EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 219 



Influence of Surfaces of Discontinuity upon the Equilibrium of 

 Heterogeneous Masses. Theory of Capillarity. 



We have hitherto supposed, in treating of heterogeneous masses in 

 contact, that they might be considered as separated by mathematical 

 surfaces, each mass being unaffected by the vicinity of the others, 

 so that it might be homogeneous quite up to the separating surfaces 

 both with respect to the density of each of its various components 

 and also with respect to the densities of energy and entropy. That 

 such is not rigorously the case is evident from the consideration that 

 if it were so with respect to the densities of the components it could 

 not be so in general with respect to the density of energy, as the 

 sphere of molecular action is not infinitely small. But we know from 

 observation that it is only within very small distances of such a 

 surface that any mass is sensibly affected by its vicinity, a natural 

 consequence of the exceedingly small sphere of sensible molecular 

 action, and this fact renders possible a simple method of taking 

 account of the variations in the densities of the component substances 

 and of energy and entropy, which occur in the vicinity of surfaces 

 of discontinuity. We may use this term, for the sake of brevity, 

 without implying that the discontinuity is absolute, or that the term 

 distinguishes any surface with mathematical precision. It may be 

 taken to denote the non-homogeneous film which separates homo- 

 geneous or nearly homogeneous masses. 



Let us consider such a surface of discontinuity in a fluid mass 

 which is in equilibrium and uninfluenced by gravity. For the precise 

 measurement of the quantities with which we have to do, it will be 

 convenient to be able to refer to a geometrical surface, which shall be 

 sensibly coincident with the physical surface of discontinuity, but 

 shall have a precisely determined position. For this end, let us take 

 some point in or very near to the physical surface of discontinuity, 

 and imagine a geometrical surface to pass through this point and 

 all other points which are similarly situated with respect to the 

 condition of the adjacent matter. Let this geometrical surface be 

 called the dividing surface, and designated by the symbol S. It 

 will be observed that the position of this surface is as yet to a certain 

 extent arbitrary, but that the directions of its normals are already 

 everywhere determined, since all the surfaces which can be formed in 

 the manner described are evidently parallel to one another. Let us 

 also imagine a closed surface cutting the surface S and including a 

 part of the homogeneous mass on each side. We will so far limit the 

 form of this closed surface as to suppose that on each side of S, as far 

 as there is any want of perfect homogeneity in the fluid masses, the 

 closed surface is such as may be generated by a moving normal to S. 



