4] THE SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. 123 

 Non-Periodic Term in Second Equation, 



0- 



dt 



4 dn da ( 

 ~3di~ H ~dt 



tub., mn 2 Sa 2 + n -~ (2 2m) 6 5 (2 2m) n"Ba s + n -~ 

 - (2 - 3m) & |~(2 - 3m) rr Sa 8 + n ^ 8 1 - (2 - m) & 9 f (2 - m) w'So, + w $H 

 + ma. |~ - wm'8& 3 + n ^1 + (2 - 2m) a 5 f - (2 - 2m) n 2 S6 5 + n ~0 

 + (2 - 3m) a 8 |~ - (2 - 3m) w'Sfe. + w '^1 + (2 - wi) a, f - (2 - m) i^St, + ?i -^ 



Coefficient of sin fi in First Equation, 

 = mWSa,, + 2mn - 



- (2 - 2m) aj (2 - 3m) n 2 Sa 8 + n -^ 8 + (2 - 2m) a, (2 - 2m) n 2 Sa 9 + n C -j"\ 



\_ clt J |_ at j 



+ 2mn 2 Sk, - 2n -j- 2 + {(2 - 3m) & - (2 - m) & 9 } (2 - m) w 2 86 5 - ?i -^- 5 



- (2 - 2m) 6 5 1"(2 - 3m) n 2 86 8 -J + ( 2 - 2m ) 6. |( 2 - ) '8& - n -^' 



3 33 



a 2 + - n 2 (u s - u,) Sa, - - nfufa + -^ 



Coefficient of cos^>' in Second Equation, 



db 

 = wiV86, + 2mn -^r 



rfn o?a ~| f~ 2 cj c?a 2 "l 



162 



