THE 

 POPULAR SCIENCE 



MONTHLY. 



MAKOH, 1901. 



CHAPTERS ON THE STARS. 



i 



By Professor SIMON NEWCOMB, U. S. N. 

 STATISTICAL STUDIES OF PROPER MOTIONS. 



The number of stars now found to have a proper motion is suffi- 

 ciently 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 



Fig. 1. 



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 eases 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 mov- 

 ing in the direction of a straight line, S D. It must not be under- 



VOL. LVIII.— 29 



