J 293 



variatiotis, which are treated by the method of Lagrange, together 

 witli la, which is also in the ordinary theory treated in the same 

 way. We can say that all small divisors have been concentrated in 

 the eqnations of condition for the constants of integration of the 

 intermediary orbit. Once these eqnations have been solved, the small 

 divisors have disappeared, and they cannot reappear in subsequent 

 approximations. 



, 2. Formation of the diferential equations. 

 We take an arbitrary system of coordinate axes through the 



centre of Jupiter, and we put : 

 ƒ rr: the Gaussian constant of attraction, 

 m^ = the mass of Jupiter, 



im = the mass of the body with index /, expressed in m^ as unit, 

 Si = the latitude of the body i referred to the plane of Jupiter's 



equator, 

 n = the distance of the body i from Jupiter, 

 Ajj = the distance between the bodies i and j, 

 Vij= the angle between the radii- vectores ri and rj, 

 180° — 1|> = the ascending node of Jupiter's equator on the plane 



of {xy), 



jt = the inclination of this equator on the same plane, 



J,K = two constants connected with the compression of Jupiter, 



b = the equatorial radius of Jupiter, 



and further 



where 



i 1. Jb' Kb* 



Hi —fm^ ( 1 f m/ ) - + i -^T ( 1 -3 «"*' 'i) + TO ~-r(l - 1 Osm''s/+y sin*si)-\-. 

 n ri' ri" 



( 1 n 



-it-fm^:Emjlj- ^ cos Vij 



' . Jb' . Kb' , 



l-\ {l-hsi7i'sj)-\ {^-7sin'sj-\-^-^sin*Sj)-{-. . 



.; ''/ 



'(7) 



axi+fyi+yzi . 

 — Ó sm s i 



Jb' Kb' 



The sums are to be taken over the values 1, 2, 3, 4 of J, with 



89 

 Proceedings Royal Acad. Amsterdam. Vol. XX. 



