3^ 



Neglecting- terms like e"" stn' - , e' .sin' ~ we get: 



2* 1 1 /3 5 



— =: sm' i( 1— cos2 Sl)+^H --{-- <^os 2co 



«7 2 4 ^ -^t;^ ^^ -r^ 



^^i 1 5 . ^ 



— = — sin' i shi 2rk-\ e^ sin 2co 



a'/' 4 . 4 



§? 1 . . '■ l^ . « ^ 3 • I 

 =: sin /' St?/ Q. -I- ^'^ sin — ( — sm (2 to — \/) .sin \ }, } 



if 11 /3 5 .A 



a'/ 2 4 ^ ^ ■ .^ V4 4 y 



1/^1 M 5 , 3 ) 



=:— ain i cos {l -\- e^ sni — I t'os(2to — Q,) -j cos 0, } 



a '••= 2 2 j 2 ^ • -^^ 2 i 



-' 2 2 



2(a^ — c'') sm ./.s?7? / cos (Q,— 0) I a, V7, 



Substituting in li these expressions we get 



p^^^^i^«/^r ^^ ,,2 , ^^^^1 ,.^A,.„... ^^ ^ 



1 



7 



The only perturbations to be considered are those ol' the longitude 

 of the perigee and of the node. 



The differential equations required are : 



.7tó__ I dR , ,d^f,_ I dR 



dt 7ia^'^ de dt na^^ di 



One easily perceives that the last term in the expression for R 



gives no sensible perturbation on account of the factor a^ — c', the 



6 

 vahie of which is about — , and of the fact that ^l has a period 



lOo 



of 18\3 years so that the coefficient we get by integration is about 

 thirty time» as small as would have been the case if ,ft had been 

 absent. In the same way 1 omit the term 6V«' — cyi\ in the coeffl- 



cient of ^m" — and thus We have the following expression fur R ; 



R _1 a/ 

 k^jrqa^c 2 a^' 



1 get C2 = 0.678 ; —-■=: 1.030 from whicli follows taking as unit 

 P 

 of time the centurv : 



