dJ dJ cl .f' óiy 

 Fi-üiii these expressions we eau (leleriiiiiie .^^>,.' x-^^ ^. t''^" 



c|uaii(ities required for the computation of the derivatives of li with 

 regard to these elements. In view of the calculation of tlie perturbation 

 of the obliquity of the ecliptic I do not use the elements / and i) , 

 but the elements /; and q thus defined : 



p = tan i sin ^ ^ = tan i cos j^ 



I get : 



— — cos i cos^ — sin (4' — ü)) + sin' — sin (ip — co -f 2^) ) 

 Ö/) I 2 ^ 1 



— =z — cos i j cos^ — cos {\p — io) — si7i- — cos (ip — ('J + 2ft) 

 d§' I 2 2 1 



dilJ i I ' _ Ï ~ /^ I 



sm J — ^-sinJtan—cosicos^^-cosJcosi\cos"-—cos{i\)-(Ji)-{-sin'' — cos{\\)-vi-\-2Q,)\ 



dp 2 ( ^ '^ ) 



sin J — =sz«J tan -cosisin ^ + cosJcos i ) cos'- sin(i|;-to)-si?i'-sm(if?-tö+ 2ft) . 

 dq 2 ( ^ '^ ) 



■ The differential equations for p and q are 'j : 



c;p_ 1 OF 



dq __ I OF 



dt ~ 7ia,^\/ l—e^cosH ^P 

 To verify these formulae I have used them for the computation 

 of some of the perturbations of / and ft, wdiich are given by 

 Seeliger ^). 



To compute the perturbation of the obliquity of the ecliptic I take: 



sin^ J /-Y 2 



F= — k'.iqa^c {a- — c^) C^a^ . 



According to SeelicxEr's data a = 0.2400, c= 0.0239, /=6°57'.0; 

 I get C\ = 0.426 ; taking as unit of mass the mass of the sun, as 

 unit (^f time the mean solar day I get locj q:=0.711d — 5 and I 

 tind : 



') TissERAND, Traite de Mécanique Celeste I p. 171. 



2) For Mercury I get: ^' = +ö".573; sm ^ V" = - 0"-0^9 ; Seeliger gives : 

 ^ ^ dt dt 



+ 0".574 and — 0".O49. For Venus I get: -^ = +0".163; sini^' = +0".0^\\ 



dt dt 



Seeliger: + 0".1o9 and +0".088; the small difrerence is owing to the value I 

 get for C3 = 2.286. while from Seeliger's data lollows C3 = 2.217. 



