no Mr. Ivory on the figure requisite to maintain the equilibrium 
piped to move in directions tending to diminish y and z. 
Again, the accelerating forces X,Y, Z, acting on every paral- 
lelopiped produce the motive forces Xd oc dy dz, Ydxdy dz, 
Xd oc dy dz, tending to increase the lines x,y,z. But the 
equilibrium of the parallelopiped requires the equality of the 
opposite forces : wherefore, 
d <P ___ d (p y ^ P r j 
dx ’ dy ’ dz 
Hence, we get, 
d(p — Xdoc-\-Ydy-\- Z dz. 
Wherefore if we trace a stratum of the fluid so that <p shall 
every where have the same value, the figure of the stratum 
will be defined by the equation 
X dx -\-Ydp-\-Zdz=zo; 
which likewise shows that the resultant of the accelerating 
forces is perpendicular to the stratum. 
In what has been said, the equilibrium of every parallelo- 
piped is established with respect to all the outward forces 
extrinsic to its own matter. If the question relate to no other 
forces, the whole fluid mass, and all the level strata of which 
it consists, will be in equilibrio, and the problem is solved. 
But when the particles of the fluid attract one another, there 
are forces not yet taken into account, inherent in every paral- 
lelopiped, by means of which it will act upon all the exterior 
matter, and the efforts of which must be balanced, other- 
wise the equilibrium could not subsist. Now, if we suppose, 
as before, that all the level strata are possessed of such a 
figure as to act upon particles in the inside with equal forces 
in opposite directions, it is evident, that every parallelopiped 
will be in equilibrio by its action upon all the matter on the 
