J. W. Gibhs — Equilibrium of Heterogeneous Substances. 471 





dG^\ 



E \ 



the last clifFereiitial coefficient being determined by the same condi- 

 tions as that in the preceding equation. It will be observed that the 

 value of ^ will be positive in any oi'dinary case. 



These equations give the elasticity of any element of the iilm when 

 the temperature and the potentials for the substances which are found 

 in the contiguous gas-masses are regarded as constant, and the poten- 

 tials for the other components, /<, and yu^, have had time to equalize 

 themselves throughout the element considered. The increase of 

 tension immediately after a rapid extension will be greater than that 

 given by these equations. 



The existence of this elasticity, which has thus been established 

 from a priori considerations, is clearly indicated by the phenomena 

 which liquid films present. Yet it is not to be demonstrated simply 

 by comparing the tensions of films of different thickness, even when 

 they are made from the same liquid, for difference of thickness does 

 not necessarily involve any difference of tension. When the phases 

 within the films as well as without are the same, and the surfaces of 

 the films are also the same, there will be no difference of tension. 

 Nor will the tension of the same film be altered, if a part of the inte- 

 rior drains away in the course of time, without affecting the surfaces. 

 In case the thickness of the film is reduced by evaporation, the tension 

 may be either increased or diminished. (The evaporation of the sub- 

 stance /S'j, in the case we have just considered, would diminish the 

 tension.) Yet it may easily be shown that extension increases the 

 tension of a film and contraction diminishes it. When a plane film 

 is held vertically, the tension of the upper portions must evidently 

 be greater than that of the lower. The tensions in every part of the 

 film may be reduced to equality by turning it into a horizontal posi- 

 tion. By restoring the original position we may restore the original 

 tensions, or nearly so. It is evident that the same element of the 

 film is capable of supporting very unequal tensions. Nor can this be 

 always attributed to viscosity of the film. For in many cases, if we 

 hold the film nearly horizontal, and elevate first one side and then an 

 other, the lighter portions of the film will dart from one side to the 

 other, so as to show a veiy striking mobility in the film. The differ- 

 ences of tension which cause these rapid movements are only a vei-y 



Trans. Conn. Acad., Vol. III. 60 March, 1878. 



