[[Categoria:Pagine che usano RigaIntestazione|Scientia - Vol. VIII.djvu{{padleft:44|3|0]]only the direction of the group-motion, and its numerical amount (compared with the average haphazard motions of the individuals). Reversing the process we can test our observed proper motions to see whether they can be accounted for in this way; and if it is found that they do correspond to a haphazard group, we can deduce mathematically the direction and amount of the motion of the group as a whole.

When this test is applied to the observations it becomes plain that there is some very considerable deviation from the haphazard distribution. The differences are fundamental, so that the true law of stellar motions must be something radically different from the law of chance. Even the first condition fails utterly; it is found that the direction in which fewest stars are moving is not by any means opposite to that in which the maximum number move. Moreover there is generally besides the chief maximum a secondary maximum in another direction. We will take as an example the stars of Cassiopeia and parts of neighbouring constellations. Indicating directions by position angles running from 0° to 360°, it is found that the greatest number of stars are moving in the direction 10°. Therefore if the individual motions were governed only by chance, the fewest should be moving in the direction 190°, and the motions should be distributed symmetrically on either side of this direction. Now compare this with the facts; the actual minimum is in the direction 275°, very nearly at right angles to, instead of opposite to, the direction of maximum. The numbers are:

Nor is there any approach to symmetry about the direction of maximum; on the one side there is the rapid decrease from the maximum 66 to the minimum 6 followed by a steady rise to 17; on the other side the number falls more slowly to 19 in the direction 95°, then rises to a secondary maximum of 26 moving in the direction 135°, and falls again to 17 in the direction 190*. These peculiarities can be best seen by reference to Fig. I., in which the distance from the origin to the curve represents the number of stars moving in the corresponding direction.