THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 
The last two of (7) give also 
ea Gals Os 
= Bo les 
C eee Difeo = (Ove 
r= (x ae ates) 
Nn Nn 
Introducing the values of f, F, given by (11), putting 
L=72+4.y2. 7p. cos °F 
Ua=y—4.y2 A . sin °” 
we have 
G7 eine 
so that 
C=y+ %.sin*f. 
Moreover, since 
v2— 6 = x . cos, 
we find from the expressions for &, 7, given above, 
Boek 6 jane nein 
m—n=f.n'.cos Ff, 
if 
g=14+2—(4) 
a1 (4) 
Substituting these in the expressions for gsin Q, gcosQ, they become 
gsin Q=/f.&. sm 
gq cos Q = f. 7’. cos F. 
19 
(19) 
(21) 
