4] THE SECULAR ACCELERATION OP THE MOON'S MEAN MOTION. 125 



. r, rf 9 ~| 



m6 2 (2 m) ?roa 9 + n -j- 



+ { - (2 - 3m) 8 + (2 - m) a,} - mn 2 S6 2 + n -^ 



r __ db B ~\ 



2 L dt \ 



+ ma., (2 m) w 2 Sfr 9 + n -^ 

 " L rt? J 



+ ^'" (PS +Ps) ^^2 + 2w 2 j> 8& 6 + ?rja,S& 8 + n'p^Sb,. 

 Coefficient of sin(2-<') in First Equation, 

 = (2 - 3m) 2 n 2 8a 8 + 2(2- 3m) n-^ + 2a a -j- 



Lvt Ct't' 



I *^ (if) da I cLct I 



- 2 (2 - 3m) a ^ 77 + n 77 ~ ( 2 ~ 2m ) a mw2 oa 2 + n -^-' 



r/ \ o ^ 5 ~i 



ma,\ (2 2m)n-ca 5 + n~j- 



f dfe.l , f/ ^ 



(2 2m) & 5 mn 2 86, n -^ + m/> 2 (2 2m) woo t n - 



2 (2 - 3m) rrS& 8 - n ~ 



dt 



Q Q 



^> o CV . " 'l C . 



Coefficient of cos(2f-(') in Second Equation, 



8 



- m& 2 [(2 - 2m) n 2 8a 5 + n ^] - 2 [(2 - 3m) n 2 8a 3 + n 8 



