographic meteors analyzed by Whipple (1954). The median absolute photographic magnitude for the bright meteors is —3.8. Shower meteors, representing over 50 percent of Whipple’s data, are included in both histograms.

The difference between the two sets of photographic data suggests that orbital characteristics vary considerably with meteoroid size, a conclusion supported by other evidence to be presented. The bright meteors do not represent a completely random sample. A very few meteor trails with closely spaced shutter breaks were not suited for measurement, and possibly a few slow meteors—those whose semi-major axes are statistically small—were excluded. Nevertheless, the two samples exhibit about the same percentage of orbits with mean distance greater than 5 a. u. The major difference lies in the distribution of short orbits; except for the Geminids, Whipple’s data contain almost no examples with a<1.3 a. u.

Davies (1957) has presented a distribution of 1/a for radar meteors, sporadic meteors weighted for observational selection but not for the probability of collision with the earth. Davies’ weighted distribution and our observed numbers of sporadic meteors are compared in figure 2b. The sensitivity of the photographic technique is inversely proportional to the velocity of the meteor. However, the greater area of sky observed at the greater heights where high velocity meteors occur compensates to some extent for the diminished photographic sensitivity. To place our data on a basis comparable with the radar data, we must weight the photographic data by a small power of the velocity, say V ¾. Generally, this will give greater weight to meteors with small values of 1/a and will accentuate the differences seen. Figure 2a, b shows that the proportion of short orbits increases gradually as one proceeds from the bright photographic to the faint photographic to the still fainter radar meteors. However, in the progression to radar meteors the proportion of long orbits decreases abruptly (table 3). Whipple (1955) has suggested that rapid diffusion of the ion column of high altitude (high velocity) meteors inhibits their observation by radar. Since the meteors with long orbits enter the atmosphere at high velocity, statistically this abrupt decrease with magnitude may result from limitations in the experimental technique rather than from radical differences in the nature of the orbits.

The difference in orbital characteristics as a function of magnitude is further indicated by Whipple’s (1954) empirical comet-asteroid criterion, K. He found that the parameter

is positive for 96 percent of known comet orbits, and negative for all but 3 asteroid orbits. Of the 144 meteors in Whipple’s analysis, only 8, or 5.6 percent, had a negative K, a fact that suggested a cometary origin for most meteors. The faint meteors also are of cometary origin, as indicated by their fragility and the degree of fragmentation observed, but on the basis of the K criterion, 25.5 percent of their orbits are indistinguishable from those of asteroids (see fig. 15). The region of negative K embraces the orbits of small aphelion distance, and thus small semi-major axis. Any effect of selection for velocity in the bright meteor data is certainly not large enough to account for the appreciable difference in the proportion of meteors with negative K between the bright and faint photographic meteor samples.

TABLE 3.—Proportion of long orbits in photographic and radar meteor data

Eccentricity.—The distribution of the eccentricity of meteor orbits is given in figure 4, which shows a smooth rise to a maximum at about 0.9. The 12.5 percent that filter into the hyperbolic range are an indication of the errors made in reduction. The number of sporadic meteors increases approximately as e^2. The appreciable number of orbits with small values of e is characteristic of these faint meteors. Whereas only 8 percent of the sporadic orbits discussed by Whipple had e less than 0.6, 25 percent of our orbits are within this range.

Figure 10a shows the observed distribution of orbits as a function of the semi-major axis and the eccentricity. The areas of the circles are proportional to the numbers of meteors in a cell representing a range of values of the semi-major axis and eccentricity. The distribution is bounded by envelopes which are described by the limits on q and q' for observability at the earth. Figure 10b shows a similar distribution, for weighted numbers, for those orbits within 15° of the ecliptic plane. Both direct and indirect orbits are included. Figure 10c shows the same distribution as in figure 10b, but for those orbits with inclination between 15° and 165°.

A large majority of small orbits has both low inclination and low eccentricity. The tendency of small orbits to exhibit low eccentricity is also evident in figure 11, and is particularly striking in view of the small area in the a-e plane available at low eccentricity. The Geminids are responsible for a large number of orbits at a=1.25 and e=.775. Other showers are all but indistinguishable in these distributions.

FIGURE 4.—Distribution of meteor orbits in eccentricity, e.

