EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 313 



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 difference of composition still exists. If therefore 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 

 masses of liquid. The latter may be formed by gently depositing a 

 liquid drop upon the surface of a mass of the same or a different 

 liquid. This may be done (with suitable liquids) so that the con- 

 tinuity of the air separating the liquid drop and mass is not broken, 

 but a film of air is formed, which, if the liquids are similar, is a 

 counterpart of the liquid film which is formed by a bubble of air 

 rising to the top of a mass of the liquid. (If the bubble has the 

 same volume as the drop, the films will have precisely the same 

 form, as well as the rest of the surfaces which bound the bubble 

 and the drop.) Sometimes, when the weight and momentum of 

 the drop carry it through the surface of the mass on which it falls, 

 it appears surrounded by a complete spherical film of air, which is 

 the counterpart on a small scale of a soap-bubble hovering in air.t 

 Since, however, the substance to which the necessary differences of 



* 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. 



t These spherical air-films are easily formed in soap-water. They are distinguish- 

 able from ordinary air-bubbles by their general behavior and by their appearance. 

 The tv/o concentric spherical surfaces are distinctly seen, the diameter of one appearing 

 to be about three-quarters as large as that of the other. This is of course an optical 

 illusion, depending upon the index of refraction of the liquid. 



