OF ARTS AND SCIENCES. 



I have assumed as before, — 



^ = 259''50'8 Z)= 32^29'!. 

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



sin m sin M= sin D ; 



sin m cos J/= cos D cos (« — A), 



we can more readily use the formula}, which then become 



cos X = sin m cos {8 — M); 



sin ;{ cos xp' = sin 7/1 sin (d — M) ; 



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



53 



tan xp' = 



cot m 



sm X 



sm (S — J/)' 

 cos m 

 sin <|/' 



by tabulating m, iJi^ and log. cot m, log. cos w, or like functionsfwith 

 the argument a. 



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 of z/ ? and \p (Bonner Beobachtungen, Bd. VII. S. 109-11.')), 

 and those of xp', xp' — xp, and log. sin /, which I have computed by the 

 preceding forraulaj. 



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 xp' — xp in groujis of twenty- 

 five stars each ; the meanfe of the natural sines of )r are not syste- 

 matically variable to any great extent throughout the table. 



