A = a x Qkk'k" x JJ 
B 
C 
of homogeneous Ellipsoids. 
cos. a i p . sin, (p . d<p . dp 
367 
) A* + e* sin. cos. *4* + c 1 sin. sin. 2 4" j 
= ho. - f cos. >4- ■ . ,/i^ .I 
= C X 2 kk'k" X ffj 
k 2 4- e 2 sin. 2 <£> cos. 2 p 4- e' 2 sin. z <p sin. z p 1-| 
sin. sin. *4- . dip . dp 
k z -}- e 2 sin. 2 <p cos. 2 4 -f sin. 2 p sin. ^p 
the several fluents to be taken from cp = o to q> = and from 
l|/ = 0 tO Ip = 2-5T. 
Let 
r r sin. <p . dip . dp 
JJ | k z + e z sin. z (p cos. 2 4 4 - e' z sin. 2 <p sin. 2 4 1 § 
then the last values of A, B, and C will be expressed by the 
partial fluxions of Q, as follows : 
A = a x zkk'k" x { - y (-^r ) + T (l?r ) + T 7 (ir) } 
B = b x sM" x - 7 (#) 
C=cx Qkk'k 11 x — • p • 
For the sake of brevity, let P 2 = e 2 cos. 2 ^ -f <?' 2 sin. : then 
/ rfQ\ sin. . 
\ dk I J J {k z 4 - e z sin. z <p)£ ‘ 
and, by integrating relatively to <p, 
I dQA r_J±_ f if2i L£__l • 
“* \ rfjfc J J A 2 4- p 2 ‘ t (" 2 + P 2 sin - 2 <P) i S ■ 
and, by taking the whole fluent from cp = o to q>= - , and 
restoring the value of P % 
Let r = 
/ dQJ 
1 - f- 
1 dk j 
1 —J l 
e y x 
sin. 4 > 
e z j X 
COS. ip ’ 
dp 
~m = 
‘“)i I > 
dr 
dk I (k z + e z )k (A 2 4 - e' z )i J 1 4 - t 25 
and, by integrating from = 0 to 4* = 
3 B 2 
