of a homogeneous fluid mass that revolves upon an axis. 1 35 
Now, in the equation of the ellipsoid of which k, k 1 , k" are 
h 
the axes, if we substitute R,v/l f'X Sm - R ' x/l ^ p' C os -£ 
for the equivalent quantities, -f;> y , ; we shall obtain, 
I p' 2 | (i — p' 2 ) Sin. 1 q' . (i — p' 2 ) Cos .‘ 1 q' 
iv 2 — T z "• F 2 ‘ F 
And, by a like procedure in the other ellipsoid, we obtain, 
i p 2 . (i — p 2 ) Sin. 2 q . (i — p 2 )Cos. 2 y 
~ "F "T F* I F 2 ’ 
Thus R' is a radius of the ellipsoid that passes through the 
attracted point, and r' a radius of the given ellipsoid which 
is entirely within the first figure. The last integral may 
therefore be developed in a series of the ascending powers of 
r' : and then, applying the same reasoning as in the former 
case of the developement of Q* it will be found that all the 
terms are evanescent, except the first. Thus the general term 
of the expansion is, 
r n x f* C c ^ d P' d< i ' . 
fJtJ R '* — 2 
and, when i is an odd number, this integral is equal to zero ; 
because the increment at any point on the surface of the sphere, 
is just equal to the decrement at the point diametrically 
opposite : and, when i is an even number, it is evanescent ; 
because — X— contains no terms except such as are evanescent 
r/ Z-2 
in the integral, according to the theorem in § 5. Wherefore, 
the integral being reduced to the first term of its expansion, 
we get, 
p' and q' being taken between the same limits, as p/ and t$. 
* Section 5* 
