2i0 CATALOGUE OF POLAR STAKS. 



/2mn' + nm'\ vrn «' 'Amn^ _ 



— ( I sin « — "7^7 cos « — — sin^ a cos « — ^^ ,,, sin 2 « tan S 



_ — -— sin^ a tan 8 — ^77 sm- « cos u tan- 0. (00; 



Substituting the preceding numerical values of tlie constants for 1875.0, and 

 adopting the convenient form which Hill has given on p. xix for -— and -^, the 

 foriuulas become : 



'ill' = + o!'000032'21 + [4.6338048»1 — +[5.9877809] — cos a tan 5 

 dt'^ dt dt 



+ [4.8116896?i] ^-- sin « sec'' fi. (36) 



fj^'l ^ + ot'0000000145 + [".i-GSgiOSg] cos 2 « + [0.9237867/?] sin 2 « + [2.617G279«] sin u tan d 

 dl^ 



+ [2.5787978] sin a cos 2 a tan fi + [0.8598285«] cos a tan ("i + [2.9401389] cos 2 a tan- S (37) 



-1- [1.2248167«] sin 2 a Vm\- d + [2.4027065] sin « tan" S + [2.70373G5] sin « cos 2 u tan' d. 



^ = + [4.0338048)1] — + [7.1638722«] -^ sin «. (38) 



c?<2 L -^ dt dt 



— - = 4- [2.0359378] sin u + [4.0004500«] cos a + [3.2777G78h] sin= a cos u (39) 



dt^ 



+ [3.8152002«] sin 2 a tan ^ -f- [2.4009130] sii.- a tan 8 + [3.7548891w] sin- « cos « tan= 3. 



d^ii d'S 



Menten has introduced a convenient modification of the expressions for ^^— and ^^^j. 



(See Astronomische Beobachtungcn auf der Sternwarte zu Bonn, VII. pp. 147-14:8.) 

 Let 



n^ m n 



A = m' + sin 2 «. ' A' = h' cos a - sin u. 



2Ii Ji 



log ^ = log cos a + n' sin ,t . log ^' = log ( - " sin- a j. 



(40) 



n- 

 I02: C = losr — sin 2 «. 



In which A, B, and C are expressed in seconds of time, and A' and B' in seconds of 

 arc. Or, 



