142 MR. IVORY ON THE EQUILIBRIUM OF FLUIDS, 
and the attractions of the matter between the two surfaces upon the particle, 
will be 
(A' - A") x, (B' - B") y, B' - B") 2 . 
As these forces act upon every particle of the mass a b c, they will cause an in- 
ternal pressure ; let p' denote the hydrostatic pressure at the point (x, y , 2 ) 
caused by the attraction of the external matter ; then, by the general theory, 
we shall have 
d p' + (A' — A") x d x + (B' — B") {y dy + zdz) = 0 ; 
and, by integrating, 
p' = C'- (A' - A") ~ - (B' - B”) . (11) 
Further, the joint effect of the centrifugal force and the attraction of the 
whole mass ABC upon the particle (x, y, z) in the respective directions of 
the coordinates, is expressed by these forces, 
A' x, (B'-f)y, (B '-/)*: 
and if p be the pressure thence arising, we shall have 
d p -\- A' x dx (B' — f) {y dy + zdz) — 0 ; 
and consequently, 
p = C-A'±-(B'-f)':£±l (12) 
which is equivalent to the equation (10), and expresses the whole hydrostatic 
pressure at every point (x, y, z) within the mass ABC. 
In order to form a just notion of the pressures p and p', we shall suppose 
that the point ( x , y , z) is in the interior surface, at am: conduct a narrow 
canal from G to a m, and continue it outward to the upper surface of the fluid, 
at A M. Now p is the effort of all the molecules in the canal A«mM pro- 
duced by all the forces that urge them along the canal ; and p’ is the effort of 
the canal a G m caused by the attraction of the matter between the two sur- 
faces upon the particles contained in the canal. The pressure p is always 
directed inward ; but the direction in which p' acts will depend upon the na- 
