241 
Ai = doo + Mio + (ei — 2) 7, 
ler. 
The first term for g=1... 4 gives the inequalities of group II, 
and for q=ö it represents the libration. The second term for 
q=—1...4 represents the equations of the centre. 
We have 
g 1 2 3 4 
tty -+ 0.96453  — 0.03905 +0,02481 + 0.00229 
T29 + .03186 + .95599 + 16287 + 01492 
T3g — .00661 — „08662 + (99461 + .08847 
Tag + „00006 — „00012 — .12098 + 1.00000 
For ¢=5 this term is better written in the form 
— 3 (is + 15) &5 cos (l; — U'5) 
+ (¢i5 + €15) €5 sin (l; — Ys). 
It then represents, like the third term for all values of yg, small 
periodic inequalities, whose periods differ little from that of. the 
equations of the centres. 
It should be pointed out that the theory here given (intermediary 
orbit and variations) covers the same ground as SourLLart’s, with the 
exception of the small periodic perturbations and the terms of very 
long period arising from the action of the sun, Saturn, etc. SovuILLART 
does not give any term of the perturbative function, nor any inter- 
action of two terms leading to a term of higher order, which is 
not taken into account here too; and he omits many terms which 
are included here. The above theory is certainly complete up to the 
numerical limit of accuracy which was fixed beforehand. This can 
certainly not be said of Souirrart’s theory, though it generally gives 
many more decimais. The new theory has proved eminently suitable 
for numerical computation. 
