OF ARTS AND SCIENCES. 



53 



I have assumed as before, — 



^ = 259="o0'8 i)=32''29'l. 



I noticed, ioo late for use in this series, that if we put 



sin m sin M := sin 2) ; 



sin m cos J/= cos D cos (a — A), 



we can more readily use the formulae, which then become 



cos 1 = sin m cos (d — 31); 



sin ;f cos \p' =^ sin ni sin (8 — M) ; 



sin ^ sin xp' =. cos D sin (a — A) = cos m, 



or 



tan 1/;' = 



cot m 



sin X = 



sin (S — J/)' 

 cos m 



sin ij/' 



by tabulating w, J^ and log. eot m, log. cos m, or like functions, with 

 the argument «. 



In the following table, the stars are indicated by Argelander's num- 

 bers, and arranged in the order of their annual proper motions, the 

 largest (Groombridge, 1830) first. 



The columns contain in their order the star's number, Argelander's 

 values oi /I g and \p (Bonner Beobachtungen, Bd. VII. S. 109-113), 

 and those of ■^)', ip' — \p, and log. siu ^, which I have computed by the 

 preceding formula. 



In order to get an approximate idea of what these stars indicate, 

 with reference to -the relation between distance and annual motion, I 

 have taken the means of the cosines of ip' — xp in groups of twenty- 

 five stars each ; the means of the natural sines of ^ ^''6 not syste- 

 matically variable to any great extent throughout the table. 



