660 RICE ART. L 



the surface tension initially, but after two hours produce a drop 

 of about one-third in value. This fact should be borne in mind 

 in considering the variations in the tension of soap films which 

 are instanced by Gibbs, and of which many illustrations can be 

 found in A. S. C. Lawrence's book on Soap films: A Study in 

 Molecular Individuality (London, 1929). 



Of course the thin film between two gaseous phases is not to be 

 regarded merely as a very thin layer. As Gibbs clearly states 

 at the top of page 301, it is in general a hulk phase with two 

 surfaces of discontinuity each with its appropriate dividing 

 surface and superficial energy or tension. One point must 

 however be noted; owing to its thinness any extension of its 

 area finds no large source of the capillary active substance to 

 draw on so as to maintain the surface layers in the same condi- 

 tion, and the resulting reduction in excess surface concentration 

 produces an increase in the surface tensions and therefore in the 

 combined tensions or "tension of the film." This gives rise to 

 the conception of an elasticity of the film, analogous to that of a 

 stretched string or membrane. This will of course have different 

 values according to the conditions imposed, just as occurs in 

 the case of deformable solids. A formula for the value under 

 the conditions prescribed at the bottom of page 301 is worked 

 out by Gibbs on pages 302, 303. In the case of solids or 

 fluids, what is called the "bulk modulus of elasticity" is defined 

 by the quotient of an increase of external uniform pressure on 

 the surface by the resulting decrease in unit volume, i.e., by 

 — 8p/{8v/v) . The definition of E in [643] is analogous to this. 2cr 

 being regarded as the tension of the film. If Gi and G^ are the 

 total quantities of Si and S2 per unit area, as defined in [652] 

 and [653], then under the conditions prescribed GiS and G^s are 

 constant, so that 



Gids + sdGi = 0, 



Gids -\- sdGi = 0. 



These yield [644]. The rest of the analysis on pp. 302, 303 is of 

 a simple mathematical character and can be easily followed. It 

 will be noted that the statement after [655], that E will be 



\ 



