172 



SECULAR VARIATIONS OF THE ELEMENTS OF 



J,' == U-\- 9-N" \ cot h-\- -.-tan7i > sh 



/I / J 



- 



9W cot 

 /i 



sin 



_ ? JV 2 " I cot A-|-^tan A V sin (/ 2 <+/3 2 ) 



^2 I /2 



_9?-N 3 " { cot A-f }.-tan 7t 1 sin (/ 3 <+/3 3 ) 



/3 I / 



/6 



cot 7t- 



sn 



_^JV 6 " cot ^+ tan 7t sin 



/a / 



- 



/7 



-2-Jw cos 



cot 



sn 



Precession of the 

 Equinoxes on the 



(552) 

 Apparent Ecliptic. 



cos 



COS 



-^iV 3 cos 



/3 



^-J\K COS 



/6 



Apparent obliquity 



(553) 

 of the Ecliptic. 



In equations (550) and (552), is to be determined so that ^ and # shall be 

 equal to nothing when <=0. We may determine I and h as folio ws:- 

 If we take the differential of equation (552), we shall obtain 



dt 



^2" { 



co t 



co 



cot 

 cot 



cos 



tan 7i cos 



cos 



1 



tan 7t 1 cos 



I 



cot fc+-tanA 1 



- 





cos 



-flf^V.* | cot /i+ j tan h J c 



^JV/ { cot A+-^tan A 1 cos (/ 7 <+/3 7 ) 



I /7 



(554) 



Now at the epoch of 1850, at which time we have supposed <=0, we have 



e=23 27 31."0; and ^1=50".23572 according to the investigations of BESSEL. 



dt 



