558 RICE 



ART. L 



tension determined in the manner pointed out earlier. Practi- 

 cally, however, any surface in the film will serve, provided that 

 the values of Vi and r2 are adapted, as we have shown, to the 

 chosen situation. It has been customary to choose the position 

 of the surface so that the actual amount of one of the com- 

 ponents in the discontinuous region is the same as if its density 

 were uniform in each phase right up to the surface. This 

 makes one of the excess concentrations (say Ti) zero, and the 

 equation becomes 



da = — Fgd) dfi2 . 



Gibbs, himself, originally suggested this procedure and gives an 

 example of its application in the footnote to page 235. In a 

 number of the measurements, the simple formula for the 

 chemical potential 



H = Hq -\- Rt log c 



has been used, and these on the whole indicate that a solute 

 which lowers surface or interfacial tension is concentrated more 

 at the surface than is deduced by the use of this formula. 

 Measurements of the activity of solutes are not yet very numer- 

 ous, but wherever the more accurate expression for the potential 



fi = Ho -{■ Rt log a 



can be used, the agreement is very much better, though there 

 still appears to be a greater concentration than the equation 

 would lead us to expect. However, in addition to direct tests 

 of the vaUdity of the equation, it has been used to investigate 

 the structure of the surface region, and the comparison of the 

 results with the properties of films of insoluble substances at 

 the surface of a liquid, obtained by Langmuir, Adam and others 

 by different means, seems to lend considerable support to its va- 

 lidity. 



There are a number of early investigations which show 

 that a concentration of capillary-active solutes at the surface 

 actually does take place. Plateau {Pogg. Ann., 141, 44, (1870)) 

 showed that the viscosity of the surface layers of a saponin 



