THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 65 
the expressions which have been given for the forces, together with the perturbing 
function, are 
=—po(s) 2 Zain Ge ery 
9 3 sin r’ . 2 
+ $ua2(4) S22 7 sin (f’ +11’) 
¢ oe | = Buai(“)’ 2 =. = sin *( f’ + Il’) — u(“) 
aa (77) =0e(G) eG sin (F + 1) 
dQ a\SF 2? 1. 75) sin ip . 
Call ZV Se A) is egy ee r 
ae Dee 4 a”? a2 a sin Gi oe Il) 
— Sua? (“)" pesintd = sin (f+) —(Z)’ 
aa (<,) =— Buai(*)”, eo: - “sin(f + Il’ )= sin( f+ 11) + ua (4 cos FT _ (dD 
The form given to these expressions is the one best adapted to numerical compu- 
tations; and the equations are readily derived from the preceding in which the magni- 
tudes occur in linear form. 
Thus from 
2 m’ py? 1 - 
pe = [=e — an Fz] 
dr 1+m 24° 24 r? 
A. P. S.— VOL. XIX. I. 
