extensive Class of Spheroids 
cosines : on this account, we may make 
r* . Q (2) = a* . ( | ^ - |) + 6 s . { f ( i - n") cos. V- 1 } 
therefore, 
T Q (2) = T '^QTlog. * • ^'-(l ^ ,3 ~ I) 
+ y -Jlf\o^s .df . dm' . j-i (l — p/*) cos. V— f j 
4 ~ s . dp/* d ™' • { t ( 1 — p/*) sin. V — 4 } • 
Let the term multiplied by — be integrated by parts with 
respect to df, then J^^og. s . df . J ^ 4) = log. s x 
• ~ • 4 *': but - £4 . (£) = n'-n". •*: 
therefore, observing that the term without the sign of inte- 
gration vanishes both when p/ = — 1 and p/ = 1 ; the value 
of the coefficient of ~ will be equal to 
If 
•(j! 2, • dp! . dzj 
and because — = 
s 
s 
dii 
- p/ a . df . dm' i 
V p . q 
tity sought will be equal to 
a P pp-.dyl 
; therefore the first term of the quan- 
2 v.a 
which is equal to 
2 tt . a? f* x 2 . dx 
J v TT 
2w . a" 
Vif~ 3 
the fluent here being taken from x = 0 to x ■= 1. Seeking to 
express this value by means of the integral F, I have found 
