118 Mr. Ivory on the figure requisite to maintain the equilibrium 
the same body H I K be in equilibrio with respect to the pres- 
sure and attraction which the exterior matter exerts upon it. 
It has likewise been proved that all the surfaces OPQ, LMN, 
&c. similar to the outer surface R S T, are level surfaces ; 
and this ensures the equilibrium of the interior body H I K 
with respect to the pressure it sustains. Its equilibrium with 
respect to the attraction of the exterior matter, requires far- 
ther, that all the strata between the surfaces R ST, OPQ, 
LMN, &c. attract every particle within them equally in 
opposite directions. We are therefore to conclude that the 
homogeneous fluid body R ST, which revolves about the 
axis A B, and the particles of which attract one another in 
the inverse proportion of the square of the distance, cannot 
be in equilibrio, unless both these conditions be fulfilled ; ist. 
The level surfaces must be all similar to one another ; 2dly. 
Every stratum contained between two level surfaces must 
attract particles in the inside with equal force in opposite di- 
rections. 
In the Proposition that has just been proved, the similarity 
of the level surfaces is an accidental property connected with 
the supposed law of attraction. In the general hypothesis of 
an attractive power between the particles, the conditions of 
equilibrium are no more than these : ist. The resultant of 
the accelerating forces acting at every point of the outer sur- 
face must be directed at right angles towards that surface : 
2dly. All the level strata must possess such a figure as to 
attract particles in the inside with equal force in opposite di- 
rections. It may not be altogether superfluous to prove, by 
a synthetic demonstration, that these conditions are sufficient 
for the equilibrium. This is done in the following Proposition. 
