554 EQUILIBRIUM OF INCOMPRESSIBLE FLUIDS. 
molecule and the centre, the equilibrium will necessarily take place. 
For the molecules situated at the same distance from the centre of at- 
traction must all be moved in the same manner: if one of them ap- 
proaches the centre-all the others must approach it also, and within the 
same distance; and they cannot approach it in such a manner, that all of 
those situated on the same spherical surface described from the centre 
of attraction would retain the same motion ; for the consequence of this - 
would be a diminution of volume. The liquid will thus remain in equi- 
librio; but it is evident that the force which attracts each molecule 
situated in the interior surface of the shell has its direction outside of 
the liquid mass. Let f (7) represent the attractions, a the radius of 
the inferior surface, and 5 the radius of the superior surface, we shall 
have 
dp=—f(r)dr, 
P=fPpoarafCF@ ar. 
b 
The pressure on the inferior surface will then be f Ff (r) dr, and 
e/ @ 
this pressure certainly differs from zero, a fact which is contrary to the 
generally received opinion. 
Here then we have a singular case of equilibrium, which the esta- 
blished theory of liquids is not sufficient to explain, and which shows 
therefore that this theory is not yet sufficiently comprehensive. 
whence 
