SURFACES OF DISCONTINUITY 661 



generally positive, is based on the assumption that /i2 in general 

 increases in value with G2. It is clear that the elasticity is not 

 simply dependent on the thickness of film. The extension 

 must produce some change in the concentration of the com- 

 ponents in the actual surfaces of the films, so that in a film held 

 vertically, for instance, the conditions of distribution of the 

 components in successive elements of the film must be different 

 as we move up and down. Draining away of the liquid from 

 the interior of the film does not of necessity cause a change in 

 tension even although the thickness diminishes. The statement 

 in parenthesis at the very bottom of page 303 may be justified 

 as follows. All the other potentials except those of Si and S2 

 remaining constant, a change in composition with respect to 

 these components produces a change in a given by 



da = —Tidni — T2dfi2. 



In the argument just preceding we have chosen the dividing 

 surface so that Fi is zero. Then r2(i) is positive on the assump- 

 tion that *S2 exists in greater proportion at the surface, as 

 compared with the interior, than Si. Suppose, however, that 

 we choose the dividing surface so that r2 is zero. This makes 

 ri(2) negative, and we have of course 



d(T = — Ti(2) d/JLi. 



But a reduction of ^Si by evaporation, S2 remaining constant, 

 makes the potential of Si diminish so that dfxi is negative in 

 value. In consequence Ti(2)dpLi is positive and therefore da is 

 negative. 



Pursuing the commentary for the moment, before reference to 

 more recent experimental evidence on these matters than that 

 offered in Gibbs' treatise, we find that on page 305 we meet some 

 remarks on films gradually approaching the tenuity attained by 

 the films which show interference colors by reflected light. The 

 elasticity of a thin film is greater than a thick one as we can see 

 from the equation [650] ; for E increases as X diminishes so long 

 as the interior retains the properties of the matter in bulk, and 

 so the quantities 71, dr/dn2, dT2a)/dii2 are not different in value 



