THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 81 
we have 
== sen Lt {(x- sae Sr\dt+ ae ee jens aah) Sr dt (10) 
Now multiply the first of (9) by y, the second by «, putting for | Ps its value 
V2 
given by (6), noting that 
we have 
sae nar Sr)dt 
( 
2 (11) 
+ poe f (H+ Eee. sryac 
c Czas 
We can write Spe the form 
; 
a ue v) = —( +7. 24¥.% 
lt dt 
We have 
na df dz df a 
aby) = eS Ss Se LS oe 
(EY) ae al CE GR GG ?s 
df 2 AS) oD 
df = pe eo COS Po, UN = Ay Nh. 
dt r 
Making use of these relations we find 
de 
di (C55) Pyne 
ale 
and for 5, given above we have 
Zz lz y 
@ = Al +0). 2 — Ve + Ve, 
A. P. S.—VOL. XIX. K. 
