ABSTRACT BY THE AUTHOR. 369 



of the system with reference to the possible formation of surfaces 

 between A and C, or between B and D, it is farther necessary that 

 the tensions <r A c an d O- B D should be greater than the diagonals ay and 

 /3S respectively. The conditions of stability are entirely analogous 

 in the case of a greater number of surfaces. For the conditions of 

 stability relating to the formation of a new phase at a line in which 

 three surfaces of discontinuity meet, or at a point where four different 

 phases meet, the reader is referred to the original paper. 



Liquid films. When a fluid exists in the form of a very 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 most important case is where the film is 

 liquid and the contiguous fluids are gaseous. If we imagine the film 

 to be divided into elements of the same order of magnitude as its 

 thickness, each element extending through the film from side to side, 

 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 contiguous gases than for the attainment 

 of equilibrium 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 con- 

 ditions 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. It is from this point of view that these bodies are 

 discussed. They are regarded as satisfying a certain well-defined 

 class of conditions of equilibrium, but as not satisfying at all certain 

 other conditions which would be necessary for complete equilibrium, 

 in consequence of which they are subject to gradual changes, which 

 ultimately determine their rupture. 



The elasticity of a film (i.e., the increase of its tension when ex- 

 tended) is easily accounted for. It follows from the general relations 

 given above that when a film has more than one component, those 

 components which diminish the tension will be found in greater pro- 

 portion on the surfaces. When the film is extended, there will not be 

 enough of these substances to keep up the same volume- and surface- 

 densities as before, and the deficiency will cause a certain increase of 

 tension. It does not follow that a thinner film has always a greater 

 tension than a thicker formed of the same liquid. When the phases 



G. I. 2A 



