300 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



of the four masses A, B, C, D will be stable unless V E (calculated for 

 the case of the five masses) is of insensible magnitude. This will 

 only be the case when p E is greater in general considerably greater 

 than the second member of (642). 



Liquid Films. 



When a fluid exists in the form of a thin film between other fluids, 

 the great inequality of its extension in different directions will give 

 rise to certain peculiar properties, even when its thickness is sufficient 

 for its interior to have the properties of matter in mass. The fre- 

 quent occurrence of such films, and the remarkable properties which 

 they exhibit, entitle them to particular consideration. To fix our 

 ideas, we shall suppose that the film is liquid and that the contiguous 

 fluids are gaseous. The reader will observe our results are not 

 dependent, so far as their general character is concerned, upon this 

 supposition. 



Let us imagine the film to be divided by surfaces perpendicular to 

 its sides into small portions of which all the dimensions are of the 

 same order of magnitude as the thickness of the film, such portions 

 to be called elements of the film, it is evident that far less time will 

 in general be required for the attainment of approximate equilibrium 

 between the different parts of any such element and the other fluids 

 which are immediately contiguous, than for the attainment of equi- 

 librium between all the different elements of the film. There will 

 accordingly be a time, commencing shortly after the formation of the 

 film, in which its separate elements may be regarded as satisfying 

 the conditions of internal equilibrium, and of equilibrium with the 

 contiguous gases, while they may not satisfy all the conditions of 

 equilibrium with each other. It is when the changes due to this want 

 of complete equilibrium take place so slowly that the film appears to 

 be at rest, except so far as it accommodates itself to any change in 

 the external conditions to which it is subjected, that the characteristic 

 properties of the film are most striking and most sharply defined. 



Let us therefore consider the properties which will belong to a film 

 sufficiently thick for its interior to have the properties of matter in 

 mass, in virtue of the approximate equilibrium of all its elements 

 taken separately, when the matter contained in each element is 

 regarded as invariable, with the exception of certain substances 

 which are components of the contiguous gas-masses and have their 

 potentials thereby determined. The occurrence of a film which pre- 

 cisely satisfies these conditions may be exceptional, but the discussion 

 of this somewhat ideal case will enable us to understand the principal 

 laws which determine the behavior of liquid films in general. 



