21] ON THE SECULAR VARIATION OF THE MOON'S MEAN MOTION. 149 



= -. 1 - 2a Su + m 4 ( 1 - 5e' 2 ) + wiV* + ~ m'e* + f m'e* 

 dv 7a 1 2 



-m 2 



- e' sin (2i> 2mi> + c'mv) 



3m 2 aSw J c?v ( 1 - e' 2 ) sin (2v 2mv) +-e' sin (2v 2mv c'mv) 



a, J L\ 2 / 2 



- - e' sin (2v 2mv + c'mv) 



6m- \dv\ ( 1 - e' 2 j sin (2v 2mv) + ^.e' sin (2v 2mv c'mv) 



a ,j L\ ^ / 



- - e' sin (2v 2mv + c'mv) a 8' 



+ m 4 (-) \\dv\ (l --e' 2 ) sin(2i'-2m^)+~e'sin(2^-2mi' 

 \ a // U L\ ^ / 



- fi' sin (2v 2mv + c'mv) 



14. Develope this equation as before, retaining m 4 only when it occurs 

 in the non-periodic part, and we have 



3 / 5 \ 21 



- m 2 ( 1 - e' 2 ) cos (2v 2mv) m 2 e' cos (2^ 2mv c'mv) 



4 \ 2 / 8 



g 



+ - m'e' cos (2^ 2mv + c'mv) 

 8 



m? - sin (2v 2mv) + m a - r, sin (2v 2mv c'mv) 



8 nat ' 16 ndt 



de. 



