386 Rev. J. H. Pratt on the Equilibrium of Fluids, 



equals zero. From this it follows, that near the surface dp\^ 

 positive; therefore ILd x -\-Y dy -^Ijdz > 0, which requires 

 that the resultant of X, Y, Z should be directed towards the 

 interior of the fluid mass. 



But the pressure at the surface of a fluid in equilibrium 

 does not always equal nothing. For what do we mean by the 

 surface^ when we speak of pressure ? Not the geometrical sur- 

 face, but the external layer of particles. The term pressure 

 implies the contact of two molecules ; and the equation of 

 fluid pressure at any point is deduced upon the supposition, 

 that at the point two molecules are in contact. Therefore un- 

 less we can show that the pressure upon the interior surface 

 of the external layer is an infinitely small quantity, we cannot 

 say that the pressure at the surface is equal nothing. Because 

 there is no pressure at the geometrical surface, (for the con- 

 ception of pressure has no place there,) we must not say that 

 the pressure at the surface equals nothing ; for this would 

 imply thai the analytical expression for the pressure at any 

 point in the fluid becomes zero at the surface, which is not 

 always the case, as we shall now show. 



In the cases of ordinary stable fluid equilibrium (for ex- 

 ample the external surface in the instance advanced by 

 M. Ostrogradsky), the pressure decreases as we approach the 

 geometrical surface ; and the pressure on the internal surface 

 of the external layer is an indefinitely small quantity, and is 

 smaller the less the thickness of the external layer. Hence, 

 in these cases, it happens, that the function expressing the 

 value of the pressure does become zero at the geometrical 

 surface. 



But in cases of unstable equilibrium of the nature of that 

 of the internal surface in M. Ostrogradsky's example, the 

 pressure increases as we approach the geometrical surface, 

 and is greater the less the thickness of the outward layer ; but 

 this layer must always have some thickness, for immediately 

 we reach the geometrical surface, the conception of pressure 

 vanishes, and the equation of fluid pressure has no existence. 

 If we could discover a function which would represent both 

 the magnitude of the pressure at any point of the fluid, and 

 the fact that there is no pressure at the geometrical surface, 

 this function would be discontinuous at the geometrical sur- 

 face. 



This seems to be the explanation of the difficulty. In or- 

 dinary cases of stable equilibrium (as has been shown) there 

 is no actual necessity for these distinctions, though they may 

 be very useful, even in those instances, to clear up our views. 



March 19, 1838. 



