THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 95 
Multiplying the first of these equations by cos (f— a), the second by sin (f —o), 
and adding the results, we have 
he cos (y%—7™%—o) = (re — 
—h) cos (f—0) +2 sin (f—a). 
Substituting this value of h.¢.cos (y—7,—«) in the expression for W,, noting 
that 
1 pe 
hyd, Cos*g, — #(1-+m)? 
we have 
7 — _2hop _ pl. 2h,.p fey OT, 
y= Fim) Reon a) TT 7 + Baum .sin (f- 0) 
(eas (Ft) ST 
cay? J, COS? go 
Differentiating relative to the time ¢ alone, 7 remaining constant, and haying care 
that all the terms of the expressions be homogeneous, we have 
dW, 2hop dv 2hp a&r 
= —o)r ‘ ae 
aE ae (f—2) = + Batm in (f—o).—, a 
re ++ dh 
= cos’ ¢ 5, le aS Gh a) 14 SFR 
and 
dh 04m) @e PF de 
aan a) dae OED 
Y ha — 
dt 
Substituting 
