Theory of Surface Forces. 295 



/ denoting the distance of the element of the fluid dx dy dz 

 from the point at which the potential is to be reckoned. The 

 hydrostatic equation of pressure is then simply 



dp=dV ; 

 or, if A and B be any two points, 



Pb— Pa=V b — V a . 



.... (26) 



Suppose, for example, that A is in the interior, and B upon a 

 plane surface of the liquid. The potential at B is then exactly 

 one half of that at A, or V B = i Va ; so that 



Pa-Pb 



*Vj 



Jo Jo 

 Now p A — p B is the intrinsic pressure K ; and thus 



>=27r^n(f)fdf= ^ytf)fdf 



K, 



as before. 



Again, let us suppose that the fluid is bounded by concen- 

 tric spherical surfaces, the interior one of radius r being either 

 large or small, but the exterior one so large that its curvature 

 may be neglected. We may suppose that there is no external 

 pressure, and that the tendency of the cavity to collapse is 

 balanced by contained gas. Our object is to estimate the 

 necessary internal pressure. 



Fig. 1. 



In the figure B D C E represents the cavity, and the pres- 

 sure required is the same as that of the fluid at such a point 

 as B. Since p A = 0, p B =Y B — V A . Now V A is equal to that 

 part of Vb which is due to the infinite mass lying below the 

 plane B F. Accordingly the pressure required (p B ) is the 



