of a homogeneous fluid mass that revolves upon an axis. 121 
outer surface, and the pressure of the uppermost stratum 
upon the fluid below it, as both independent of the attractive 
force of the matter of the stratum. But the attraction of the 
same matter upon all the particles within the stratum is a 
force of the same order with the pressure p x k, and com- 
parable with it, and which must not be neglected. Thus it 
appears, that the uppermost stratum acts upon the fluid below 
it both by pressure and by attraction ; and, as all the level 
strata are derived from one another by the same law, it 
follows, that every stratum in the interior likewise acts upon 
the fluid below it both by pressure and by attraction. 
Now it has already been shown, that the pressure of the 
uppermost stratum is the same over all the surface of the 
fluid below it ; and the same thing, it is manifest, is equally 
true of any level stratum. Wherefore, since the strata press 
equably upon one another, any fluid body in the interior, 
bounded by a level surface, will be in equilibrio with respect 
to the pressure it sustains from all the superincumbent strata. 
But, according to the second condition in the hypothesis of 
the proposition, the same body will also be in equilibrio with 
respect to the attraction of all the exterior strata. Thus, 
every interior fluid body bounded by a level surface, is in 
equilibrio with respect to all the forces which the exterior 
matter exerts upon it. And, as this is true independently 
of the dimensions of the interior body, we may suppose that 
it is ultimately reduced to a quantity infinitely small, which 
exerts no force, and is in equilibrio by the external forces 
acting upon it. Then the whole fluid mass will be resolved 
into level strata, that are in equilibrio with respect both to 
the pressures and to the attractive forces, which they exert 
MDCCCXXIV. R 
