19U] 



on The Stars around the North Pole 



131 



average velocity of these stars iu the direction perpendicular to the 

 sun's motion is 18 "7 kil/sec. This is readily seen in the diagram 



Table IV. 



(Fig. 6) — the sun moves from S to S^ while the star moves from 

 a- to o-^ — the parallactic motion is the angle S or S^ and the cross motion 

 crSo-\ and the angle o-SS^ is 125° for this part of the sky. S o- 

 is very large compared with S S^ or cr a-^. 



Fig. 



22. We shall now make the assumption that some of these stars 

 are moving faster than this velocity, and some slower, just as errors 

 of observation are distributed about a mean error. With a mean 

 velocity of 13*7 kil/sec. there will be in 1000 stars — 



If now the observed proper motions are arranged it is found that the 

 number less than any value r can be represented satisfactorily by an 



algebraic formula N 



where N is the total number of 



(t2 + «-2)t 



stars and a is the mean value of r. The following table shows the 

 actual number of stars with proper motions between certain limits 

 compared with the number given by the formula : — 



K 2 



