28 



— = — P.^qa'c ia'—c-) C, .nn J cos J — = — [0.5986—81 — 



where the niiniber within brackets is a logarithm. 

 Further: 



dJ dJ 



^ — — sm ; -- = - cos <P ; <P = 40°1'.8 ; 

 op Oq 



therefore 



therefore 



dJ dJ 



— =—[0.8083-1]; —= — [0.8841 — 11; 



op Oq 



dR dR 



— + [0.4069-81; -- — + [0.4827-81; 



op oq 



from which follows, taking as unit of time the century : 



-^= + 0".065; ^zi= — 0".054. 

 dt dt 



Perturbations caused bij the second ellipsoid. 

 Here the calculation is much simpler. Introducing: 



XX X 



du r du „ f du 







we find : 



3 (13 5) 



S£^ — E,-a,'E, - ^a.'Ey-— {a~—c')a,-E,si?i^ j\-j--e^ e' cos2xp\ . 



2 ' I 2 4 4 ] 



As a verification I have here also computed the perturbations of 

 the inclination and longitude of the node for some of the other 

 planets ^). 



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



sin^ J 

 V = — k-JTqa''c (a^ — c") -^30^* . 



According to Seeliger's data « = 1.2235 and c=: 0.2399; I get 



di d^ 



^) For Mercury I find : — = — 0".060; sin i -— = — 0".013 ; Seeliger gives: 



Civ €LZ 



di da 



— 0".057 and — 0".0l6. For Venus 1 find: - =+0".007; sin i -^ = + 0" .IbS- 



dt dt 



Seeliger: +0".009 and +0''.144; the results ditïer somewhat; however, cal- 

 culating according to Seeliger's formulae, for Venus 1 find : sini -r- = + 0".154. 



dt 



