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 / (r) represent the attractions, a the radius of 

 the inferior surface, and b the radius of the superior surface, we shall 

 have 



dp = —f(r) d r, 

 whence 



p = r^ f (r)dr = 1^' f (r) dr. 



/"•ft 

 f (r) d r, and 



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 Avhich shows 

 therefore that this theory is not yet sufficiently comprehensive. 



