99 
THE GENERAL PERTURBATIONS OF THE MINOR PLANETS 
adding to the preceding, it becomes 
[ r cose a 2e | (“) 
=— Oe © 
a y/1—e Wg Ne dr 
Further, we have 
cos f e sin?f resin ?f 
m= Vl1—é a (1—e?)3 
Gd TP .. r’ sin 
== || = Sun =-cosf /1—@ 
dg Lis eas a (1— re lak Oy Ay ae 
Reducing this expression in the same manner as employed before, it becomes 
2rcos f+ sae 
7? sin 
dg _sin Ha aia l= ale 
Multiply this by dg, the last expression for Fae becomes 
recos f+2 ae 
dQ 
= (7) ar ( 
a 1/ 1—e* ar] ” 
d¥ 2 2rcos f+ 3ae 
= ——— g a 
1—e?’ Jj ay/1—e* J dg 
the integral to be so taken that it vanishes at the same time with g 
dY dv 
> ndt? ndt’ 
Substituting these values of <.— 
dW dz  dY¥ /p j : 
ndt — ndt a ndt e GUS @ a e) +° ndt a sin 2 
this expression can be made to take the simple form 
7) + Bar (|) 
dw 
= adele 
in which 
; fe 2psinw 297 * 
f ( cos f 
Qa 
a’ (1—e’) —1 
a y/ l—e? 
: .4 (2% c08 o + 3¢) ae 
r sin f 2p sino (F cos +2¢) bo 
1 2p 
J G cos @ + 30) ———— —— 
a a / 1—e* a7 \—e* 
(31) 
+ 3e) dg } 
