214 INVESTIGATION OF THE SECULAR ACCELERATION [27 



Differentiate the first of these equations and put 



n' 



- 

 n 



-----~ 



du 4 \ L I Ib 



= 1 - m 2 (l - 1 e' 2 ) cos (25 - 2n't) - 7 j- m*e' cos (25 - 3n't) + y mV cos (25 - n't), 



ndt 9 1 1 / 5 \ 



or -j =l+- ?ttV- + 3mV cos ' - ??r f 1 - - e' 2 ] cos (25 - 2n't) 



77 11 



- mV cos (25 - 3iV) + - m-e' cos (25 - n't), 



o o 



since the other terms only give rise to terms of higher orders than we 

 have here taken into account. 



cos 2 - 



Hence H a = -, , = u 

 \?r(// 



+ 5m 4 ( 1 - Se 78 ) + 4 - mV J + mV' 2 + - m^ + 6wV cos w' 



- 4m 2 M -| e /2 J cos (20 - 2n't) - 14mV cos (2^ - 3n'<) + 2wtV 



x 1 1 - 9mV 2 + 1 mV' 2 + |f m' (1 - 5^) + ^ mV + f^ m^- 



- 6mV cos n' + ~ m 2 ^ - ^ e") cos (25 - 2nV) + ^ wtV cos (20 - 3n't) 



~m 2 e'cos(20-rit)\; 

 or, by actual multiplication, 



5 39 11 Q 



_ m V 2 - ~ W V* + ^ m 2 1 - e 2 cos 2 - 2 

 4 4 2 \ 2 



21 ^ 1 



+ my cos (25 - 3n') - - m?e' cos (25 - n't) V 



