EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 309 



then tend toward conformity with condition (614), the lighter portions 

 rising to the top, more or less slowly, according to the viscosity of the 

 film. The resulting difference of thickness between the upper and 

 the lower parts of the bubble is due partly to the greater tension 

 to which the upper parts are subject, and partly to a difference in 

 the matter of which they are composed. When the film has only 

 two components of which the potentials are not determined by the 

 contiguous atmosphere, the laws which govern the arrangement of the 

 elements of the film may be very simply expressed. If we call these 

 components S l and $ 2 , the latter denoting (as on page 301) that 

 which exists in excess at the surface, one element of the film will tend 

 toward the same level with another, or a higher, or a lower level, 

 according as the quantity of 8 2 bears the same ratio to the quantity 

 of S 1 in the first element as in the second, or a greater, or a less ratio. 



When a film, however formed, satisfies both the conditions (613) 

 and (614), its thickness being sufficient for its interior to have the 

 properties of matter in mass, the interior will still be subject to the 

 slow current which we have already described, if it is truly fluid, 

 however great its viscosity may be. It seems probable, however, 

 that this process is often totally arrested by a certain gelatinous 

 consistency of the mass in question, in virtue of which, although 

 practically fluid in its behavior with reference to ordinary stresses, 

 it may have the properties of a solid with respect to such very 

 small stresses as those which are caused by gravity in the interior 

 of a very thin film which satisfies the conditions (613) and (614). 



However this may be, there is another cause which is often more 

 potent in producing changes in a film, when the conditions just 

 mentioned are approximately satisfied, than the action of gravity on 

 its interior. This will be seen if we turn our attention to the edge 

 where the film is terminated. At such an edge we generally find a 

 liquid mass, continuous in phase with the interior of the film, which 

 is bounded by concave surfaces, and in which the pressure is therefore 

 less than in the interior of the film. This liquid mass therefore 

 exerts a strong suction upon the interior of the film, by which its 

 thickness is rapidly reduced. This effect is best seen when a film 

 which has been formed in a ring is held in a vertical position. Unless 

 the film is very viscous, its diminished thickness near the edge causes 

 a rapid upward current on each side, while the central portion slowly 

 descends. Also at the bottom of the film, where the edge is nearly 

 horizontal, portions which have become thinned escape from their 

 position of unstable equilibrium beneath heavier portions, and pass 

 upwards, traversing the central portion of the film until they find a 

 position of stable equilibrium. By these processes, the whole film is 

 rapidly reduced in thickness. 