Perihelion.—Perihelion distance q is a particularly well-determined element and details of the distribution (fig. 5) are worthy of scrutiny. The observed and the weighted distributions of perihelion distance are both approximately linear with q if the shower component is neglected. This relationship holds for both long and short orbits. There is a slight departure from linearity in the vicinity of Venus (.72 a.u.), perhaps because there is a relatively high probability of capture by Venus for meteors with perihelion in the vicinity of the planet.

FIGURE 5.—Distribution of meteor orbits in perihelion distance, q (a.u.).

A comparison of the distribution of perihelion for meteors with that for comets is of interest. Figure 7 shows the distribution of cometary perihelia for 369 comets with q<1.9 a.u. and discovered since 1800, as listed in the Baldet and De Obaldia catalog (1952). These are observed numbers and should be corrected for observational selection. One expects comets with small perihelion to appear brighter than average; on the other hand, observations may be hindered by their small elongation from the sun. Comets of large perihelion may have a wide range in brightness, depending on the earth-comet distance. The observational selection factors are complicated and an empirical approach is indicated.

FIGURE 6.—Distribution of meteor orbits in aphelion distance, q' (a.u.).

FIGURE 7.—Distribution of perihelia for 369 comets with q<1.9 a.u.

R. J. Dunn has kindly supplied a previously unpublished analysis of cometary brightness as a function of q. Figure 8 is Dunn’s compilation of the absolute magnitudes of 83 comets derived by Bobrovnikoff (1941, 1942) and Vessviatsky (1925). When both catalogs give the brightness, Bobrovnikoff’s value is chosen. It should be noted that this plot represents a select list of well-observed comets, with apparent magnitudes less than the average. They represent only a fifth of those shown in figure 7, and are not necessarily representative of all observed comets. Had absolute brightness played a role in observational selection, one would expect the mean magnitudes to be distributed with q somewhat in the fashion indicated by the schematic dotted line in figure 8. In fact, the absolute brightness of the comets in any given range of q is relatively constant. One can, then, accept the observed distribution of perihelia of comets as a true distribution out to 1 a.u., excepting at very low q where the photometric data are sparse. With the exception of the marked and unexplained peak at 0.75 a.u., and the neighboring minimum at 0.85 a.u., the distributions of the perihelia of comets and of the meteors they have presumably produced are essentially identical.

FIGURE 8.—Cometary brightness as a function of perihelion distance, q. The mean M over an interval of 0.2 a.u. in q is plotted with the symbol +. The broken line defines the relationship between M and q that would be expected if absolute cometary brightness influenced observational selection.

FIGURE 9.—Distribution of meteor orbits in inclination and aphelion distance.

Aphelion.—The low accuracy in the determination of aphelia does not permit any significant conclusions. The distribution shown in figure 6 perhaps allows us to say that the meteor population is roughly constant with aphelion as far out as Jupiter’s orbit, at which distance a substantial decrease in numbers occurs.

Line of apsides.—The tendency of asteroids to align their lines of apsides with Jupiter’s is well known (see fig. 16). The asteroidal alignment is a function of aphelion distance. The ratio of the number of asteroids aligned within 15° of Jupiter to those similarly opposed is twice as large for asteroids with 3.5 a.u.<q'<4.0 a.u. as for those with q'<3 a.u., the proportions being 4.3 and 2.2. Of 29 short-period comets with i<30° and with aphelion within Jupiter’s orbit, twice as many are aligned within 90° of Jupiter as have their perihelia in the remaining two quadrants. It is of interest to look for this same alignment in meteor data.

The influence of Jupiter is largest for low inclination orbits with aphelia inside its own orbit. Therefore, we sought the effect only for those meteors with i<30° or i>150°, and with q'<5 a.u. In this range of inclination, the line of apsides and the longitude of perihelion, π, define essentially the same direction, and so the following distributions are based on the values of π for our meteor orbits. For meteors observed at the earth, π is a marked function of the time of year, 40 to 50 percent of the meteors recorded in any one month having a π within a range of 50°.

The data for each month were weighted for three effects: (1) the number of hours of exposure in each month; (2) the proportion of the observed meteors that were reduced in a given month; and (3) the seasonal variation in proportion of ecliptic orbits observed, which results from the varying elevation of the radiants of ecliptic orbits. This last correction was determined empirically by noting the proportion of orbits with small i and q' (i<30° or i>150°, q'<5 a.u.) to the total number of meteors reduced for each month. The reciprocal of this ratio was used as the weighting factor for “(3).”

