172 



SECULAR VARIATIONS OF THE ELEMENTS OE 



4,'=U4-Z—JLN" { cot A4-i-tan h } sin (/*+£ ) 

 / I / 



_^LiV" 1 "|cot7i-fi-tan7i 

 — J^iV 2 " 1 cot 7i_|_^tanA 

 — &]Sr 3 " | cot fc-f-l-tan h 

 _|iiV 5 " | cot A+i-tan 7* 

 _liiV 6 " | cot 7i+-ttan /> 

 — ^N 7 " 1 cot 7i-|-^-tan A 



sin (.#+&) 

 sin (/ 2 *+/3 2 ) 

 sin (/ 3 £+&) 

 sin(/ 6 <+/3 e ) 



sin (/,<+&) 

 sin (/ 7 *+/3 7 ) 



Precession of the 

 Equinoxes on the 



(552) 

 Apparent Ecliptic. 



e=h+9N" cos (ft+0 )+|^" cos (.#+&) 

 +^i^ 2 " cos (fj+pj+to-NJ cos (/ 3 * + &)' 



+J^iV 5 " COS (/ 8 <+ / 3 B )+!^a' COS (/,*+&) 



+| 7 iV 7 "cos(/ 7 <+/3 T ) 



/7 



Apparent obliquity 



(553) 

 of the Ecliptic. 



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

 equal to nothing when t=0. We may determine I and Ji as follows : — 

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



dt'~ 



(554) 



-gN"\ 



cot h-\ — jrtan h 



> cos (/*+£) 



-giW< 



cot 7;-j — ^tan7i 



> cos (.AH-ft) 



-g^'\ 



cot h-\ — j-tan h 



J2 



► COS (/ a <+&) 



-gJW < 



cot h-\-— -tan h 



Jz ■ 



> COS (/ 3 *+/? 3 ) 



-g&" - 



cot A-| — —tan h 



Jh 



> COS (/,*+&) 



—pA" " 



cot 7t-| — j-tan 7i 



Js 



> COS (/ 6 tf+0 6 ) 



— giNf ■ 



cot 7i-| — —tan h 

 Ji 



> COS (/ T «+&) 



J 



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

 £=23° 27' 31. "0; and -^=50".23572 according to the investigations of Bessel. 



