extensive Class of Spheroids. 
On account of the equation (2), we get. 
f(l — p) • < LS- . P . dp = — i _ n . i -1- n -f I ' 
53 
d. {(!_*•)■ + ' 
1 V r J 
and, by integrating by parts, 
r. yn d»cM |3 ji 1 / *\ H + X . 
J C 1- ^) ' dft n ' ' P i—n.i+n+i ^ ^ ^ 
. P . + L f ( , _ ^) »+ ' . f . . dp . : 
J/x n+i * — n.i + n + l J > dp.n + 1 ' «A* 
and, by rejecting that part of the fluent which is evanescent 
at both the limits, we have 
.n r {i) 
n + 1 
d" + 1 C^ d? 
dp 
dy. nJ r 1 
ar a 
• — • dp. 
In this last equation the expressions on both sides are 
entirely similar ; and therefore by a repetition of the same 
operations we shall obtain 
r,, M » + 1 df + 'c^ dp 1 
J ^ ' ’ di* n + l * d(j. * — i _ „ _ 1 . i + n + 2 
,«+ 2 c (i) d* P , 
“ - c - - 3v • 
r , i\» + 2 « 
y (i — ^ ) • ^ M+2 
and exterminating the integral common to both these equa- 
tions, we shall get 
d n cW T» J 1 1 
n a ^ . 1 . du = — — — x — — 
j n * i — n . z— « — 1 A z-J-«+l.z-f-tt + 2 
/(W) 
x r ( ,_*•)”+*. d r . 
^ ^ ’ d^n + 2 d t S 
It is evident we may continue the like operations as far as we 
