Mr. IvoRY on the Attractions 
one another and similarly placed, whose surfaces envelop the 
same attracted point ; it is plain, from what has just been re- 
marked, that the attractions of these ellipsoids upon the point 
will be precisely equal. Thus it appears, that the matter in- 
closed between the surfaces of the two solids, does not alter 
the attractive force of the inner ellipsoid ; which could not be 
the case, unless the attraction of the superadded matter in any 
one direction were precisely equal to the attraction of the 
same matter in the contrary direction, so as to produce an 
equilibrium of opposing forces. Hence we may extend to a 
shell of homogeneous matter, bounded by any finite surfaces 
of the second order, which are similar to one another and 
similarly placed, what Sir Isaac Newton has demonstrated in 
the like hypothesis for surfaces of revolution ;* as in the fol- 
lowing theorem : 
“ If a point be situated within a shell of homogeneous mat- 
“ ter, bounded by two finite surfaces of the second order, 
<c which are similar and similarly placed ; then the attraction 
“ of the matter of the shell upon the point, in any one direc- 
“ tion, will be equal to, and destroy, the attraction of the same 
“ matter, in the opposite direction 
6 . Nothing more is wanting to complete a theory of the 
attractions of homogeneous ellipsoids, than to integrate the 
fluxional expressions (5) already obtained. In the case of a 
sphere, we have k = k' = k", and x* -J- y -f- % 2 = k 2 : there- 
fore 
now 2x . dy . d% is equal to a prism of the matter of the solid. 
Prin. Math. Lib. I. Prop. 70. Prop. 91. Cos. 3. 
