220 INVESTIGATION OF THE SECULAR ACCELERATION [27 



Hence, taking the periodic parts of this equation, we have 



- '' 



*' cos (20 -<()]-; 



Ct t 



1 fl *i rfc' 21 r// 



... 2 (8) = M mV - sin (20- 2n't) -~m*=j- sin (26- 3w') 

 v /; n [ 4 oft 8 a 



+ 1 m'f sin (20 -<<)}. 



7. Substitute this in the first equation, putting -. = 1 in the co- 



re a 



efficients of the periodic terras, as these are only required to the order of 

 ??i 2 , and we obtain 



+ 8w = - - J20mV d f sin (26 - 2n't) - 14m 2 ~ sin (26 - 3n'<) 

 ^ 8 n ( a< at 



fjp' 1 5 ^7p' 



+ 2m= sin (2^ - n't) + = mV sin (2tf - 2') 



91 dp' "\ rlt>' 



- TT ' TT sin ( 2 ^ - 3ft/< ) + ^ 2 ^f sin (2^ - n' 



8 cf 8 a 



1 f95 .die' . 133 ,de' . 



= J.~- m>e' -T- sm (2(9 - 2n't) - -rrf-j- sin (2^ - 3n't) 

 n ( 4 dt 8 dt 



19 



. 133 ,de' . 



- 77, -r- sm (2(9 - 2n't) - - - m? -j~ sin (2^ - 3w') 

 n (12 dt '24 o? 



+ J| * sin (- ')}. 



Substitute this value of Su, and also the value of -==- , viz. 



xz?t 



- -j 1 + 3mV cos n'< - ^ m 2 cos (2^ - 2n't) - mV cos (26- 3n't) 

 n { 4 8 ' 



-n'tn, 



