J. W. Gihhs — Equilihrimn of Heterogeneous Suhstrnices. 473 



here notice, although it rehates 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 distri- 

 bution 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 aifecting 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 pro- 

 perties 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 film 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 con- 

 tiguous gas-masses — and consider what conditions are necessary for 

 equilibrium in sxach 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. 

 Witli 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 

 cases in which the film exhibits a decided viscosity. That is, the 

 relations (613), (<il4), (615) will hold true, when by a we understand 

 the tension of the film regarded as a simple surface of discontinuity 

 (this is equivalent to the sum of the tensions of the two surfaces of 

 the film), and by /^its mass per unit of area diminished by the mass 

 of gas which would occupy the same space if the film should be sup- 

 pressed and the gases should meet at its surface of tension. This 



