94 Mr. Ivory on the figure requisite to maintain the equilibrium 
Again, we have, 
r z — 2 rR'y + R' 1 , 
v ( r ) ~S : 
and, by taking the fluxions with regard to r, 
_ | rf- V(r) j rz= _Jdm{r'-rR'y) 
P 
But, 
r* — rR'y =/ 2 + r R' y — R'® ; 
wherefore, 
fd.V(r)\ gdm , ^ >« (r R' y — R' 2 ) 
- ( Jr J r -J~T+J 7 ; 
and, by adding the equivalent quantities, a V (r) and 2 f ij-, 
we get 
v ( r ) — ( 
d.V(r) \ 
dr 
= PP+J 
dm (r R ' y — R /z ) 
r 
and by substituting the value of d m, 
V(r) - r = jjd ✓ ./( . { i*y R ' + jjm* - *■) «' 
or, which is the same thing, 
/■ 
} 
c? r 
-IP™ PS)*™ 
In the present paper, we confine our attention to a homo- 
geneous body, or fluid mass ; and, ^ being constant, we may 
suppose it equal to unit ; then, having integrated the last 
equation with regard to the variable R', we shall get, 
w ' -If- 
d. 
y> 3 aoMH 
R 13 du' dzj' 
f 
In this formula, R' is the line drawn from the origin of the 
co-ordinates to the surface ; and the integration with respect 
to p, is to extend from jj/= i to g = — i ; and that with 