While the correction for “(2)” was always small, there was a large variation in the weights applied for “(1)” and “(3).” Table 4 gives the weighting factors for each of these corrections, and the median π for each month. The weights for July—a month of short nights, low elevation of the ecliptic, and perpetual bad weather in New Mexico—are, of necessity, very high. The weighted distributions of the lines of apsides of low inclination meteors are given in figure 17 for meteors with 3≤ q'<5 a.u., and in figure 18 for meteors with q'<3 a.u.

In both distributions, there is a minimum at 20°, where the asteroids exhibit a maximum. Since much of the contribution at this longitude comes during the month of July, the significance of this minimum may be questioned. However, the data for July have probably been overcorrected already. An additional multiplicative weight of 3, to reproduce the asteroidal maximum at 20°, is certainly not reasonable.

In our data, the aphelia are relatively ill-determined and so the data of figure 17 probably include orbits whose aphelia are, in reality, outside Jupiter’s. Thus, figure 18 is a better representation of the alignment of our orbits inside Jupiter.

As a check on the reality of the distributions shown in figures 17 and 18, we have analyzed 106 meteors with i<30° and q'<5 that were reduced by Jacchia (fig. 19). The same weighting factors were used for seasonal effect and for proportion of low i, low q' orbits. The weights for the proportion of meteors reduced to those observed were derived from Jacchia’s numbers. The correction factors are uncertain for so small a collection of data, but these data have the marked advantage of considerable accuracy in the determination of q', and are not contaminated by those orbits whose q' is, in reality, greater than 5 a.u., which would not be expected to show the same degree of alignment. Figure 19 shows the same general features found for the fainter meteors reduced by the approximate method: minima at 20° and 190° and a significant maximum around 100°. The second maximum, centered about 315°, also shows to some extent in the faint meteor data. In fact, we must apparently account for a double-humped curve in the distribution of lines of apsides of meteors, rather than for the single-humped curve displayed by the asteroids. There is a preferential direction for the line of aspides of small meteor orbits at about 90° from that of Jupiter.

TABLE 4.—Correction factors applied in the distribution of longitude of perihelion (π)

FIGURE 10a.—Distribution of meteor orbits in eccentricity and semi-major axis: observed numbers, all orbits.

We suggest that the observed distribution of the lines of apsides of meteors is a chance result due to contributions from a limited number of comets. The association between individual comets and meteor showers is well known. Nearly half the meteor showers are attributable to known comets. Probably, however, the reverse correlation has not been sufficiently emphasized: a stream has been found for about half the known comets that might produce a shower (say, those approaching within 0.1 a.u. of the earth’s orbit). Such comets may also supply meteors that are perturbed into broad streams and hence are not recognizable as a distinct shower. The most difficult element to perturb is the line of apsides, and the streams associated with particular comets might maintain this partial identity with the parent comets.

FIGURE 10b.—Distribution of meteor orbits in eccentricity and semi-major axis: cosmic-weighted numbers, orbits within 15° of the ecliptic plane. The areas in figures 10b, c have been normalized to the same total.

Porter (1952) lists 19 approaches of short-period comets within 0.1 a.u. of the earth’s orbit. Ten of these, including 1819 IV (see McCrosky and Posen, 1959) and 1917 I (Whipple, 1954) have produced recognized showers. For 5 of the remaining 9, meteor radiants have been predicted at declinations south of —20° and generally out of the range covered by observatories making comprehensive photographic observations of meteors. Of the 19 close approaches, 8 are for comets with i>30°, outside the ecliptic range considered in our distribution of the line of apsides. The values of π for the 6 approaches of comets with i<30° and with radiants north of δ= —20° are plotted with arrows in figure 19. The lines of apsides of all of these comets avoid the regions of minima around 20° and 200° observed in the meteor data. Although the data on both meteors and comets are limited, one must consider the hypothesis that the distribution of the lines of apsides of meteors varies with time, and is related to the distribution of the elements of particular comets that chance to approach the earth’s orbit.

FIGURE 10c.—Distribution of meteor orbits in eccentricity and semi-major axis: cosmic-weighted numbers, high inclination orbits (1>15°). The areas in figures 10b, c have been normalized to the same total.

