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Volume 72, 1942-43
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The Physical Characteristics of Meteors.

[Read before the Wellington Branch, August 8, 1942; received by the Editor, July 27, 1942; issued separately, March, 1943.]

The accumulation in New Zealand over the past fifteen years of more than 12,000 observations of individual meteors recorded by regular observers on a prearranged plan presents an opportunity for statistical studies of the physical characteristics not to be neglected.

In the years 1925–40 various observers of the Meteor Section of the New Zealand Astronomical Society have contributed to the total as follows:—

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Observer. Period. Meteors.
Bateson, F. M. (B) 1927-33 1,524
Fairbrother, S. (F) 1935-38 851
Geddes, M. (G) 1931-37 4,698
McIntosh, R. A. (M) 1925-40 3,518
Others 218
Total 12,809

We have thus available for study the work of two experienced meteor observers (assuming that accuracy increases with numbers recorded) and others in various stages of proficiency.

The present paper has three principal objectives:—

  • (1) The determination of the average physical characteristics of a meteor, and the relations which can be established between them;

  • (2) An attempt to estimate from the divergencies revealed the accuracy to be expected in the recording of these features; and

  • (3) The effect of increasing experience upon the work of an observer.

With regard to (2) one cannot be certain that an examination of divergencies from the mean reveals the true state of affairs. The mean itself, based on the whole of the data of all the observers, irrespective of their experience, may not necessarily be the best representation of the truth, but it is the only standard available.

It should be noted that the data relate only to normal meteors recorded during the progress of routine observations. The hundreds of telescopic meteors and bright fireballs reported by persons not regular observers are not included in these statistics.

Magnitudes.—The distribution in brightness of the observed meteors is shown in Table I, where the results are expressed in numbers per thousand meteors observed.

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Table I.—Distribution of Magnitudes.
Observer. Magn. > 1 1 2 3 4 5 6 Total.
F 13 42 153 367 243 158 22 851
G 32 75 146 248 297 156 45 4,698
M 59 153 183 186 187 177 53 5,518
Others 12 86 124 235 321 173 49 1,742
All 40 108 160 227 250 168 48 12,809
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As is to be expected, more faint meteors are seen than bright ones, the number increasing inversely with the brightness. After the fourth magnitude, however, a marked falling off in numbers occurs, due probably to the majority of fainter meteors eluding observation. Some individual eccentricities are evident in the table, McIntosh overestimating the brightness of meteors in the middle magnitudes, while Fairbrother underestimated the brighter objects. The mean magnitude is 3.0.

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The ratio of increase of numbers with decreasing brightness is steadier than one would expect in view of these personal equations. In Table II the ratio Nm + 1/Nm is detailed, Nm representing the number of meteors of magnitude m.

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Table II.—Ratio of Increase with Magnitude.
Magnitude. Mean.
Obs. 0–1 1–2 2–3 3–4 4–5 5–6 0–4
F 3.2 3.6 2.4 0.7 0.6 0.1 2.5
G 2.3 1.9 1.7 1.2 0.5 0.3 1.8
M 2.6 1.2 1.0 1.0 0.9 0.3 1.5
All 2.7 1.5 1.4 1.1 0.7 0.1 1.7

It is uncertain at what stage of faintness the observer begins to miss seeing meteors. Down to the second magnitude the ratio is 2.1, which agrees closely with values found in other countries and with that shown by the naked-eye stars themselves (2.4). The ratio-falls only gradually to the fourth magnitude, revealing that only a small proportion of these meteors are overlooked, but the rapid decline thereafter shows that only a few of the fainter meteors are seen. Portion of the decline in ratio may be real, arising from the fact that, as in the case of the stars, meteors are finite in number, but the greater portion of the decline must arise from the difficulty of detecting faint meteors in a large area of sky (generally about 50° square). The ratio between various magnitudes of telescopic meteors (to be dealt with in a later paper) confirms that the naked-eye records of the fainter meteors are not an indication of the true numbers present.

Assuming that the final line in Table I represents the truth (which is probably not the case), the average error in magnitude estimations can be determined. The deviations of the observers from the mean values are: F 4% error, G 2%, M 3%, others 2 ½%. From this it can be inferred that an experienced observer over or underestimates by one magnitude or more the brightness of three meteors in every hundred recorded. The mean deviations in ratio of increase are more consistent, being: F 0.7, G 0.3, M 0.2.

