110 A NEW METHOD OF DETERMINING 
= e ° iP Tm e a ° . ° 
Substituting the values of —cosf, —sin f, given before, and similar ones for 
a a s 
® cos o, © sin w, we find 
My My 
Ca ( d.p* ) (<7) mr. (oe) () 
ma: aedg ¥ \agedg/ \ade/* 
My le 
Substituting the values of these factors we obtain for C’ the expression 
C=(1—te) sn(y— g) 
— (8¢ — 3) sin y 
+ (Le— 32 &) sin (y — 29) 
+ § @ sin (y—8y) ee) 
+ $e sin (y—4y) 
—7,¢ sin (y + 29) 
. 5 d du 
Haying found the expressions for and : 
nat ndt . cost 
we have, finally, for determining the perturbations, the following expressions : 
noe =n f W dt, 
dw 
n f a dt, 
— = (Oa (>). 
tos 7 dZ. 
| 
n= 
° : dw 
Two integrations are needed to find ndz. We first find W from Fae then, form- 
pa Re an) td . oS ge 
ing W and — $ ip from JV we have néz and » by integrating these quantities. In 
: : dw . . F 
the integration of aa We Sive to the constants of integration the form 
ky + k, cos y + k sin y + 9 k, cos 2y + 7°) & sin 2 y + ete. 
