EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 305 



interior to have the properties of matter in mass. Its properties are 

 then entirely determined by those of the three phases and the two 

 surfaces of discontinuity. From these we can also determine, in part 

 at least, the properties of a film at the limit at which the interior 

 ceases to have the properties of matter in mass. The elasticity of 

 the film, which increases with its thinness, cannot of course vanish 

 at that limit, so that the film cannot become unstable with respect 

 to extension and contraction of its elements immediately after passing 

 that limit. 



Yet a certain kind of instability will probably arise, which we may 

 here notice, although it relates to changes in which the condition of 

 the invariability of the quantities of certain components in an 

 element of the film is not satisfied. With respect to variations in the 

 distribution of its components, a film will in general be stable, when 

 its interior has the properties of matter in mass, with the single 

 exception of variations affecting its thickness without any change of 

 phase or of the nature of the surfaces. With respect to this kind 

 of change, which may be brought about by a current in the interior of 

 the film, the equilibrium is neutral. But when the interior ceases to 

 have the properties of matter in mass, it is to be supposed that the 

 equilibrium will generally become unstable in this respect. For it is 

 not likely that the neutral equilibrium will be unaffected by such a 

 change of circumstances, and since the film certainly becomes unstable 

 when it is sufficiently reduced in thickness, it is most natural to 

 suppose that the first effect of diminishing the thickness will be in the 

 direction of instability rather than in that of stability. (We are here 

 considering liquid films between gaseous masses. In certain other 

 cases, the opposite supposition might be more natural, as in respect to 

 a tilm of water between mercury and air, which would certainly 

 become stable when sufficiently reduced in thickness.) 



Let us now return to our former suppositions that the film is thick 

 enough for the interior to have the properties of matter in mass, and 

 that the matter in each element is invariable, except with respect to 

 those substances which have their potentials determined by the 

 contiguous gas-masses and consider what conditions are necessary 

 for equilibrium in such a case. 



In consequence of the supposed equilibrium of its several elements, 

 such a film may be treated as a simple surface of discontinuity 

 between the contiguous gas-masses (which may be similar or different), 

 whenever its radius of curvature is very large in comparison with its 

 thickness, a condition which we shall always suppose to be fulfilled. 

 With respect to the film considered in this light, the mechanical 

 conditions of equilibrium will always be satisfied, or very nearly so, 

 as soon as a state of approximate rest is attained, except in those 



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