FIGURE 11.—Distribution of meteor orbits in perihelion distance and aphelion distance.

The table of data

A large number of the more important statistical relations among the orbital elements of meteors are given in the distribution graphs (figs. 2–6, 9–14). However, to facilitate the work of other investigators who may wish to analyze the data further, we present in tabular form (table 7) all of the geometrical and physical parameters of each meteor. Table 5 gives the code for identifying the shower meteors, and table 6 explains the column heads used in table 7.

It should be stressed, however, that because of the nature of the reduction method, these data have only statistical significance. In our experience, when a meteor with anomalous parameters has been investigated more carefully, the cause of the abnormality has always been found in the approximate reduction and not in the meteor.

Masses have been determined from the integrated intensity, I, and the equation

where T is the lifetime of the meteor, and τ_0 is the luminosity coefficient. Integrated intensities have been derived from limiting and maximum magnitudes in the manner described by Hawkins (1957). Considerable uncertainty remains as to the proper value of τ_0, and the masses given should be considered as only relative. The value of τ_0 used here is that determined by Öpik (see Whipple, 1943) and the masses are therefore based on the same scale as others published by the Harvard Meteor Project. Scaling factors of as great as 220 (Cook, 1955) have been suggested.

The number given in the column for “abruptness” (A) refers to the special meteors discussed by McCrosky (1955), which show a pronounced discontinuity in the light curve, usually at the beginning of the meteor’s path.

There was no precise criterion for establishing shower membership for the graphically reduced meteors. The orbital elements exhibit too much scatter to serve as a criterion. The radiants were plotted, and compact clumps of points with similar velocities were called showers. This particularly misrepresents extended showers like the Taurids, and overlapping showers like the ι and δ Aquarids and α Capricornids. Although some nonmembers of showers must have been erroneously included, the error is mainly one of omission.

For 31 meteors reduced by the graphical method, photometry was not possible. For these, the column entries Mpg and m∞, have been left blank. Blanks throughout the table appear for those elements not obtained.

A dash appearing as an entry in the table represents an undefined element, such as q' and K, for those meteors whose computed orbits are hyperbolic.

FIGURE 12.—Distribution of meteor orbits in inclination and semi-major axis.

FIGURE 13.—Distribution of meteor orbits in inclination and eccentricity.

FIGURE 14.—Distribution of meteor orbits in inclination and perihelion distance.

TABLE 5.—Code for identifying shower meteors

1

α Capricornids

2

Southern Taurids

3

ι Aquarids (southern branch)

4

Geminids

5

δ Aquarids (southern branch)

6

Lyrids

7

Perseids

8

Orionids

9

Draconids

10

Quadrantids

11

Virginids

12

κ Cygnids

13

Leonids

14

χ Orionids

15

Ursids

16

σ Hydrids

17

Northern Taurids

18

Southern Arietids

19

Monocerotids

20

Coma Berenicieds

21

α Virginids

22

Leo Minorids

23

є Geminids

24

μ Pegasids

25

δ Arietids

26

δ Aquarids (northern branch)

27

κ Serpentids

33

ι Aquarids (northern branch)

FIGURE 15.—Distributions of the 2529 meteors (solid line) and the bright photographic meteors (broken line) in the comet-asteroid criterion K. The areas under the two histograms are equal.

TABLE 6.—Explanation of column heads used in table 7

FIGURE 16.—Distribution of longitude of perihelion for asteroids.

FIGURE 17.—Distribution of longitude of perihelion for meteors with 3≤q'<5 a.u. The observed numbers of meteors have been weighted for seasonal observational selection. They were also weighted for the proportion rejected for graphical reduction.

FIGURE 18.—Distribution of longitude of perihelion for meteors with q'<3 a.u. The observed numbers of meteors have been weighted for seasonal observational selection. They were also weighted for the random variation throughout the year of the proportion rejected for graphical reduction.

FIGURE 19.—Distribution of longitude of perihelion for accurately reduced meteors with orbits in which q'<5 a.u. The observed numbers of meteors have been weighted for seasonal observational selection, and for the random variation throughout the year of the proportion accepted for reduction.

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TABLE 7.—Orbital and physical parameters of 2,529 double-station meteors