108 Mr. Ivory on the figure requisite to maintain the equilibrium 
that the forces acting at any point in the interior, must be so 
modified by the figure of the fluid, as to render every level 
surface, and the gravity at every point of it, independent of 
the exterior matter. 
We may cite as examples of the two different cases of the 
equilibrium of a homogeneous fluid, the hypothesis of Huy- 
ghens respecting the figure of the earth, which falls under 
the first case ; and the Newtonian theory on the same subject, 
which belongs to the second. Huyghen’s supposed an attrac- 
tive force residing in the earth’s centre, and acting with the 
same intensity at all distances. Therefore, in the case of a 
revolving mass, every particle is urged by a constant force 
directed to the centre, and by a centrifugal force proportional 
to the distance from the axis of rotation. As there is no 
attraction between particle and particle, a level stratum will 
act by pressure only upon the fluid below it ; and the only 
condition requisite to the equilibrium, is an equable pressure 
over all the outer surface. But, according to Newton, every 
particle attracts every other particle ; and a level stratum 
will act upon the fluid below it, both by the pressure of gra- 
vitation and by its own attractive force. In this theory, 
therefore, the adjustment of the equilibrium requires the joint 
application of both the principles of the second case. 
The method of investigation followed in what goes before, 
is similar to a process of reasoning in Clairaut’s theory of 
the figure of the earth ; and it is certainly surprising that 
the difference of the two cases was not remarked by that 
acute geometer. Other authors have very generally adopted 
a more simple procedure introduced by Euler. It will be 
