( 756 ) 
terms, which we have determined in § 4. For 
independent of the relation. 
those terms are 
So we find that the disturbing function expressed in the @’s and 
the 8's takes the following form: 
—R=~y, (aa a) + oh’a, + ma, Va,a, cos p‚ 
where again , represents a homogeneous, quadratic function of the @’s. 
The second term is inserted because we take as first approximation : 
Va 
AT 
1 
I> — Va, COS (nt nn 2n,B.), 
n 
Wa, 
Q == — 08 {(2n, + n,)t + 2(2n, + n,)B,}; etc. 
ry les ci 
Furthermore we find 
p= + 2n,8, + An‚B, — U2n, En, 3, = + 2n,(8,—8,) + 4n,(8,—,)- 
$ 18. We can again suppose the differential equations written down, 
determining the variability of the @’s and 2's. We then immediately 
find : 
a, 
However, 8,,8..... .3 are variable. The coordinates q, ¢ 
> M495 i 14 
= constant, a, — constant, .....-.. Ak == constant. 
rk 
experience the influence of the relation in their phase, but not in 
their amplitude. 
Let us regard in particular the equations for «,, 
spat ae AOE: 
= + 2m,n,a, V a,a, sin p, 
a, = + 4m,n,a, V a,a, sin p, 
We deduce from this: 
GE GGase A. 
a, a, a, a, a, 
44 
2 
den 2(2n, + n,) mia, V aa, sin (p. 
and «, 
ater Oe an 
…) ») : 7 
2n, 2n, Zn, tn, IN 
| 
where C, and C, are positive constants. 
If we put 
Gt, = (2n, + n,) hb, 
