484 J. W. Gihbs — Eqidlibriufn of Heterogeneous /Substances. 



mally by stretching is identical with that which must be spent in 

 fornung an equal infinitesimal amount of new surface. But when one 

 of the masses is solid, and its states of strain are to be distinguished, 

 there is no such equivalence between the stretching of the surface 

 and the forming of new surface.* 



With these preliminary notions, we now proceed to discuss the 

 condition of equilibrium which relates to the dissolving of a solid at 

 tlie surface where it meets a fluid, when the thermal and mechanical 

 conditions of equilibrium are satisfied. It will be necessary for us to 

 consider the case of isotropic and of crystallized bodies separately, 

 since in the former the value of c is independent of the directiori of 

 tlie surface, except so far as it may be influenced by the state of strain 

 of the solid, while in the latter the value of <7 varies greatly with the 

 direction of tlie surface with respect to tlie axes of crystallization, and 

 in such a manner as to have a large number of sharply defined 

 minima.f This may be inferred from the phenomena which crystal- 

 line bodies present, as will appear more distinctly in the following 

 discussion. Accordingly, while a variation in the direction of an 



* This will appear more distinctly if we consider a particular case. Let us consider 

 a thin plane sheet of a crystal in a vacuum (which may be regarded as a limiting case 

 of a very attenuated fluid), and let us suppose that the two surfaces of the sheet are 

 alike. By applying the proper forces to the edges of the sheet, we can make all stress 

 vanish in its interior. The tensions of the two surfaces, are in equilibrium with these 

 forces, and are measured by them. But the tensions of the surfaces, thus determined, 

 may evidently have different values in different directions, and are entirelj^ different 

 from the quantity which we denote by o, which represents the work required to form 

 a unit of the surface by any reversible process, and is not connected with any idea of 

 direction. 



In certain cases, however, it appears probable that the values of o- and of the 

 superficial tension will not greatly differ. This is especially true of the numerous 

 bodies which, although generally (and for many purposes properly) regarded as solids, 

 are really very viscous fluids. Even when a body exhibits no fluid properties at its 

 actual temperature, if its surface has been formed at a higher temperature, at which 

 the body was fluid, and the change from the fluid to the solid state has been by 

 insensible gradations, we may suppose that the value of (t coincided with the super- 

 ficial tension until the body was decidedly solid, and that they will only differ so far 

 as they may be differently affected by subsequent variations of temperature and of the 

 stresses applied to the solid. Moreover, when an amorphous solid is in a state of 

 equilibrium with a solvent, although it may have no fluid properties in its interior, it 

 seems not improbable that the particles at its surface, which liave a greater degree of 

 mobility, may so arrange themselves that the value of a will coincide with the super- 

 ficial tension, as in the case of fluids. 



•j- The differential coefficients of cr with respect to the direction-cosines of the surface 

 appear to be discontinuous functions of tlie latter quantities. 



