124 THE SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. [4 



- {(2 - 3m) b a + (2 - m) b s } |(2 - 2m) 



(2 2m) b 5 (2 3m) n 2 8 8 + n 



(2 2m) b s \ (2 m) n 2 8 9 + n -r~ 



\_ d* _ 



+ {(2 - 3m) 8 + (2 - m) a 9 } |~ - (2 - 2m) n 2 8b s + n -^ 



L dt 



+ (2 - 2m) a, - (2 - 3m) n 2 86 8 + n 



+ (2 - 2m) a, I" - (2 - m) w s 86, + n ~] 



G6i J 



Coefficient of sin 2f in First Equation, 

 = (2 - 2m) 2 n 2 8a 6 + 2(2- 2m) n ~ + 2a 5 ^ 



(.( ( (.(/{/ 



[^ f/ii f/fy I f/fy ~1 



-77 + 74 ; {(2 3m) 8 + (2 m) a 9 } mw 2 8a 2 + ?i -r- a 

 3 ar ofr J L t J 



r/o \ ->5 ^i , r/o \ 5 ^ a n 



/y<a., (2 3m) n*oCL + n -^ + ma., (2 ?n) rr Sa 9 + w ^~ 

 L dt J L dt J 



+ {(2 3m) b s (2 m) 6 S } mn"&b., n -~ +2(2 2m) n~8b s n j^ 



r dl) ~i r db~\ 



+ mo. 2 (2 3m) n~ob x n -*- + mb., (2 m) w 2 S6 n r-" 



L rf J L rf J 



3 2 , ,rj 2j; 3 S 3 "S 



-n (u a -u s ) a 2 + n a 5 + -nw 2 a 8 +-7iw 2 da 9 



Sb, + n-q,, S6 8 - n 2 q., 8b 3 . 

 Coefficient of cos 2f in Second Equation, 

 = - (2 - 2m) 2 2 S& 5 + 2 (2 - 2m) n ^ + 2b 5 ^ 



- 2 f(2 - 2m) n 2 8 5 + n ^1 - mb y f(2 - 3m) 



n 



