238 



CATALOGUE OF POLAR STARS. 



(It 4 



3tt 



tan 3 8 [sin 4 a — 4 sin 2 a cos 2 «] + 



6 n 8 m 



1 8 n s m 



Ii 



- tan 2 8 sin « + 



i? 



3 



tan 2 8 sin a cos 2 a 



+ 



7 w 2 m 2 



E 



- tan 5 sin- a 



3 ?i 2 m 2 



n 



^• 



n m (m 2 + ?i 2 ) 



— sin a 



Ii 3 



tan 8 + ~ tan 8 (sin 4 a — 8 sin 2 a cos 2 a) 



6 n z m 



sin <* cos- a 



&c, 



&c, 



&c 



(23) 



For the computation of the numerical coefficients, we have the following con 



stants for 1875.0. (See Pub. XIV., p. 51.) 

 For the reduction in Right Ascension, 



m = 



s. 



: 3.072245 



n = 



s. 



: 1.336949 



m' - 



s. 



= +0.0000189933 





Sm 



l<x;m = 



: 0.4874558 



log?i = 



: 0.1261147 



log m 1 = 



= 5.2786011 



log E = 



= 4.1383338 



log m 2 = 



= 0.9749116 



log n 2 = 



: 0.2522294 



m 





log Ji 2 = 



= 8.276C676 



losr m 8 = 



= 1.4623674 



log ?i 3 = 



: 0.3783441 



n' = 



= -0.00000575333 



log i? 3 = 



= 12.4150014 







log n 4 = 



: 0.5044588 



lou n f = 



= 4.7599145k 







For the reduction in Declination, 



m = 



= 46.08367 



n - 



= 20.05423 



m' = 



-- +0.0002849 





ft 



logm = 



a 1.6635471 



logn = 



= 1.3022060 



log m' = 



= 6.4546924 



log Ii = 



= 5.3144251 



lose wv 8 = 



= 3.3270942 



log V? - 



= 2.6044120 







log IP = 



= 10.0288502 







log W 8 = 



= 3.9066180 



n' - 



= -0.0000863 



log Ii 3 = 



= 15.9432753 







log ft 4 = 



= 5.2088240 



log w' - 



= 5.9360108k 







Substituting in the 



da 

 dt 



preceding equations, we have: 



s. 



+ 3.072245 + [0.1261147] tan 8 sin a 



(24) 



cPa 

 dt- 



d*a 

 ~d? 



S. 



- [6.1138956] tan 2 8 sin 2 « + [6.4752367] tan 8 cos a + [5 

 + [4.7599145k] tan 5 sin a. 



(2d) 



.9. 



+ 0.0000000145 + [2.4027065] tan 3 8 sin 3 a + [2.9401389] tan 2 3 cos 2 a + [2.2777678] tan 5 sin 3 a 



+ [2.7811577/,!] tan 8 sin « -I- [2.6391089] cos 2 « + [0.8598285n] tan 8 cos a C 26 ) 

 + [1.2248167^] tan 2 8 sin 2 a + [0.9237867] sin 2 a. 





