144 
MR. IVORY ON THE EQUILIBRIUM OF FLUIDS, 
answering to the same centrifugal force, when the exterior one is the less 
oblate, the greatest interior surface of equable pressure, which is not a level 
surface, stands upon the equator ; and the rest are within this, similar and con- 
centric to it, as in this figure 
When the exterior spheroid is the more oblate of the two, the greatest inte- 
rior surface is described on the less axis, and the rest are similar and concen- 
tric to it, as thus, 
When the centrifugal force f has a certain relation to the attractive force, 
the two dissimilar spheroids ABC and a b c coincide in one ; and in this case 
there are no interior surfaces of equable pressure except the level surfaces. 
It has now been demonstrated that, in every oblate spheroid in equilibrium 
by a rotatory motion, there are two sets of interior surfaces equably pressed by 
the action of the exterior fluid ; and, in consequence, that there are two dif- 
ferent figures of equilibrium, and only two answering to the same velocity of 
rotation. But in the hypothesis of the first problem of this paper, and accord- 
ing to the theory of Clairaut, which as far as regards a fluid entirely at liberty, 
is equivalent to that problem, there is in every case of equilibrium, only one set 
of interior surfaces equably pressed by the exterior fluid ; and this is an incon- 
trovertible proof that the theory of the French geometer is insufficient for de- 
termining the figure of equilibrium of a homogeneous planet in a fluid state. 
