of the Surface Layers of Liquids. 265 



terms of T , T 1 and the densities. Since the constancy of 

 p and 6 involves the constancy of p , p \ pi, pi, T and I\, 

 we have from equations (3) and (4) 



T da- + p dY + p 'dY'=0 .... (5) 

 and 



r 1 rfo- + / MV + /Oi'dV'=0 (6) 



Since 



o = V + V (7) 



we have 



dv = dV+dV (8) 



From equations (5), (6), and (8) we readily obtain the 

 desired relation 



V^/fijp PoPi—poPi 



Substituting this value in equation (2) we obtain the 

 equation 



Pi 



r*i r p o'pi—popi (^l\ no) 



— /V Po— po' _ (po—po) (pi—pi) \dp)e ' 



This is the most general relation possible (in the case of 

 a binary system) between the surface magnitudes and 

 quantities capable of experimental determination. 



§ 3. The Principle of the Relativity of the Surface 

 Magnitudes. 



It will be seen that in the case of a binary system our 

 theory gives only one equation connecting the two quantities 

 r o and Y 1 with quantities capable of experimental determina- 

 tion. We cannot obtain separate equations for T and Y 1% 

 At first sight, this seems to imply some incompleteness or 

 imperfection in the thermodynamical theory. A closer ex- 

 amination of what is meant by the term " surface excess " 

 shows, however, that this idea is wrong, and that the theory 

 yields all that could be expected of it. 



Suppose that we take as abscissae the distances of points 

 from some reference plane parallel to the surface, and as 

 ordinates the values of the density of a component. The 

 graph will consist of two straight lines parallel to the axis 

 of abscissae (corresponding to the interiors of the two phases) 

 joined by a curved line (corresponding to the region of 



