EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 315 



other component substances may then be denoted by our usual 

 symbols (see page 235), 



s(D> ^s(i)> r 2 (ij, r 3(1 ), etc. 



Let the quantity or be defined by the equation 



<r = e 8 (D ~ ^s(i) faTw) /x 3 r 3 (D etc., (659) 



in which t denotes the temperature, and // 2 , yu 8 , etc. the potentials 

 for the substances specified at the surface of discontinuity. 



As in the case of two fluid masses (see page 257), we may regard 

 a- 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 upon the work spent in 

 stretching the surface, while the quantity or depends upon the work 

 spent in 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 

 matter in the surface) the work spent in increasing the surface 

 infinitesimally by stretching is identical with that which must be 

 spent in forming 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.* 



* 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 entirely different 

 from the quantity which we denote by <r, 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 a 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 <r coincided with the superficial 

 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 have a greater degree of mobility, 

 may so arrange themselves that the value of <r will coincide with the superficial tension, 

 as in the case of fluids. 



