150 A NEW METHOD OF DETERMINING 
The other expression for (7 ) is 
(HI) = Shy’ — 8] cos (— Bg’) + My’ — V8] sin Bg) 
+ Mhy! + Wy] cos (H— g) ~ — Sly’ + 18] ein (B— 9’) 
— ehy, cos (— 9’) + el’/dy sin (— g’) 
+ 2[ hy.’ — h’d,'] cos (— #— 29’) + 2[ ly.’ — U,'] sm (— # — 29’) 
+ 2[hy.! + h’d:'] cos (H — 29’)  -- 2[ty.’ + Vd,’] sin (H — 29’) 
— 4ehy,! cos (— 29’) + 4el’d,’ sin (— 29’) 
+ ete. -++ ete. 
In both expressions for (#7) we have 
h =" keos(1I1— KX) 
> V 
hi = — cos pcos q’ ky cos (Ml — KG) = Su — 
a a 
p. : > —_ 7, Osim | 
1 =~-—coso¢k sin (ll— KX) = s4u—, 
a a 
pee aN, : > — 1. pecosP 
U = cos @’ k, sin (11 — #) = 
or 
a. 
where as before 
w= ,206264.”8 and a=“. 
1-+m a 
In the second expression the eccentric angle of the disturbed body appears and we 
must transform the expression into one in which both angles are mean anomalies. 
With the eccentricity, ¢, of the disturbed body we compute the J functions just as 
we did in case of e’ of the disturbing body. 
