98 A NEW METHOD OF DETERMINING 
we have 
(2) ay (7°) a =n (2) resin f 
df) Nil) Me dr/ a(1—e?) © 
Eliminating = from the expression for — , we have 
na 
dV 2 | a (1—e?)— 7? 7d r sin f dQ 
= ala) ae) 
jel; ~~ ae dg a/1l—eé dr 
In the same way we find 
CP 2 P 2 sin a cos f e sin ?f 
mile | i sys Wee ()— r vI—e+ V1= 
resin*f = 
a (1—e’)? we ) 
But if we employ the relation 
as r recos f 
— ad) * aie) 
f /1—e’, of the preceding expression, the whole term becomes 
r cos f e re dQ 
alle (1—e? yo ‘1—e? a a ail ae ) 
. @ COS 
in the term, 
Using the equation 
0=—recosf—r+a(1—e), 
multiplying by 
