SURFACES OF DISCONTINUITY 663 



where the suffixes a and b refer to the two faces of the film. 

 This means that in a vertical film both these conditions cannot 

 be established, and in the thick film apparently in equilibrium 

 the liquid is in reality draining away between the faces towards 

 the bottom.. As was noted in somewhat similar circumstances 

 on pages 283, 284, there will also be considerable doubt as to 

 the adjustment of the various potentials to equation [617]. 

 If this adjustment took place, then by [98] 



dp = yid/ii + y^dni 



= - g(yi + 72 + ...)dz 



since Hr + gz would be constant in the film if the condition 

 [617] were true for the r"* component. But this is equation 

 [612] which we have just seen cannot hold; so the assumption 

 that [617] is true for all the components leads to a contradiction. 

 Thus there must be at least one component for which the con- 

 dition [617] is not true. It might appear that this requirement 

 could be met if this one component were a component not 

 actually present in the contiguous masses, since then iir + gz 

 in the film for such a component cannot exceed a certain 

 constant Mr, viz., the value of the potential in the gas at the 

 level, 2 = 0, but is not necessarily equal to it. However, as 

 Gibbs points out, one such component is not enough, the 

 situation being similar to one already discussed on page 286. 

 If there were only one such component, it must satisfy equation 

 [617] or else the condition [614] will not be obeyed. For by [508] 



dar = — Tidni — Vidii^ ... — T^ dyir, 



where the suffix r refers to this special component not found 



in the gaseous masses. 



Hence 



da = g{Vi + Tj . . . + Vr-i)dz - T, d^r. 



But by [615] (which, unlike [612], must be satisfied even for 

 apparent equilibrium) 



d(T = g{Vi + V2 ... + r,-i + Vr)dz, 



