402 TRANSACTIONS OF SECTION A. 
MONDAY, AUGUST 30. 
Discussion on Positive Electricity.* 
Opened by Professor Sir J. J. Tuomson, F’.R.S. 
The following Papers and Reports were then read :— 
1. The Law of Distribution of Stellar Motions. 
By A. 8. Eppineton, M.A., M.Sc. 
Professor Schwarzschild’s hypothesis accounts for the existence of two 
favoured directions in the distribution of the proper motions of the stars 
by assuming an ellipsoidal modification of Maxwell’s frequency law, so 
that the frequency of a stellar velocity (wu, v, w) is proportional to 
E—g?u?—h* (0° +?) 
He has shown how to determine the constants of the ellipsoid from the 
observed statistics of the numbers of stars moving in the various directions. 
The method can be extended so as to make use of the mean proper 
motions of stars, instead of the numbers of stars moving in the various 
directions, as the observed data. This can be done quite rigorously; but 
by making an approximation (which is always amply sufficient in practice) 
the following simple rule results: the radius of the velocity-ellipse in 
the direction @ is the geometric mean between the mean P.M. of stars 
moving in the direction 6 and the mean P.M. of stars moving in the 
direction 6 + 180°. In this way it is easy to determine the velocity-ellipse 
for any region. For the seven regions of the stars of Groombridge’s cata- 
logue, I find the following values of the ratio of the minor and major 
axes of the velocity-ellipses (1) derived in this way and (2) derived from 
the numbers of proper motions. 
Mean P.M.’s ... °59,°56, *76, *82, -65, ‘53, -66, respectively. Mean ‘65 
No. of P.M.’s ... °59, °58, ‘70, ‘81, ‘72, -61, -72, respectively. Mean ‘68. 
The agreement region for region is very satisfactory, and there appears 
to be no systematic difference between the results derived from the two 
kinds of data, 
Another development of Schwarzschild’s theory which it seemed worth 
while to investigate is the consideration of a velocity-ellipsoid having three 
unequal axes, in place of the spheroid which has hitherto been considered. 
It was conceivable that some of the discordances of the various determina- 
tions of the vertex might be reconciled in this way; but the special interest 
of the discussion lies in the question whether the distribution of stellar 
motions has a special relation to the galactic plane. It is now fairly well 
established that the greatest axis of the velocity-ellipsoid lies accurately 
in the galactic plane; but, apart from this preference for a particular axis 
in the galactic plane, is there a preference of stellar motions for the 
galactic plane in general? If the distribution of the stars is comparatively 
limited in the directions of the galactic poles, it might be expected that 
their velocities in these directions would be, on the average, smaller. 
We should then have a velocity-ellipsoid with three unequal axes, of which 
the least would point to the galactic poles. On comparing observation 
with theory, the evidence, though inconclusive, appears to be unfavourable 
to the hypothesis of an appreciable deviation of the velocity-ellipsoid from 
the form of a prolate spheroid. 
* Published in Hngineering, Sept. 17, 1909, 
