AND THE FIGURE OF A HOMOGENEOUS PLANET. 
Ill 
As the quantities ti x, tiy, tiz } $5, a may be assumed as small as we please, the 
force f may be considered as retaining the same value for all the particles of 
the cylinder or prism; and therefore f dm is the motive force of the cylinder 
or prism, or the effort it makes to move in the direction of & s from the point 
(.r, y, z ) to the point ( x + lx,y + ly, * + &*). 
Let p represent the hydrostatic pressure of the fluid at the point (, x,y,z ). 
This term is used to denote the pressure relatively to the surface pressed : it is 
the whole pressure any surface sustains divided by the extent of surface ; or it 
is the actual pressure reduced to the unit of surface. The hydrostatic pressure 
is obviously variable in the different parts of a fluid, the particles of which are 
urged by accelerating forces ; and as it can vary only when its point of action 
is changed, it must be a function of the coordinates of that point. The whole 
pressure upon the end of the cylinder or prism at the point (r, y , z) will be 
equal to p X ; for we may suppose that p undergoes no change in the small 
extent of the surface u : and, in like manner, the whole pressure upon the 
opposite end will be equal to (p + tip) X *>■ As the pressures upon the two 
ends act against one another, their effect to move the cylinder or prism in the 
direction of tis from the point (x + & x, y + ti y, z + ti z) to the point ( x , y, z) 
will be equal to Ip X ; and this force, on the supposition that the particles 
of the fluid are at rest, must be equal to fdm, the directly opposite effect 
caused by the accelerating forces. We therefore have this equation for ex- 
pressing the non-effect of the equal and opposite forces, viz. 
tip X 00 -f- f d m — 0 : 
and, if we substitute the value of fdm found before, we shall get 
tip + Xc5,r + Ydy + Z'bz = 0. (1) 
This equation must take place at every point of the mass of fluid without any 
relation being supposed between the variations tix,tiy,tiz; which condition 
will not be fulfilled unless p be a function of the three independent variables 
x, y, z. We therefore have 
