EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 237 



make p'p", t, yu 3 , // 4 , etc. constant is in this case equivalent to making 

 t, fjL l} /* 3 , /z 4 , etc. constant. 



Substantially the same is true of the superficial density of entropy 

 or of energy, when either of these has the same density in the two 

 homogeneous masses.* 



Concerning the Stability of Surfaces of Discontinuity between Fluid 



Masses. 



We shall first consider the stability of a film separating homo- 

 geneous 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 com- 

 ponents, 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 suffixes a , &, 

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

 the surface of discontinuity by the suffixes g) h) 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 discontinuity, 

 while the entropy of the whole system and the total quantities 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 supposed 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 thermodynamic state. 

 The remainder of the surface of discontinuity is also supposed to 



* With respect to questions which concern only the form of surfaces of discontinuity, 

 such precision as we have employed in regard to the position of the dividing surface 

 is evidently quite unnecessary. This precision has not been used for the sake of the 

 mechanical part of the problem, which does not require the surface to be defined with 

 greater nicety than we can employ in our observations, but in order to give 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 product <rs 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 temperature and 

 the potentials ftj , /*2, etc. or the differences of these potentials and the gravitational 

 potential (see page 148) when the system is subject to gravity are maintained sensibly 

 constant. The value of <r, as well as that of , is sensibly independent of the precise 

 position which we may assign to the dividing surface (so long as this is sensibly coin- 

 cident with the surface of discontinuity), but e s , the superficial 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. 



