THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 87 
n . ( “a 9 
If we put |» =1-+ 34, substitute the values of ——, and cos *, we get 
) VT. 
r D U0. TONG) 
él ance : ooo 2 
(1—2¢6,&—cos *¢,5’— cos *¢97")? 
0 
(20) 
dz 
qa =U + 6) 
Further, in the case of », we have 
r 
1lt+v= = 
=~ 
Then since 
OG 2 9 n 
Oi = Osos 5 = (1 + 5b), 
0 
and 
cos * 2 £2 Da 
£ = (1— 26, £ — cos oy &? — cos 7"), 
COS "gy 
we have 
: 1—2e,E—cos *¢,.’—COS “gy. 
G7) = Panne: 26 rare 
(1+ —cos f+ —sin f.7)* (1--6)8 
CP Ay 
If we let 
a - iP ° 
Al = 2 eat +—.sinf.7, 
a My 
B= 1— 2¢,& — cos *@, &? — cos *y 7”, 
i  GeauOy 
hy a BS ? 
we find 
diziares: Ai ') = Fea 
ae = (ae) fap (Lar?) = Fae 