The increase in the number of faint meteors detected with increasing experience is worthy of comment. In Table III the totals of fifth and sixth magnitude meteors recorded are tabulated and smoothed for McIntosh's records. The smoothing formula used is × = ¼ (Xr–1 + 2X + Xr + 1). A steady increase in numbers with increasing experience to a maximum after five years' experience is revealed. The small drop in numbers in 1936 coincided with the observer's removal from a relatively dark suburb to a position where the glare of city lights caused considerable sky glow.

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Table III.—Number of Fifth and Sixth Magnitude Meteors recorded in every thousand meteors seen.
Year Number. 5th + 6th Mag. Number. Smoothed.
1919–21 30 (30)
1925 6 18
1926 28 28
1927 52 74
1928 165 113
1929 236 236
1930 306 270
1931 232 257
1932 257 241
1933 217 241
1934 276 260
1935 273 271
1936 263 252
1938 209 250
1940 318 (318)

Dr. E. Opik (Harvard Annals, 105, p. 562) has applied to estimations of meteor magnitudes the criterion better known for its use in star counts—statistical photometry. Briefly, the magnitudes are smoothed to eliminate the “decimal equation” arising from the fact that meteor magnitudes are recorded only as whole magnitudes. The limiting magnitudes of certain fixed percentages of the total meteors are determined. If an observer is consistent in his magnitude determinations the limiting magnitudes for any percentage should lie close to those determined at other epochs.

In Table IV the limiting magnitudes for 10, 30, 50, 70 and 90 per cent. of the total meteors are given for each observer in each year.

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Table IV.—Limiting Magnitudes of Fixed Percentages of Meteors.
Obs. Year. 10% 30% 50% 70% 90%
F 1935 2.08 3.17 3.88 4.60 5.43
1936 2.00 3.22 3.97 4.73 5.53
1938 1.60 2.64 3.19 3.76 4.62
Mean 1.89 3.01 3.68 4.36 5.19
Mean Deviation 0.17 0.26 0.29 0.66 0.38
G 1931 1.18 2.91 3.87 4.74 5.58
1932 1.24 2.98 3.88 4.68 5.53
1933 1.90 3.25 3.99 4.70 5.56
1934 2.14 3.49 4.24 4.93 5.63
1935 2.14 3.26 3.96 4.69 5.55
1936 1.90 3.23 3.98 4.67 5.54
1937 1.68 3.12 3.88 4.62 5.38
Mean 1.74 3.18 3.97 4.72 5.54
Mean Deviation 0.27 0.13 0.09 0.07 0.05
M 1925–28 0.65 2.55 3.52 4.52 5.50
1929 0.70 2.50 3.62 4.59 5.58
1930 0.74 2.75 3.95 4.87 5.68
1931 0.34 2.12 3.34 4.53 5.60
1932 0.25 2.46 3.68 4.70 5.62
1933 0.75 2.54 3.58 4.55 5.55
1934 0.93 2.88 3.92 4.86 5.63
1935 0.83 2.62 3.87 4.81 5.64
1936 0.65 2.56 3.70 4.63 5.64
1938 0.20 2.14 3.46 4.53 5.52
Mean 0.65 2.55 3.70 4.68 5.60
Mean Deviation 0.15 0.04 0.02 0.01 0.00
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The fact emerges that the two experienced observers remain remarkably consistent in their estimations of brightness, as is shown by the small deviations, while those of Fairbrother are very erratic, the mean deviation in his case even increasing with the percentage when, from the nature of the analysis, it should decrease to a small residual at 70% and 90%.

Inspection of the table reveals that while the observers remain consistent in their estimations (with the exception of Fairbrother) the data for one observer do not agree with those of another. While McIntosh finds, for example, 30% of his total meteors equalling or greater than magnitude 2.55, Geddes needs to include meteors down to magnitude 3.18 to reach a similar percentage. While portion of this discrepancy is due to over-estimation in the middle magnitudes by McIntosh (as mentioned earlier), the figures also reveal that Geddes sees more faint meteors than McIntosh. As the former has always observed from country districts and the latter in the suburbs of Auckland the difference may possibly arise from sky glare. From a consideration of meteor rates it has already been shown (Popular Astronomy 46, 9, 516; 1938, Nov.) that, for every ten meteors seen by Geddes, McIntosh can expect to see only seven, an indication of the value of dark skies for meteor observing.

Durations.—The numbers of meteors of various durations per thousand meteors seen are shown in Table V, which reveals the short duration of the meteor's flight, more than half the observed meteors (54.2%) having durations between 0.4 and 0.6 seconds inclusive, while only 3% endure for more than one second. In this short interval the observer must record the numerous physical details studied in this paper.

