Astronomy. — “Theory of Jupiter's Satellites. IL. The variations.” 
By Prof. W. pe Sitter. 
(Communicated in the meeting of June 28, 1919). 
We still restrict ourselves to the non-periodic part [ 2;| of the 
perturbative function, as in the determination of the intermediary 
orbit.') The quantities hj, k;, »;, w;, which were zero in the inter- 
mediary orbit, are now determined by the equations (23), *) of 
which the solution is given by (24). For the determination of the 
five values of 8,7 we have the determinant (28). Then c’;, and c';, 
are determined from (27) and cj, and c'’;, from the first and last of 
(25). The expressions for the coefficients a;;, a';;, bis, bis, dis, d'; 5, 
Eij, C'ij are given in Vol. XII, Part I, of the Annals of the Leiden 
Observatory, page 31. Then we have 
Aig = 2) (aitaig + bids), 
Bij= Zi(eiubij + brveiy), 
Cig = 21 (Ciraiy + esids;), 
D;; = 21 (ai bi5 + eters): 
The details of the computation of the quantities a;;, a’;;, ete. and 
A;;, Bij, ete. will be published in the Annals of the Observatory 
at Leiden. Here we shall only give the results. The determinant 
(28) is: (see formula A, next page). 
The coefficients are given in units of the eighth decimal place. 
Denoting the columns by roman, and the rows by arabic numerals, 
we now perform the following operations: 
add £.(V)+2.(VI) to (VID 
pes (Ve Sen URE (AVP See) 
=d. (1) TG) 
” 2. (7) Su (6) ” (5) 
ee (Oi 2 5 Gi 4) 
The determinant then becomes: (see formula B, next page). 
1) See Outlines of a new theory of Jupiter’s Satellites, These Proceedings, 
Vol. XX, p. 1289—1308, and Theory of Jupiter’s Satellites. 1. The inter- 
mediary orbit, These Proceedings, Vol. XXI, p. 1156—1163. 
2) “Outlines”? p 1301. The definition of hi and k; is slightly different here, in 
consequence of the introduction of e; instead of ni. We now have 
e; cos gi — @: + hi 
ei sin gj = hy. 
