J. TF. Gihhs — EquillbriuDi of Heterogeneous Suhstances. 483 



between solids and ilnids with reference to the tendency toward 

 solidification 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 siirface {^. 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 wnth respect to surfaces of discontinuity betAveen fluids 

 (see pages 380 and 386), will evidently apjdy without modification to 

 the present case. We shall use the suflix j with reference to the 

 substance of the solid, and shall siippose 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 

 other component substances may then be denoted l)y our usual sym- 

 bols (see page 397), 



%l)i %(l)5 -f 2(1)) ^ 3())) 6tC- 



Let the quantity (J be defined by the equation 



^=^S(i)-^Vs(i)-/'2 ^'2U)-/^3^'3(l)-etC., (659) 



in which t denotes the temperature, and /<2, /^3, etc. the potentials 

 for the substances specified at the surface of discontinuity. 



As in the case of two fluid masses, (see page 421,) we may regard 

 as expressing the work spent in forming a unit of the surface 

 of discontinuity — under certain conditions, which we need not here 

 specify — but it cannot properly be regarded as expressing the tension 

 of the surface. The latter quantity depends uj^on the work spent in 

 stretching the surface, while the quantity depends upon the work 

 spent m forming the surface. With respect to perfectly fluid masses, 

 these processes are not distinguishable, unless the surface of discon- 

 tinuity has components which are not found in the contiguous masses, 

 and even in this case, (since the surface must be supposed to be formed 

 out of matter supplied at the same potentials which belong to the mat- 

 ter in the surfiice,) the work spent in increasing the surfiice infinitesi- 