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Table V.—Distribution of Durations.
Obs. Duration in seconds.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0
F 14 156 244 136 202 50 44 45 7 68 36
G 18 92 127 218 207 144 76 44 12 20 45
M 16 52 192 256 194 102 71 50 4 41 21
All 16 76 174 231 199 112 70 47 7 36 31

While it is relatively easy for an observer to distinguish between short durations it becomes more difficult to distinguish between longer ones, such as 0.9 and 1.0 secs. In such cases the observers normally have preferred the whole number, which accounts for the excess recorded as of duration 1.0 secs. The mean residuals are: F 3.4%; G 1.5%; M 0.9%; or a mean for the three observers of 1.9%.

Length of Flight.—The New Zealand observers draw the paths of observed meteors on gnomonic maps of the sky. The lengths of these paths have been measured by reference to a standard scale, instead of by the more accurate graticule superimposed on the maps, There is therefore a systematic error in the measurement of paths increasing with distance from the centre of projection. Path measurements are exact if they occur near the centre of the map, while others near the edge may be several degrees in error. Assuming even dis-

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tribution on the maps, the average measure should be 5% greater than the truth, which amounts in the average meteor to an excess of ½°, less than the error of observation.

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Table VI.—Distribution of Path Lengths.
Obs. 10°
B 1 0 94 110 143 219 64 43 94 14 139
F 0 2 9 32 65 71 103 100 119 70 75
G 6 10 40 99 146 188 137 104 74 47 34
M 4 6 29 51 72 85 79 85 61 60 59
All 4 7 32 69 100 125 110 92 75 55 54

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Obs. 11° 12° 13° 14° 15° 16° 17° 18° 19° 20° >20°
B 0 33 0 0 33 0 0 0 0 1 0
F 67 56 41 27 29 23 18 20 12 12 45
G 16 16 11 9 3 3 3 3 3 2 20
M 52 48 32 30 34 30 26 22 13 17 96
All 38 37 24 21 23 19 17 14 10 11 61

The distribution of path lengths per thousand meteors seen reveals some variations. Whereas Bateson and Geddes record very few meteors with paths greater than 10°, with very large numbers about the mean, Fairbrother's and McIntosh's records reveal smaller numbers about the average and more long-pathed meteors. The mean values for the various observers are as follows: B 6.1°, F 9.4°, G 5.9°, M 10.3°.

The figures exhibit a well-marked personal equation. As the two experienced observers differ by 4.4° in their mean values, and the less experienced observers also are grouped in two classes, there is no way of determining where the true mean lies. The only independent value for mean length of path available is that of I. Astapowitsch (Mirovedenie No. 24, 1929 May), who finds a mean length of 8.3°, only 0.4° from the New Zealand value. It would therefore appear that Bateson and Geddes consistently plot their paths too short and Fairbrother and McIntosh record theirs too long. The deviations of the various observers from the mean amount to: B 3.4%; F 1.7%; G 1.9%; M 1.3%.

Colours.—The statistics concerning the colours of meteors present some interesting features. In the first place Table VII reveals that colour in meteors is surprisingly rare, less than one meteor in every four exhibiting any deviation from whiteness. In the fainter objects, however, colour cannot be observed, and therefore 5th and 6th magnitude meteors are excluded from this data.

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Table VII.—Colours of Meteors.
Obs. Red. Orange. Yellow. Green. Blue. White. Per cent. Coloured.
F 64 17 42 3 16 860 14.0
G 79 30 38 12 36 786 21.4
M 66 39 20 26 94 754 24.6
Others 66 13 14 39 22 843 15.5
All 71 31 33 21 57 784 21.6
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Once again the value of experience is seen, the less-experienced observers failing to notice one coloured meteor in every four. The only outstanding variation between observers' records is that McIntosh records many more blue meteors than the others. This may arise from the fact that McIntosh records in this colour meteors no bluer than Sirius, while the others apparently class such meteors as white and reserve the blue classification for objects more prominently coloured. The mean deviations of the various observers are: F 2.7%; G 1.1%; M 1.7%; others 2.6%.

Relations between Features.—In the tabulations which follow, revealing the inter-relations between various physical features of the observed meteors, it has been considered advisable to draw a distinction between normal meteors (with durations not exceeding one second) and all meteors recorded, irrespective of their duration.

Magnitude-Duration.—In Tables VIII and IX are shown the dependence between brightness and duration for all meteors and for normal objects. In both tables it is seen that greater brightness in a meteor results in a longer duration of visibility. The only difference between the normal objects and the total meteors observed is that the elimination of the abnormal objects in Table IX not only numerically smoothes the relationship but also considerably reduce the average durations, indicating that the abnormal meteors excluded are to be found among the brighter objects.

