240 
later on these three accounts, the values of % and y; as given here 
are certainly exact and complete to the last decimal place given. 
The values added for comparison are those of my theory of 1908 °), 
reduced to the masses adopted here. This theory is SOUILLART's 
with some errors corrected. The computation of the motion of the 
argument of the libration, however, was carried one order further 
than was done by SourLLART. 
The values of the coefficients cjg, C'iy, ¢'ig and cj, are: 
9 1 2 3 4 5 
cig + 0.96868 + 0.02754 +4 0.02479 + 0.00230 — 0.00054 
fay — 04420 A ogden Re ATB — 01h84 AE 00032 
c3g — 00686 + 03813 + .98970 + .08804 + .00004 
tg + .00006 + .00012 — .12098 + 1.00000 „00000 
cig +0.96038 + 0.05057 + 0.02483 + 0.00229 — 0 00287 
da me ONO4A 42 OTT EE Ahab — DTA0D Beenie 
cso — 00637 + .04010 + .99952 + .08891 +4 .00018 
Esp + .00006 + 00012 — .12098 + 1.00000 00000 
c'ty + 2.7649 . + 0.9617 — 0.07900 —0.00718 + 0.15668 
Slant x COBO. ci 1.8535. ht 57340. 19 05039 OE 
oly 1400800.) 1 0.7824 .— 11738 I— 01082 AS 02150 
oe .0000 0000 + 00001 „00000 „00000 
e'ig + 0.01195 + 0.00363 — 0.00028 — 0.00002 + 0.00012 
d'or — 02934 + ..01486 + .00405- + 00085 — .00048 
er = 200052 == 01118 SR 00149 00013 00007 
cae 0 0 0 0 0 
If we neglect the squares and products of &, (as well as products 
ejé,), and if we put 
Wig = st 4 (Gq Frei), 
where the lower sign must be taken if either z or q, but not both 
of them, are 2, then the effect of the variations on the radius- 
vector and the longitude is: 
dr; 3 pe 
aa sat C lig Eq COS Wg — Eg Tig Eq cos (Ai; — Wy) — 
— } Zy (Cig —C'ig) & cos ( + Wo) 
Swi Eg eig Eq sin Wy + 2 Ly tig egsin (Mi) + Ly (Cig — ig) eq sin (li + Wy), 
where we have put 
On the Masses and Elements of Jupiter’s satellites and the mass of the 
System, these Proceedings, Vol. X, pp. 653 and 710. 
