242 



CATALOGUE OF TOLAR STARS. 



Then, 



— :^ = P + P^ tan 8 + P^ tan= 



+ P, tan= 



an 



_^ = Q+ Q^ tan 8 ■\- Q, tair 8. 



d(- 



Introducing the constants for 1875.0 we have : 



(4G) 



P = - 0.0000000290 + [l.-i-i4.SlG7«] sin « cos u + [-2.9401389] cos= «. 



7>, = 4- [0.0816772«] cos « + [2.8996767n] sin a + [2.8798278] cos= a sin «. 



P^ = - 0;0000000871 + [1.5258467/1] sin « cos a + [3.2411689] cos'^a. 



P. = + [3.0047665] cos= a sin a + [2.4027065n] sin «. (47) 



Q = + [2.0359378] sin u + [4.0004500n] cos a + [3.2777678h] sin= « cos «. 



<?, = + [2.4009130] sin^ a + [4.1102302«] sin a cos a. 



Q,, — + [3.7548891;*] sin^ a cos «. 



Tabular values of A log I?, log C, A' log 5', P, Pj, P., P3, (?, <?„ ^2, are 

 given in Publication XIV. of the Astronoraische Gesellschaft, but they are not 

 carried to a .sufficient number of decimal places for our purpose. 



The application of the formulae given will now be illustrated by the compu- 

 tation of the differential coefficients for Groombridge 1119, for the epoch 1875.0. 



A. m. «. 



« = 7 29 5.631 



log sin n = 9.9663226 log cos a ■■ 



log sin 2 « = 9.8460234?i log cos 2 « : 



log sin 3 « = 9.5950715m log cos 3 « : 



log sin i a = 9.9999457 log cos'' a ■ 



log sin- cc = 9.9326452 log cos' a ■■ 

 log sin* a = 9.8652904 



r- f?rt , dS 

 Computation 01 — and -— : 

 ■^ dt dt 



8 = 88 59 37.69 



9.5786708n 



: 9.8528923« 



9.9634456 



9.1573416 



: 8.7360124« 



log tan 8= 1.7553949 

 log tan= 8 = 3.5107897 

 log tan' S = 5.2661846 

 log tan* d = 7.0215795 

 log sec- S = 3.5109236 



