240 



CATALOGUE OF POLAK STAKS. 



dt* 



2mn f + nm f 



11 



) sin a 



m 2 n 



n 



3 



3 m n? 



& 



7 cos a 



11 



■i 



siir a cos a 



21i 



i 



sin 2 a tan 8 



3 n 7i T 



sin 2 a tan <5 



3^ 



sin 2 c« cos a tan 2 8. 



(35) 



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



adopting the convenient form which 

 formula) become : 



Hill has given on p. xix for 



d 2 a 



dt 



and 



d 2 8 

 ~d? 



, the 



— = + o!'00003221 + [-4.6338048?i] — + [5.9877809] — cos a tan 8 

 dt 1 dt dt 



+ [4.8116896*] 



dt 



sin a sec 2 8. 



(36) 



— = 4- o!b000000145 + [2.6391089] cos 2 a + [0.9237867*] sin 2 a 4- [2.6176279*] sin a tan 8 

 dt 3 



4- [2.5787978] sin a cos 2 a tan 8 + [0.8598285*] cos a tan 8 + [2.9401389] cos 2 a tan' 2 8 

 + [1.2248167*] sin 2 a tan 2 8 4- [2.4027065] sin a tan 3 8 + [2.7037365] sin a cos 2 a tan 3 8. 



(37) 



d*S 



dt 2 



4- [4.6338048*] 



dt 



4- [7.1638722m] 



da 

 dt 



Bin a. 



(38) 



d s 8 

 lit* 



4- [2.0359378] sin « 4- [4.0004500*] cos a + [3.2777678*] sin 2 a cos a 



4- [3.8152002*] sin 2 a tan d + [2.4009130] sin 2 a tan 8 4- [3.7548891*] sin 2 a cos a tan 2 8. 



(39) 



tf 2 « 



Men ten has introduced a convenient modification of the expressions for -— and 



dt 2 



(See Astronomische Beobachtungen auf der Sternvvarte zu Bonn, VII. pp. 147-148.) 



Let 



A 



m' + 



n 



21? 



sin 2 a 



mn . 

 J' = ?i f cos a — sin «. 



log 2? = log | — ~~ - J- -* - 



cos « 4- n 



log (7 



lo 



<T 



n - 

 i2 



sin 2 a. 



lo£ Z?' z= \o<r 



22 



sin 2 a ). 



(40) 



In which A, B, and (7 are expressed in seconds of time, and A' and 27 in seconds of 

 arc. Or, 



