Theory of Surface Forces. 211 



obtained, less analytically, by the argument employed upon a 

 former occasion*, and still more simply perhaps by considera- 

 tion of the forces operative upon the entire mass of fluid 

 included between the two strata in question regarded as a 

 rigid body. It is very important to remember that it ceases 

 to apply at places where p is varying, and that unless the strata 

 are plane it requires correction even in its application to 

 regions of uniform density. 



In the case of a uniform medium, (6) gives the relation 

 between the external pressure w, measured in experiments, 

 and the total internal pressure p, found by adding to the 

 former the intrinsic pressure Kp 2 . By the constitution of the 

 medium, independently of the self-attracting property, there 

 is a relation between p and p, and thence, by (6), between 

 «r and p. If we suppose that the medium, freed from self- 

 attraction, would obey Boyle's law, p = kpj and 



<Br=kp-Kp 2 (7) 



According to (7), when p is very small, -or varies as p. As 

 p increases, -sr increases with it, until p = #/2K, when -or 

 reaches a maximum. Beyond this point -or diminishes as p 

 increases, and this without limit. The curve which represents 

 the relationship of ts and p 

 is a parabola ; and it is evi- Fig. 1. 



dent that all beyond the 

 vertex represents unstable 

 conditions. For at any point 

 on this portion the pressure 

 diminishes as p increases. If, 

 therefore, the original uni- 

 formity were slightly dis- 

 turbed, without change of 

 total volume, one part of 

 the fluid becoming denser 

 and the other rarer than 

 before, the latter would tend still further to expand and the 

 former to contract. And according to our equations the col- 

 lapse would have no limit. 



Points on the parabola between and the vertex represent 

 conditions which are stable so far as the interior of the fluid 

 is concerned, but it may be necessary to consider the action 

 of the walls upon the fluid situated in their neighbourhood. 

 The simplest case is when the containing vessel, which may 

 be a cylinder and piston, exercises no attraction upon the 

 fluid. The fluid may then be compressed up to the vertex of 

 * "On Laplace's Theory of Capillarity," Phil. Mag". Oct. 1888 



