of the Surface Layers of Liquids. 261 



the present work is to develop the thermodynamical theory 

 of the subject in an elementary manner, preserving at the 

 same time perfect mathematical rigour and the utmost 

 generality of treatment. 



The first attempt at an elementary exposition of the sub- 

 ject was made by Milner *, who obtained a formula for the 

 " surface excess " of a solute, applicable to the case of a 

 dilute solution in contact with a third substance. 



The theory developed in the present work is applicable to 

 solutions of any degree of concentration — and therefore to 

 the case of a mixture of two perfectly miscible liquids. 

 Since in this latter case the distinction between solvent and 

 solute is a purely arbitrary one, the theory must take account 

 of the "surface excess" of both solvent and solute. This 

 consideration of the "surface excess " of both components 

 of a solution leads to a curious and interesting principle, 

 which I have termed the " Principle of the Relativity of the 

 Surface Magnitudes." This principle underlies all Gibbs's 

 theory, though it is never explicitly referred to in it. 



§ 2. Ihe General Case of a Binary System. 



We will first consider the case of the interface separating 

 two phases of a system containing two components. This 

 general case includes a number of special cases, which we 

 will consider in § 4 of the present paper. 



The most elementary method of treating the subject is to 

 consider the working of an ideal " engine " in which the 

 contractile tendency of the surface and the expansive 

 tendency of the volume are both used as a means of pro- 

 ducing an external mechanical effect. Such an engine is 

 represented in fig. 1. Q is a vessel of rectangular hori- 

 zontal cross-section, containing masses M and M 1 of two 

 components C and Ci respectively, in two phases <£ and </>' 

 separated by a plane surface of area er and tension t. The 

 area of the surface may be varied by means of a movable 

 plate P, which fits accurately to the sides of the vessel 

 parallel to the plane of the paper. The horizontal portion 

 of this plate passes through a slot in one of the vertical sides 

 perpendicular to the plane of the paper. This side is suffi- 

 ciently thick in the neighbourhood of the slot for the plate 

 to be incapable of any motion but a horizontal motion of 

 translation. The volume v of the system may be varied by 

 means of the piston R. 



* Phil. Maff. Jan. 1907. 



