400 J. W. Gibhs —Equilibrium of Heterogeneous Suhstcmces. 



Concerning the Stahility of Surf aces of Discontinuity. 



We slicall first consider the stability of a film separating homoge- 

 neous masses with respect to changes in its nature, while its position 

 and the nature of the homogeneous masses are not altered. For this 

 purpose, it will be convenient to suppose that the homogeneous 

 masses are very large, and thoroughly stable with respect to the 

 possible formation of any different homogeneous masses out of their 

 components, and that the surface of discontinuity is plane and 

 uniform. 



Let us distinguish the quantities which relate to the actual com- 

 ponents of one or both of the homogeneous masses by the sufiixes 

 „, J, etc., and those which relate to components which are found only 

 at the surface of discontinuity by the suffixes „ , ^ , etc., and consider 

 the variation of the energy of the whole system in consequence of a 

 given change in the nature of a small part of the surface of discon- 

 tinuity, while the entropy of the whole system and the total quan- 

 tities of the several components remain constant, as well as the 

 volume of each of the homogeneous masses, as determined by the 

 surface of tension. This small part of the surface of discontinuity in 

 its changed state is suj^posed to be still uniform in nature, and such 

 as may subsist in equilibrium between the given homogeneous 

 masses, which will evidently not be sensibly altered in nature or ther- 

 modynamic state. The remainder of the surface of discontinuity is 

 also supposed to remain uniform, and on account of its infinitely greater 

 size to be infinitely less altered in its nature than the first part. Let 

 jde^ denote the increment of the superficial energy of this first part, 

 Aif, Am^, Ami, ^^c-, ^"'^, ^nil, etc., the increments of its superficial 



determinate values to the superficial densities of energy, entropy, and the component 

 substances, which quantities, as has been seen, play an important part in the relations 

 between the tension of a surface of discontinuity, and the composition of the masses 

 which it separates. 



The pioduct ct s of the superficial tension and the area of the surface, may be 

 regarded as the available energy due to the surface in a system in which the tempera- 

 ture and the potentials (U,, // 2) 6tc. — or the differences of these potentials and the 

 gravitational potential (see page 208) when the system is subject to gravity— are 

 maintained sensibly constant. The value of a, as well as that of s, is sensibly inde- 

 pendent of the precise position which we may assign to the dividing surface (so long 

 as this is sensibly coincident with the surface of discontinuity), but es > the suiierjicial 

 density of energy, as the term is used in this paper, like the superficial densities of 

 entropy and of the component substances, requires a more precise localization of the 

 dividing surface. 



