454 



POPULAR SCIENCE MONTHLY. 



thing? Certainly we can not learn all that we wish, yet we may learn 

 something that will help us form some idea of the respective distances 

 of the stars and the actual velocity of their motions. An ohvious re- 

 mark is that the more distant a star the slower it will seem to move. 

 We must, therefore, distinguish between the linear or actual motion 

 of a star, expressed as so many kilometers per second, and its apparent 

 or angular motion of so many seconds per year, derived by measuring 

 its change of direction as we see it with our instruments. 



We shall now endeavor to explain Kapteyn's method in such a way 

 that the reasoning shall be clear without repeating the algebraic opera- 

 tions which it involves. Let us conceive that Fig. 2 is drawn on the 

 celestial sphere as we look up at the heavens. S is the direction of a 

 star in the sky as we see it. Let us also suppose that the solar apex, 

 situated in the constellation Lyra, lies anywhere horizontally to the 

 left of the star, in the direction of the arrow-head marked Apex. Sup- 



ApeK 



Fig. 



pose also that, were the solar system at rest, we should see the star 

 moving along the line S D. Let the length of the line S D represent 

 the motion in some unit of time, say, one year. Next, suppose the 

 star at rest. Then in consequence of the motion of the solar system, by 

 which we are carried toward the apex, the star would seem to be mov- 

 ing with its parallactic motion in the direction S B, away from the 

 apex. Let the length of this line represent the parallactic motion in 

 one year. Then by the theory of composition of motions, the star 

 moving by its real motion from S to D, and by the motion of the earth 

 having an apparent motion from S to B, will appear to us to move 

 along the diagonal S A of the parallelogram. Thus, the line S A will 

 represent the annual proper motion of the star as we observe it with 

 our instruments, and which can be resolved into the apical motion, in 

 the direction S B, and is cross-motion in the direction Sr. 



The apical motion consists of two parts, one the parallactic mo- 

 tion, equal to S B; the other real, and due to the motion of the star 

 itself along the line S D, and equal to the distance of D from the 

 line Sr. 



We have now to inquire how, in the case of a great number of 

 stars, we may distinguish between the two parts. 



