of a homogeneous fluid mass that revolves upon an axis. 99 
The English reader will likewise find the same investigations 
in a work published in 1821, under the title of Elementary 
Illustrations of the Celestial Mechanics, which is a translation 
of the first book of the Mecanique Celeste, and, in addition to 
the text, contains much valuable matter. Referring to these 
works, we shall first merely enumerate the chief properties 
of the equilibrium of a fluid mass, for the sake of recalling 
them to the recollection of the reader ; and then make such 
an application of the general principles as our present purpose 
requires. 
A heterogeneous fluid body cannot be in equilibrio, unless 
the outer surface be every where of the same density ; and 
farther, unless particles of the same density be arranged in 
distinct strata in the interior of the mass. The pressure upon 
all equal spaces of every stratum of uniform density, that is, 
the force acting perpendicularly to them, and pushing them 
inward, must be equal. Hence, these are called level strata, 
or couches de niveau, because the direction of the accelerating 
force, or of gravity, is every where perpendicular to them. 
It is easy to perceive that the densities must decrease in ap- 
proaching the outer surface. For, in two contiguous strata 
of different densities, if we take two molecules equal in vo- 
lume, and placed at the same point of the separating surface ; 
the common gravity acting upon both will produce a greater 
pressure in the denser molecule. Wherefore, if the denser 
matter were nearer the outer surface, it would penetrate into 
the rarer matter below it ; which is contrary to the perfect 
separation of the strata of different densities. 
Supposing all these conditions to be fulfilled, it readily 
follows that the fluid body will be in equilibrio. For the 
