472 J. W. Gihhs — Equilihrvmn of Heterogeneoiis Sxihstmices. 



small fraction of the difference of tension in the upper and lower 

 portions of the film when held vertically. 



If we account for the power of an element of the film to support an 

 increase of tension by viscosity, it will be necessary to suppose that 

 the viscosity ofiers a resistance to a deformation of the film in which 

 its surface is enlarged and its thickness diminished, which is enor- 

 mously great in comparison with the resistance to a deformation in 

 which the film is extended in the direction of one tangent and con- 

 tracted in the direction of another, while its thickness and the areas 

 of its surfaces remain constant. This is not to be readily admitted 

 as a physical explanation, although to a certain extent the phenomena 

 resemble those which would be caused by such a singular viscosity. 

 (See page 439.) The only natural explanation of the phenomena is 

 that the extension of an element of the film, which is the immediate 

 result of an increase of external force applied to its perimeter, causes 

 an increase of its tension, by which it is brought into ti'ue equilibrium 

 Avith the external forces. 



The phenomena to which we have referred are such as are apparent 

 to a very cursory observation. In the following experiment, which 

 is described by M. Plateau,* an increased tension is manifested in a 

 film while contracting after a previous extension. The warmth of a 

 finger brought near to a bubble of soap-water with glycerine, which 

 is thin enough to show colors, causes a spot to appear indicating 

 a diminution of thickness. When the finger is removed, the spot 

 returns to its original color. This indicates a contraction, which 

 would be resisted by any viscosity of the film, and can only be due 

 to an excess of tension in the portion stretched on the return of its 

 original temperature. 



We have so far supposed that the film is thick enough for its inte- 

 rior to have the properties of matter in mass. Its properties are then 

 entirely determined by those of the three phases and the two surfaces 

 of discontinuity. From these we can also determine, in part at least, 

 the properties of a film at the limit at which the interior ceases to 

 have the properties of matter in mass. The elasticity of the film, 

 which increases with its thinness, cannot of course vanish at that 

 limit, so that the film cannot become unstable with resj^ect to exten- 

 sion and contraction of its elements immediately after passing that 

 limit. 



Yet a certain kind of instability will probably arise, which we may 



* " Statique experimentale et theorique des liquides soumis aux seules forces mol6- 

 culaires," vol. i, p. 294. 



