222 INVESTIGATION OF THE SECULAR ACCELERATION [27 



dn I 3771 A ,de' 



and -J-- - 3m 2 - -^- m Me ' -^ ; 



new \ 32 / e 



da /_ 3771 A ,rtY 2103 4 ,de' 

 2 = 3m" - -^c-m 4 e' ^ - ----- mV -j- 



\ 32 J at 32 aY 



2937 



da /3 2937 A ,c?e' 



or j = - m- -- ^777- m* e -TT . 



2 32 / dt 



9. These equations give the rate of variation of the quantities n and 

 a. We will now shew that n denotes the actual mean motion, as it did 

 when e' was constant. 



From the values of u and H~ we find 



dt 1 I L , 9 4ft , , 11 ,/. 5 ,,\ 



- = -! 1 2ov or) + - me + 3m~e cos nt mil el cos (26 



11/ I ^ 4 \ t I 



_77 

 " 8 

 or 



m-e' cos (26 1 - 3?i'<) + ^- wiV cos (2(9 - n'm , 



O 



-yi rtf Q / ^ 



/ttrt/ _7 ' ' , o 2 / /j 2/1 ^/Q\ /r*/l 



-f 3m e cos 7t^ mil- e } cos ( 2c/ : 

 - ~ mV cos (26 - 3n'<) + ^ wV cos (2^ - n'<) 



O O 



sn 2 - 



, 

 24 new 7 48 



48 

 Divide by 



and take into account mV in the non-periodic term. 



' ^{! - 3'*' cos w '^} = 1 - ^r OT2 f 1 - 1 e'^ cos (20 - 2n') 

 cf" 4 \ 2 / 



