114 Mr. Ivory on the figure requisite to maintain the equilibrium 
is every where perpendicular to the level surfaces ; so in the 
other body, the like force is every where perpendicular to the 
surfaces similarly situated. 
Take K and k any other two points similarly situated in 
the same surfaces that contain H and h : and suppose that 
H M, K N, are the thicknesses of the level stratum, in the 
upper surface of which H and K are placed ; and, in like 
manner, let hm, kn, be the thicknesses of the like stratum in 
the other body. Farther, put G, G' for the resultants of 
the accelerating forces, or the gravitations, at H and K ; and 
g, g' for the like forces at h, k. Because H and h are points 
similarly situated, the forces G, g are proportional to any 
homologous lines of the respective bodies. The same thing 
is true of the forces G', g*. Wherefore, 
G:G'::g:g'. 
But the line H M is homologous to h m , and K N, to k n : 
wherefore, 
HM : KN : : hm : kn. 
Consequently, 
GxHM : G'xKN :: g x. hm : g' * km. 
But the proportion of G x H M to G' x KN is equal to that 
of the pressures of the stratum upon the fluid below it at the 
points H and K : for the quantities of matter in the stratum 
are proportional to the thicknesses H M and K N ; and the 
pressures are proportional to the gravitations multiplied by 
the quantities of matter. In like manner g xhm and g' x kn, 
are proportional to the pressures of the stratum upon the 
fluid below it at the points h and k. Wherefore the pressures 
at H and K are proportional to the pressures at h and k. And, 
in general, taking any points similarly placed in the two 
corresponding surfaces, the pressures of the stratum upon the 