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Table VIII.—Relation between Magnitude and Duration. (All Meteors)
Magnitude.
Obs. > 1 1 2 3 4 5 6 All.
F 1.120s 1.180s 0.644s 0.430s 0.394s 0.413s 0.490s 0.492s
G 0.924 0.552 0.543 0.512 0.497 0.459 0.420 0.510
M 0.764 0.607 0.304 0.477 0.473 0.417 0.398 0.500
All 0.837 0.608 0.531 0.488 0.480 0.433 0.411 0.506

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Table IX.—Relation between Magnitude and Duration. (Normal Meteors: Durations < 1.1s)
Magnitude.
Obs. >1 1 2 3 4 5 6 All.
F 0.867s 0.758s 0.603s 0.425s 0.378s 0.407s 0.440s 0.447s
G 0.505 0.468 0.472 0.480 0.477 0.444 0.397 0.468
M 0.624 0.565 0.481 0.463 0.454 0.416 0.393 0.475
All 0.593 0.541 0.485 0.466 0.461 0.427 0.399 0.470

Remembering that durations are recorded only to the nearest tenth of a second, it is gratifying to find, when large numbers of meteors are considered, that the mean durations of experienced observers vary by only 1/50th to 1/100th of a second. The respective divergencies are: F 0.102s; G 0.022s; M 0.011s; or an average divergence of only 0.072s for normal meteors.

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Magnitude-Distance.—When magnitude is related to length of path a similar phenomenon is exhibited, for in both classes of meteor (Tables × and XI) the brighter objects invariably cover the longer paths in the sky, although once again the removal of abnormal meteors (Table XI) smoothes the data and reduces it to lower values.

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Table × — Relation between Magnitude and Length of Path.
Magnitude
Obs. > 1 1 2 3 4 5 6 All.
F 20.8° 17.11° 12.9° 9.2° 9.0° 7.7° 7.3° 9.9°
G 20.0 8.3 6.9 6.0 5.7 5.5 6.4 6.4
M 20.4 16.0 11.4 9.6 8.7 7.4 6.4 10.6
All 20.4 14.4 9.6 8.1 7.3 6.8 6.4 9.1

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Table XI.—Relation between Magnitude and Length of Path. (Normal Meteors)
Magnitude.
Obs. > 1 1 2 3. 4 5 6 All.
F 21.8° 14.6° 12.2° 9.9° 8.7° 7.5° 7.3° 9.4°
G 12.1 7.8 6.6 5.4 5.5 5.4 5.4 5.9
M 19.2 15.4 11.2 9.5 8.6 7.3 6.2 10.3
All 18.2 13.8 10.0 7.8 7.1 7.0 6.0 8.7

It is to be expected, when the majority of meteors move at velocities close to the mean, that those which have the greatest durations (i.e., the brighter ones) should require longer paths. The observers' divergencies from the mean are: F 1.5°; G 3.1°; M 1.9°; or a mean divergence of 1.9°

Colour-Duration.—Assuming that meteors of all compositions enter the atmosphere at about the same velocity and become visible about the same height, we must conclude that those which burn out more quickly are composed of the most inflammable substances.

In Tables XII and XIII meteors below magnitude 4 are excluded (as in Table VII). The most important fact revealed is that meteors possessing perceptible colour have greater durations than those for which no colour was discerned. In both normal and abnormal classes it appears that yellow and orange meteors have the shortest durations of those exhibiting colour, and therefore represent the more volatile substances, while blue and red are in an intermediate group, with green objects possessing the greatest durations of all, and therefore probably representing the type of meteor most resistant to combustion.

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Table XII.—Relation between Colour and Duration. (All Meteors)
Obs. Red. Orange. Yellow. Green. Blue. White.
F 0.965s 1.320s 1.000s 1.750s 0.654s 0.456s
G 0.718 0.753 0.666 0.807 0.635 0.486
M 0.602 0.497 0.517 0.698 0.722 0.520
All 0.687 0.630 0.632 0.743 0.698 0.497
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Table XIII.—Relation between Colour and Duration. (Normal Meteors)
Obs. Red. Orange. Yellow. Green. Blue. White.
F 0.754s 0.740s 0.666s 0.000s 0.590s 0.488s
G 0.570 0.545 0.495 0.552 0.471 0.466
M 0.343 0.460 0.501 0.643 0.605 0.496
All 0.589 0.497 0.496 0.622 0.770 0.475

It is rather surprising to find the red meteors unrelated to the yellow and orange groups and, in mean duration, more closely allied to the blue objects. The point must be made, however, that the majority of blue meteors recorded were no bluer than Sirius, and therefore closely approach the white class, which posseses the shortest durations. Assuming that the near-white blue meteors have short durations similar to the white meteors, it is possible that the true blue objects possess durations much greater than shown in the tables, and are, in fact, allied with the green objects.

