of a homogeneous fluid mass that revolves upon an axis. 1 07 
described, will be entirely dependent upon the outer surface. 
If the uppermost stratum, or any number of the uppermost 
strata be taken away, a part of the attractive force acting 
upon every particle will be destroyed, and the curve surfaces 
will no longer be perpendicular to the resultants of the re- 
maining forces urging the particles. Suppose that the strata 
are taken away successively ; then, the figure necessary to 
the equilibrium of the remaining fluid will change as each 
stratum is abstracted ; which is contrary to the just principles 
of the equilibrium of a fluid mass. The level surfaces of a 
homogeneous fluid mass in equilibrio, are determined with- 
out ambiguity by varying the arbitrary constant of the gene- 
ral equation. And as there is no doubt that the figure of the 
outer surface has no relation to any matter placed without 
it ; so any level surface, which is defined by a perfectly simi- 
lar equation, must be independent of all the exterior matter. 
Farther, the gravitation acting at any point of the outer sur- 
face is a function of the co-ordinates of that point, and has 
no dependence upon any exterior matter ; and, the like force 
at any level surface being the same function of the co-ordi- 
nates of that surface, it must be equally independent of the 
exterior matter. And although it be admitted that every 
level surface must be perpendicular to the resultant of all 
the forces urging the particles, yet it does not follow that no 
modification of the forces is necessary to the equilibrium. I11 
reality, the foregoing observations prove that, if we reason 
consistently from what is allowed in the usual determination 
of the equilibrium of a fluid mass, we shall be led to the 
same conclusion at which we have already arrived ; namely, 
