|CHAPTERS ON THE STARS.|
STATISTICAL STUDIES OF PROPER MOTIONS.
The number of stars now found to have a proper motion is sufficiently great to apply a statistical method to their study. Several important steps in this study have been taken by Kapteyn, who, in several papers published during the past ten years, has shown how conclusions of a striking character may be drawn in this way.
We must begin our subject by showing the geometrical relations of the proper motion of a star, considered as an actuality in space, to the
proper motion as we see it. The motion in question is supposed to take place in a straight line, with uniform velocity. Leaving out the rare cases of variations in the motion due to the attraction of a revolving body, there is nothing either in observation or theory to justify us in assuming any deviation from this law of uniformity. The direction of a motion has no relation to the direction from the earth to the star. That is to say, it may make any angle whatever with that direction.
Let E be the position of our solar system, and S that of a star moving in the direction of a straight line, S D. It must not be under-