The differences between the observers' means and the mean of the combined observations are as follows: F 0.049s; G 0.042s; M 0.028s; all 0.04secs.

Remarkable Meteors.—Meteors are classified as remarkable for a number of reasons. They may appear stationary in the sky or to have curved paths (which denote special positions relative to the observer) or they may exhibit physical abnormalities such as unusual nuclei, variable brightness, halting motion, irregular paths, or leave unusual or long-enduring trains.

The frequency of occurrence of such phenomena per thousand meteors is shown in Table XIV, where the most interesting feature is found to be the comparative rarity of such abnormalities, only 32 meteors in every thousand seen exhibiting peculiarities.

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Table XIV.—Remarkable Meteors.
Obs. Stationary. Remarkaable Nuclei. Variable Magnitude. Irregular Path. Halting Motion. Curved Path. Trains Unusual > 2sec. Abnormal.
E 4 0 0 0 2 8 0 5 16
F 0 0 3 2 0 1 0 3 10
G 4 1 2 12 1 7 1 9 38
M 3 3 8 4 1 2 1 11 35
All 3 2 5 7 1 5 1 9 32

Here again the value of experience in observing is to be noted. The final column of the table reveals that the more experienced observers see twice as many remarkable objects as the others.

Trained Meteors.—When we come to examine those meteors which leave behind them luminescent trains of light, we find that such trains are comparatively rare, only 126 meteors in every thousand leaving streaks. The magnitude distribution of train-forming meteors is shown in Table XV.

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Table XV.—Magnitudes of Train-forming Meteors.
Magnitude.
Obs. > 1 1 2 3 4 5 6 Total.
F 49 166 313 337 80 55 0 188
G 147 187 241 203 147 61 12 91
M 222 379 204 102 70 18 5 142
All 178 293 229 161 95 36 6 126

Trained meteors are on the average two magnitudes brighter than other meteors, the mean magnitudes being respectively 0.9 and 3.2

The ratio of increase of numbers with decreasing brightness, shown in Table XVI, reveals the same trend as in ordinary meteors (Table II) but the ratios are only half as great and decline more rapidly.

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Table XVI.—Ratio of Numbers to Magnitude.
Obs. Magn. 0–1 1–2 2–3 3–4 4–5 5–6
F 3.4 1.9 1.1 0.2 0.7
G 1.3 1.3 0.8 0.7 0.4 0.2
M 1.7 0.5 0.5 0.7 0.3 0.3
All 1.6 0.8 0.7 0.6 0.4 0.2

Table XVII reveals the number of coloured meteors possessing trains per thousand observed meteors.

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Table XVII.—Colours of Train-forming Meteors.
Obs. Red. Orange. Yellow. Green. Blue. White. Total Coloured.
F 34 16 5 4 7 938 62
G 122 79 107 25 87 580 420
M 45 25 15 61 133 721 280
All 55 32 29 40 95 749 250

There is a slightly higher percentage coloured (25%) than in the case of ordinary meteors (21.6%). The distribution among the individual colours, however, is very similar in both groups, and it can be deduced that colour itself is not a factor in causing trains. The only exception between the two groups is that whereas blue shows a high percentage among ordinary meteors it occurs very rarely among trained objects.

The mean durations of train-forming meteors and of the trains they leave are as follows:—

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Obs. Meteors. Trains.
F 0.816s 1.189s
G 0.632 1.921
M 0.733 1.433
All 0.721s 1.621s
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The train generally lasts twice as long as the meteor creating it, and that meteor itself lasts 50% longer than the ordinary object.

The mean length of path of the train-forming meteor, according to the various observers, is as follows:—

F 14.0°; G 10.3°; M 16.0°; All 14.5°,

which compares with a length of 9.4° for the ordinary meteor.

Characteristics of Average Meteors.—Finally it may be of interest to summarise the characteristics of the average normal meteor (both trained and untrained) as revealed from the New Zealand data:—

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Untrained. Trained.
Magnitude 3.4 0.9
Duration (seconds) 0.434 0.721
Path length (degrees) 7.7 14.5
Coloured (percentage) 21.6 25.0

In the earlier tables these characteristics have slightly different values (there relating to all recorded meteors), but in the above table the comparisons are between trained and untrained meteors.

My thanks are due to the observing members of the Meteor Section whose labours have made this paper possible, and especially to Messrs. Fairbrother and Geddes, who extracted preliminary statistics from their own observations as they were secured.