314 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



tension in the film are mainly due is a component of the liquid 

 masses on each side of the air film, the necessary differences of the 

 potential of this substance cannot be permanently maintained, and 

 these films have little persistence compared with films of soap-water 

 in air. In this respect, the case of these air-films is analogous to 

 that of liquid films in an atmosphere containing substances by which 

 their tension is greatly reduced. Compare pages 310, 311. 



Surfaces of Discontinuity between Solids and Fluids. 



We have hitherto treated of surfaces of discontinuity on the 

 supposition that the contiguous masses are fluid. This is by far the 

 most simple case for any rigorous treatment, since the masses are 

 necessarily isotropic both in nature and in their state of strain. In 

 this case, moreover, the mobility of the masses allows a satisfactory 

 experimental verification of the mechanical conditions of equilibrium. 

 On the other hand, the rigidity of solids is in general so great, that 

 any tendency of the surfaces of discontinuity to variation in area or 

 form may be neglected in comparison with the forces which are 

 produced in the interior of the solids by any sensible strains, so 

 that it is not generally necessary to take account of the surfaces of 

 discontinuity in determining the state of strain of solid masses. But 

 we must take account of the nature of the surfaces of discontinuity 

 between solids and fluids with reference to the tendency toward soli- 

 dification or dissolution at such surfaces, and also with reference to 

 the tendencies of different fluids to spread over the surfaces of solids. 



Let us therefore consider a surface of discontinuity between a fluid 

 and a solid, the latter being either isotropic or of a continuous crystal- 

 line structure, and subject to any kind of stress compatible with a 

 state of mechanical equilibrium with the fluid. We shall not exclude 

 the case in which substances foreign to the contiguous masses are 

 present in small quantities at the surface of discontinuity, but we 

 shall suppose that the nature of this surface (i.e., of the non-homo- 

 geneous film between the approximately homogeneous masses) is 

 entirely determined by the nature and state of the masses which it 

 separates, and the quantities of the foreign substances which may be 

 present. The notions of the dividing surface, and of the superficial 

 densities of energy, entropy, and the several components, which we 

 have used with respect to surfaces of discontinuity between fluids 

 (see pages 219 and 224), will evidently apply without modification to 

 the present case. We shall use the suffix l with reference to the 

 substance of the solid, and shall suppose the dividing surface to be 

 determined so as to make the superficial density of this substance 

 vanish. The superficial densities of energy, of entropy, and of the 



