1227 
this argument, therefore, is of much importance; {2 is a secular 
argument, its introduction is therefore obvious; the argument @® has 
a short period and thus leads to the terms in the development of 
the perturbative function, which are of little importance. From R 
therefore all terms with arguments containing ® or a multiple of d> 
2x 
For convenience sake in the rest of this paper the line above the 
letter R is omitted. 
Putting 
L—G= A, 
NG FF 
and n’ for the mean motion of Titan, the equations for 6, ?, A, T 
become: 
| dd OR OR d6 OR 
eh BOY a aan 
dr OR db OR 
en Se A ee 
dt 02 dt or 
2. The excentricity of Titan being a small quantity, I shall try to 
develop the solution of these equations in powers of this excentricity. 
Thus, first I put e/=0; then R appears to be independent of 
{2 and to be a function of 6 only. The equations then are: 
dS OR C=0) dO. x ORE =) — 
ioe Osh eet Bn’, 
dt 00 dt Of 7 
dT db _ÒR(/==0) 
—=0 , =- ran 
dt dt or 
: M? ‘ 
Putting R, = RE (KR—R,)e=o, R=R, +R, +-R,, 
2 (4A= 7)? 
the development of R, is: 
fe ©} 
Rm, y> A) cos p, 
0 
where A,,... A,...-are functions of 4 and T. 
R (e'=0) being independent of ® and 2, the equations for A, 
r and @ form a system apart; after the integration of this system 
® is determined by a quadrature. This system admits the solu- 
tion: @=0, 4=const., F==const… However, between the constant 
values of 4 and I, which are called 4, and I,, a relation must 
