J. TF. Gibbs — Equilibrium of Heterofjeneotis Substaneen. 481 



Tliat whicli is most difficult to account for in the formation of the 

 black spots is the arrest of the process by which the film grows thin- 

 ner. It seems most natural to account for this, if possible, by passive 

 resistance to motion due to a very viscous or gelatinous condition of 

 the film. For it does not seem likely that the film, after becoming 

 unstable by the flux of matter from its interior, would become stable 

 (without the support of such resistance) by a continuance of the 

 same process. On the other hand, gelatinous properties are very 

 marked in soap-water which contains somewhat more soap than is 

 best for the formation of films, and it is entirely natural that, even 

 Avhen such properties are wanting in the interior of a mass or thick 

 film of a liquid, they may still exist in the immediate vicinity of the 

 surface (where we know that the soap or some of its components 

 exists in excess), or throughout a film which is so thin that the 

 interior has ceased to have the properties of matter in mass.* But 

 these considerations do not amount to any a priori probability of an 

 arrest of the tendency toward an internal current between adjacent 

 elements of a black spot which may differ slightly in thickness, in 

 time to prevent rupture of the film. For, in a thick film, the increase 

 of the tension "with the extension, which is necessary for its stability 

 with respect to extension, is connected with an excess of the 

 soap (or of some of its components) at the surface as compared with 

 the interior of the film. With respect to the black spots, although 

 the interior has ceased to have the properties of matter in mass, and 

 any quantitative determinations derived from the surfaces of a mass 

 of the liquid will not be applicable, it is natural to account for the 

 stability with reference to extension by supposing that the same 

 general difierence of composition still exists. If thei'efore we account 

 for the arrest of internal currents by the increasing density of 

 soap or some of its components in the interior of the film, we must 

 still suppose that the characteristic difference of composition in the 

 interior and surface of the film has not been obliterated. 



The preceding discussion relates to liquid films between masses of 

 gas. Similar considerations will apply to liquid films between other 

 liquids or between a liquid and a gas, and to films of gas between 



* The experiments of M. Plateau (chapter VII of the work already cited) show that 

 this is the case to a very remarkable degree with respect to a solution of saponine. 

 With respect to soap-water, however, they do not indicate any greater superficial 

 viscosity than belongs to pure water. But the resistance to an internal current, such as 

 we are considering, is not necessarily measured by the resistance to such motions 

 as those of the experiments referred to. 



