EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 301 



Let us first consider the properties which will belong to each 

 element 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 component 

 vanish, the thickness will vary inversely as the area of the element 

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

 sion of its surfaces. If, however, the single component of which the 

 potential is not maintained constant is confined to the surfaces of the 

 film, an extension of the element will generally produce a decrease in 

 the potential of this component, and an increase of tension. This will 

 certainly be true in those cases in which the component shows a ten- 

 dency to distribute itself with a uniform superficial density. 



When the film has two or more components of which the potentials 

 are not maintained constant by the contiguous gas-masses, they will 

 not in general exist in the same proportion in the interior of the 

 film as on its surfaces, but those components which diminish the 

 tensions will be found in greater proportion on the surfaces. When 

 the film is extended, there will therefore not be enough of these 

 substances to keep up the same volume- and surface-densities as 

 before, and the deficiency will cause a certain increase of tension. 

 The value of the elasticity of the film (i.e., the infinitesimal increase 

 of the united tensions of its surfaces divided by the infinitesimal 

 increase of area in a unit of surface) may be calculated from the 

 quantities which specify the nature of the film, when the funda- 

 mental equations of the interior mass, of the contiguous gas-masses, 

 and of the two surfaces of discontinuity are known. We may 

 illustrate this by a simple example. 



Let us suppose that the two surfaces of a plane film are entirely 

 alike, that the contiguous gas-masses are identical in phase, and 

 that they determine the potentials of all the components of the 

 film except two. Let us call these components S 1 and S 2 , the latter 

 denoting that which occurs in greater proportion on the surface 

 than in the interior of the film. Let us denote by y l and y 2 the 

 densities of these components in the interior of the film, by X 

 the thickness of the film determined by such dividing surfaces as 

 make the surface-density of Si vanish (see page 234), by r 2(1) the 

 surface-density of the other component as determined by the same 



