268 Dr. S. A. Shorter on the Constitution 



The value of the surface excess relative to a plane a 

 distance z from the " zero-plane " in the direction of the 

 <p phase is evidently given by 



T=(p-p')z. 



Consider now a system of two components C and X . The 

 " zero-plane " of each component will have a definite position, 

 and the distance between the two will have a definite value, 

 characteristic of the system. Suppose now that T and r : 

 are the respective values of the surface excesses, relative to 

 a plane whose distances from the " zero-planes " of O and 

 Cj, measured in the direction of the $ phase, are z and z\ 

 respectively. We then have 



and 



Hence, if h denote the distance of the " zero-plane ,? of Ci 

 from that of C measured in the direction of the <£' phase, 

 we have 



A-- — - r i r ° 



Pi— Pi Po — Po 



Keferring back to equation (10) — the general equation 

 for a binary system — we see at once the reason for the 

 apparent incompleteness of our theory and the particular 

 form of the equation. The quantities T and I\ are purely 

 arbitrary magnitudes which could not possibly appear singly 

 in any thermodynamical relation. They may, however, be 

 combined in such a way as to yield a quantity which is not 

 arbitrary, and this quantity appears on the left-hand side of 

 equation (10), which may be written in the form 



]h = po'pi-popi , (±\ (11) 



(po-po)(po-pi')\dpJ d 



We may, however, interpret equation (10) in another way. 

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

 plane" of C is evidently (pi-pi)h or 



i- 1 1 J- 0- 



po — po 



Let us adopt the notation of Gibbs and use the symbol 



