Astronomy. — ''Outlines oj a new theory of Jupiter's satellites". 

 By Prof. W. de Sitter. (Continued). 



(Communicated in the meeting of April 26, 1918). 



4. The variational equations. 



The constants of integral ion of (he intermediary orbit satisfy the 

 conditions (18), (19), and the conditions of symmetry (16). The 

 constants of 'integration of the actual orbit however do not exactly 

 satisfy these conditions. We now put, instead of (17) and (20) 



Xi = {a — X) T + Ttio 4- CO,. V,- =: V,- , 



m = — XT -f Tiio-{- 9i » ni = m + ^^« 



Instead of gi and (fm I introduce A, and ki by 



yji cos gi - 7ii -I- hi 

 T], sin gi = k, 



(21) 



(22) 



The equations then become 



dhi i dRi I — dRi 



^ = _ xki - (1 4- v,f _ _ i (I + vt) (^' + hi) — , 



dki - idRi , ^i, dRi 



-! =x(.i, 4 A.) + (1 H- »'.) V- - è (1 r »'<) ^. ^. 



rfto, i di2j i dRi 



-— -^ {a — x)ri — 2(1 -f vi) ai ~ hè (1 f v.) ^i.' ^— . 



at oui orii 



dvi 4 dRi 



- = ^3(1 + ..,)%--. 



We atill restrict ourselves to the non-periodic part \_Ri] of the 

 perturbative function. Then, if we neglect the squares and products 

 of hi, ki , oji, Vi , these equations are of the form 



