of the Surface Layers of Liquids. 269 



r r (,) to denote the surface excess of any component C r in 

 a system relative to the " zero- plane " of another com- 

 ponent C s . Equation (10) may then be written 



r _po'pi-poPi'(dr\ 



Vm -~7^Po'~Up)e (12) 



The value of the surface excess of C relative to the " zero- 

 plane"" of Ci is evidently equal to — (p — po)h or 



Pi" Pi 



so that equation (10) may be written 



PoPi~PoPi fdr\ 



r (D— 



^T (T) • • • • as) 



1 — p 1 \dp/ d 



The above general considerations apply, of course, to a 

 system containing any number of components. Thus in 

 the case of a system of n components, there are n l< zero- 

 planes," and the theory should yield n — 1 equations for 

 the n — 1 lengths which fix the relative positions of these 

 planes. 



In recent years the surface excess of a solute in a binary 

 liquid mixture has been determined experimentally by ob- 

 serving the change of concentration caused by a large 

 extension of surface. We have seen that the surface 

 excess of a component is a purely arbitrary magnitude,, 

 so that the interesting question arises as to what is given 

 by the above experiment. The only case which has been 

 investigated practically is that of a solution in contact with 

 a third substance. This case will be considered in Part II. 

 of the present work. We will consider here an imaginary 

 experiment with a two-phase binary system, which could 

 not be realized in practice because of the smallness of the 

 changes involved, but which will serve to illustrate the 

 point in question. Suppose that a closed vessel contains a 

 binary liquid mixture in contact with the vapour phase. 

 Let the vessel be tilted so that the area of the surface 

 separating the phases is increased from a to a -f Act. This 

 will in general cause the vapour pressure to alter, Suppose 

 that by the addition of an amount AM : of the solute Cj. the 

 initial pressure (and therefore the initial concentration of 

 the solution) is restored. One would at once say that the 

 surface excess of the solute is AMJAer. Let us examine 



