468 (T. W. Gibbs — Equilibriurn of Heterogeneous Substances. 



libriiim between all the diflFerent elements of the film. There will 

 accordingly be a time, commencing shortly after the formation of the 

 film, in which its separate elements may be regarded as satisfying the 

 conditions of internal equilibrium, and of equilibrium with the con- 

 tiguous gases, while they may not satisfy all the conditions of equi- 

 librium with each other. It is when the changes due to this want ol 

 complete equilibrium take place so slowly that the film appears to be 

 at rest, except so far as it accommodates itself to any change in the 

 external conditions to which it is subjected, that the characteristic 

 properties of the film are most striking and most sharply defined. 



Let us therefore consider the properties which will belong to a film 

 sufficiently thick for its interior to have the properties of matter in 

 mass, in virtue of the approximate equilibrium of all its elements 

 taken separately, when the matter contained in each element is 

 regarded as invariable, with the exception of certain substances 

 which are components of the contiguous gas-masses and have their 

 potentials thereby determined. The occurrence of a film which pre- 

 cisely satisfies these conditions may be exceptional, but the discus- 

 sion of this somewhat ideal case will enable us to understand the 

 principal laws which determine the behavior of liquid films in 

 general. 



Let us first consider the 2:)roperties which will belong to each ele- 

 ment of the film under the conditions mentioned. Let us suppose 

 the element extended, while the temperature and the potentials 

 which are determined by the contiguous gas-masses are unchanged. 

 If the film has no components except those of which the potentials 

 are maintained constant, there will be no variation of tension in its 

 surfaces. The same will be true when the film has only one com- 

 ponent of which the potential is not maintained constant, provided 

 that this is a component of the interior of the film and not of its sur- 

 face alone. If we regard the thickness of the film as determined by 

 dividing surfaces which make the surface-density of this compo- 

 nent vanish, the thickness will vary inversely as the area of the ele- 

 ment of the film, but no change will be produced in the nature or 

 the tension of its surfaces. If, however, the single component of 

 which the potential is not maintained constant is confined to the sur- 

 faces of the film, an extension of the element will generally produce 

 a decrease in the potential of this component, and an increase of ten- 

 sion. This will certainly be true in those cases in which the compo- 

 nent shows a tendency to distribute itself with a uniform superficial 

 density. 



