SURFACES OF DISCONTINUITY 565 



are at least two other components (such as p-tokiidine and 

 nitrogen); "their adsorption is r2 = —(9o"/ 9^2)^3 and Ts = 

 — (da/dfxs)^^ each of which is readily measured, although this 

 has never been done. It is obvious that the two adsorptions 



will mutually interfere For example, it has been stated 



that the surface tension of mercury is 10 per cent lower in the 

 presence of one atmosphere of nitrogen than in vacuo; similarly, 

 nitrogen lowers the surface tension of water by about one per 

 cent, which would correspond to the adsorption of about 3 per 

 cent as many molecules of nitrogen as of p-toluidine. However, 

 such mutual interference cannot explain the high values of the 

 observed adsorptions." 



As it can be stated here that McBain's explanation of the 

 discrepancies in terms of surface electrification effects has not 

 been universally accepted, it is clear that the evidence for the 

 complete quantitative validity of Gibbs' law, as against a rough 

 qualitative agreement, is far from satisfactory. In reflecting 

 on the various theoretical steps in the proof one naturally feels 

 somewhat dubious about the arbitrary placing of the surface 

 of division in order to get rid of one term in the differential 

 expression ; in discussing these matters the writer has, for exam- 

 ple, heard such statements as these: "Nature fixes the surface; 

 surely we cannot mess it about as we please." There is some- 

 thing to be said for this instinctive recoil from a procedure 

 apparently so arbitrary; yet a close investigation leaves us little 

 hope of evading our difficulties by pressing this instinct into our 

 service. For instance, let us look at Gibbs' equation [515], 

 where the strictly placed dividing surface is used, showing us 

 that 



r _ r _ r ^ - y" 



■I 2(1) — 1 2 J- 1 / ,/• 



7i ~ 7i 



In this r2(i) is the surface excess as calculated, while r2 is what 

 we might call, if we were disposed to press the point we are 

 presenting, the "true" surface excess, and it would appear that 

 r2 is greater than r2(i)*provided Fi is positive, which is certainly 

 in the right direction for an elucidation of the mystery. The 

 value of 7i", the concentration of the solvent in the vapor phase 



