SURFACES OF DISCONTINUITY 659 



of phase E formed is very small. In that case, for purely 

 geometrical calculations, we can regard the faces of tetra- 

 hedron abed and also the portions of the surface D-A etc. within 

 it as plane. This means that the tetrahedron a^yS is similar to 

 ahcd and the point e is situated within it just as is the point c 

 within abed (e is the point which we originally named 0). 

 This justifies the various steps in the geometrical argument 

 leading to [641]. 



XVII. Liquid Films 



[Gibbs, I, pp. S00-S14] 



56. Some Elementary Properties of Liquid Films. The Elasticity 



of a Film 



Since soap solutions are generally used for experimental 

 illustration of the properties of liquid films between two gaseous 

 phases, it may be of advantage to mention briefly some of the 

 most striking facts concerning such solutions. In the first 

 place it is remarkable how great a reduction is produced in the 

 surface tension of water by quite small concentrations of soap. 

 This is, of course, due to the excess concentration of the capillary 

 active soap in the surface layer. Actually, when the bulk con- 

 centration of a sodium oleate solution attains 0.25 per cent 

 the surface tension has decreased from about 80 dynes per 

 centimeter to about 30, a figure at which it remains during fur- 

 ther increases in concentration. However, it is known that 

 these values are only attained some time after the formation of 

 the surface layer. If the surfaces are continuously renewed 

 nothing like such a lowering of surface tension is observed. 

 Thus Lord Rayleigh obtained for a 0.25 per cent concentration 

 a "dynamic" surface tension equal to that of pure water, as 

 distinct from the "static" value given above. Even a 2.5 per 

 cent solution with a continuously renewed surface recorded 56 

 dynes per centimeter, or about twice the "static" value. This 

 can only mean that the specific surface layer with the very low 

 surface tension takes some time to form. Some work by du 

 Nouy (Phil. Mag., 48, pp. 264, 664, (1924)) on extremely dilute 

 solutions shows that concentrations as low as 10~^ hardly affect 



