[LECT. 



We notice that among these terms, one is of long period, approxi- 

 mately semiannual, and will become of greater relative importance than the 

 others on integration. 



To effect this integration, assume 



n = w + a sin 2 (6 - m) + /3 sin (2 - 2m) + y sin {(4 - 2m) 6 - 2}, 



so that the mean motion of TT is the same as that of CT, and substitute 

 in the equation. 



Then 

 dn 3 141 3 3 



+ : m- - m i + 2a--m-a + m i S--my cos2(0-sr) 



L4 16 244 



t9 39 ~I 



- m- - 6 m 3 + ' m* + (2 - 2m) /3 - 6m 2 a - '- my cos (2 - 2m) 



tl5 9 63 .9 H 



m' + - m 3 + .-g m 4 - ^- 7)^ 2 a cos (2;u<9 - 2H) 



+ | g m 2 + - Hi 3 + - m 4 + (4 - 2m) y - ? m'a - |m 2 yl cos {(4 - 2m) - 



so that if we take 



219 

 + W 



9 .15 99 



3 3 51 



"- 



