242 



CATALOGUE OF POLAR STABS. 



Then, 



a 



a 



df 



d 3 8 

 dt z 



P + P 1 tan 8 + P 2 tan 2 8 + P a tan 3 8 



Q+ Q v tan d +■ # 2 tan 2 8 



(40) 



Introducing the constants for 1875.0 we have : 



p 



Pi 



Q 

 ft 



s. 



[1.2248167«] sin a cos a + [2.9401389] 



+ [0.0816772w] cos « + [2.8996767n] sin a + [2.8798278] cos 2 « sin a. 



s. 



- 0.0000000871 + [1. 5258467m] sin « cos a + [3.2411689] cos 2 a. 



+ [3.0047605] cos 2 a sin a + [2.4027065/i] sin a. 



+ [2.0359378] sin a + [4.0004500w] cos a + [3.2777078n] sin 2 a cos a 



+ [2.4009130] sin 2 a + [4.1162302m] sin a cos a. 



+ [3.7548891/*] sin 2 a cos a. 



(47) 



Tabular values of A log 



B, log 



A' log B\ P, P lf P 2 , P 3 , 



1? 



2? 



are 



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



d to a sufficient 



mber of decimal pi 



for 



our pur 



The application of the for 



g 



will now be illustrated by the compu- 



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



a 



ft. m. s. 



7 29 5.631 



8 



88 59 37.69 



log sin a 

 log sin 2 a 

 log sin 3 a 

 loor sin 4 a 

 log sin 2 a 



log sin 4 a 



9.9663226 



9.8460234^ 



9.595071 5n 



9.9999457 



9.9326452 



9.8652904 



log cos a = 9.5786708n 

 log cos 2 a = 9.8528923» 

 log cos 3 a = 9.9634456 



log cos 2 « 

 log cos 3 a 



9.1573416 



8.7360124rc 



log tan 8 

 log tan 2 8 



log tan 4 8 

 log sec 2 8 



1.7553949 

 3.5107897 



log tan 3 8 = 5.2661846 



7.0215795 



3.5109236 



Computation of — and — 



dt dt 



log n s 

 log sin a 

 loor tan 8 



0.1261147 

 9.9663226 



1 .7553949 

 log n sin « tan 8 1.8478322 

 n sin « tan 8 + 70.442079 



da 

 dt 



3.072245 



s. 



+ 73.514324 



log n tf 



1.3022060 



log cos a 



9.5786708/* 



log n cos a 



0.8808768/1 



dti 



-7.6011 



dt 





