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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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 (X_r–1 + 2X + X_r + 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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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-

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

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:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]