102 Mr. Ivory on the figure requisite to maintain the equilibrium 
to the superincumbent matter multiplied by p, or by the gra- 
vity which urges a particle inward. But, as the density is 
constant, the quantity of matter pressing at K, will be pro- 
portional to the thickness K S. Wherefore, if $ C represent 
the additional pressure at K, we shall have 
SC=p xKS. 
Hence, 
KS = — = 
P v/ X 1 + Y a + Z z 
If now we suppose that $ C remains constant, and, by means 
of the formula just set down, determine the thickness at 
every point ; it is evident that the stratum will press equably 
upon the surface of the fluid H K I, and consequently will 
not disturb the equilibrium by its pressure. It remains to 
determine the equation of the upper surface of the stratum. 
For this purpose we have, 
jc=/>xKs = £ xKs= fxi + yl + z-)xks. 
r p \ p 1 p 1 p I 
The co-ordinates of the point K being x,y,z, let those of 
the point s be x lx, y -{- $y, z -f $ % : then K S being per- 
pendicular to the surface H K I, it is easy to prove that, 
Sx = VW ^ W t¥>‘* ks = 7 xKS > 
^ = -L x KS 
^ p 
J* = -xKS; 
P 
wherefore, by substitution, we get 
JC = X2x + Yty + Z Jz; 
that is, 
JC = 
Consequently, 
d <p 
d x 
d <p 
d z 
Sz. 
* + 4f^ + -^ + 4H*== c +' JC - 
