of a homogeneous fluid mass that revolves upon an axis. 1 33 
L il _l — 
PTF* T k in 
F 
a z . b z , e 
T z T F 1 "T" 
A" a 
A 
F 5 
== i. 
h! 2 — h 2 =zk n — k 2 ; A" 2 — Ji=.k l,1 —k'. 
Again, as in the former part of this Paper, let 
.r = Rj(/ a=.r p 
j 1 = R / 1 — f* /2 . Sin. ■nr 7 , b = ry/ f i — ^“Sin.^jr 
z = R'V/i — ^'\ Cos. gt 7 , c = rV l — p Cos. w ; 
then R and r are respectively radii of the two ellipsoids. 
Farther, assume 
4* = A Rf feR'/ 
-p y = -p R 1 — Sin. ^ /=c RVi — -^> 7 * Sin. 
izzrpRVl-p'* Cos. 3r'= R 7 l/l — p n Cos. g 7 
A A „/ . 
7 a = r rp=* r p 
Y>b = ~rV i — ft* Sin. = r 7 Vi — p* Sin. ^ 
^ r = — p Cos. = r 7 Vl—p* Cos. ?. 
From these formulae we get 
R 2 = «x a -f- y* + £ a ; 
and hence, 
In like manner, it is shown that 
r a — r ,2 ~ A 2 — k . 
= A a — A*. 
Wherefore, 
R 2 4.r 2 =R 72 +r ,s . 
