SURFACES OF DISCONTINUITY 549 



surface film the first; a is the surface energy per unit area of the 

 film, meaning by that the energy possessed by the molecules 

 in unit area of the film in excess of what they would possess 

 if they were in the body of the fluid. Hence the da- in (18) will 

 refer to an increase in this, i.e., the work required to extract from 

 the bulk and bring to the surface a number of molecules given 

 by N^dp, where N is the number of molecules in unit mass of the 

 solute; for f is equal to the volume of unit area of the film and 

 ^dp the increase in the mass of the solute in it. Hence, since 

 R refers to the gas constant for unit mass of the solute, 



R^dp = Nk^dp, 



and we see that (l/R) {da/dn) is equal to the work required 

 to bring one molecule from the interior to the surface divided 

 by k, i.e., to {0(ni) - e{n2)]/k. Thus by (10) 



P 



-, = exp 



P 



\ Rt dKj ' 



which is just Thomson's equation. Thus, not only in the form 

 of the equation but also in the possibility of deducing it in this 

 way, one might state with some show of reason that it is really 

 more akin to some recent results obtained by Langmuir and 

 others than to Gibbs' law. 



It should be mentioned as a matter of interest that Warburg 

 in 1890 made use of an equation, which is virtually Gibbs' ap- 

 proximate result, in his well-known paper on "Galvanic Polari- 

 zation" (Ann. d. Physik, 41, 1, (1890)). By means of it he 

 made some calculations on the forcing of the solute out of the 

 surface layer in the case of inorganic salts which raise the 

 surface tension of water and so are desorbed. He used a 

 thermodynamical argument; in an addendum to the paper he 

 refers to the earlier proofs of Gibbs and Thomson. 



Quite a number of proofs of Gibbs' equation, usually in the 

 approximate form, have been published from time to time. 

 (See Swan and Urquhart's paper cited above.) Porter, in the 

 Trans. Faraday Soc, 11, 51, (1915), has derived an equation for 



