216 INVESTIGATION OF THE SECULAR ACCELERATION [27 



also 



' 2 vn- f Q Q / T \ 



= J i + f m y cos n' - H m* ( 1 - s e '* ) cos ( 2 # ~ 2ra '0 

 .ffV a ^ 2 2 \ 2 / 



fiS 91 



- mV cos (20 - 3n't) + - mV cos (20 - n't) I , 



and 



jj' 2 r/?/ m~ ( I T \ 



7^- 4 ^ = - 1 - 2TO ' J ( l ~ 7> e/9 sin ( 2 ^ - 2 ' rt/ - 7wV sin (20 - 3rit) 



Al \L-0j\j (t I \ Zi J 



+ vre'sm(26-n't)[. 



Hence, substituting in the first differential equation and transposing, 



we find the quantity which is to be equated to 't, to be 



07 ->7 



= '" ' = 



m' ( 1 - 5,.) + iV= + mV" 



~ .7 e ' 2 cos (2^ - 2w') - mV cos (2^ - 3n'<) + iV cos (2^ - n'< 



3 / 5 \ 21 



- - m 2 ( 1 - - e' 2 ) cos (20 - 2n't) - mV cos (20 - 3n't) 



3 1 



- tree' cos (20 n't) [ . 



Comparing this with the former expression and observing that --j is 



IV Ct 



nearly =1, we see that the periodic terms agree, and by equating the non- 

 periodic parts, we have 



3231 



4 ,,} 



me j 



< /. 

 e - 



