STARS IN COMA BERENICES. 353 



sufficiently accurate on account of the small value of the proper 

 motion for all of my stars. 



In the above formulae, a, fi, d and /// denote respectively the 

 right ascension and corresponding proper motion and the dec- 

 lination and corresponding proper motion for 1875. In calcu- 

 lating the constants, the right ascensions and declinations were 

 taken uniformly from the Astronomische Gesellschaft Catalog, 

 Zone IX ; the proper motions either from Auwers' ^'Neiie Reduc- 

 tion der Bradley schen Beobachtungen" or from Safford's " Cata- 

 logue of Mean Declination 0/2,018 Stars." 



If now we put 



and let 



T= the epoch of any catalogue, and 



tty, Oj,= the right ascension and declination as there given, 

 then will 



as is evident at once when we remember that the above expres- 

 sions are the first few terms of the expansion by Taylor's for- 

 mula of a and o, thus 



/da\ /d^a\ /d^a\ . 



and similarly for d. Here o.^ is the right ascension at the epoch 

 for which the precession is to be computed, 1875 in the present 

 case, and t is the interval from this epoch to the epoch of a. 

 For dates later than 1875, t is plus ; for those earlier, it is min- 

 us. Hence, transposing a^ to the first, and a. to the second 

 member, changing the signs and introducing the previous nota- 

 tion, we obtain the series in the form given above. 



(13) 



