THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 17 
Equations (16) give 
q-q- Csin’?Q= (8+ &).-£. 
The equation 
y= C—_.qnsin’Q 
then becomes 
(Yo + S)S = (Go + &)& (a) 
From (16) we haye, also, 
PO C= (nae Qe a> Waa 
from which, since y,=q.q, and C= y, + ¢, we obtain 
Oar 6) 9% = (Gnae BE Se (aaa (b) 
Equations (16) give again 
(yi —n)& = (Go + &) n. : (¢) 
When ¢ is known, & is found from (a) ; and the difference between (a) and (0) 
Got) 62—5) =O: 5%). (d) 
gives 7 when ¢ is known. 
The equations (a) and (c) give 
Bo +4 (yo + 6) 5 = (Bo + 28)" 
Bo+2E= 71-33 
and hence 
Bi 4 t+ )S=ye.5 
A. P. S.— VOL. XIX. C. 
