THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 63 
As before the origin of angles here is at the ascending node of the plane of the dis- 
turbed body on the plane of the disturbing body, and the plane of reference is that 
of the disturbed body. 
E ; : dQ dQ 
If we differentiate the expressions for ip? - yp we find 
1 OZ 
o @2 AQ ml 
Sa pO aT TNS 
dp le ~ Bl vr Hf) 
eo -=o) ipa nae 
1=Em \ 2 Tage ° oP 
r a ee : = (7? — rr’ HZ) sin Tr’ sin (f’ + 1’) 
a = a ( 7 =) sin Z.r sin (f+ 1) 
x os =— ties : = (7° —rrH) sin 7.r sin (f+) + S 
ae —— =e : = .sin “J. rr’ sin (f+ I) sin (f’ + I’) + aon (4-3) cos L 
To eliminate H from some of these expressions we find from 
2 nat Al 2. ) 
Y= + r?— err’ . A, 
that 
: dQ 
The expression for Uae then becomes 
ar 
dQ a rey? 1 r i | 
Oise 1m 248 2A te 
From the value of A’ we have, further, 
PoaTp Tl | eee 1 
i = uae DE? 
