546 RICE 



ART. L 



not very different from unity the argument of the exponential 

 function is sufficiently small to permit us to write 



1 + (s/Rt) (da/dO 



for the right-hand side of (16), and so 



P — p' s da 



P ~ ~ Rt' d^ 



Now, if the dividing surface is placed at the boundary between 

 the film and the vapor, then p — p' is the same as r/f, where 

 ^ is the thickness of the surface film. Hence 



sf dcr 

 ^ ^ ~ ^Rtd'^' 



But ^/(sf) is equal to p, and so 



P dcr , , 



which under the limitations assumed is practically the approxi- 

 mate form of Gibbs' equation. The details of Thomson's work 

 will be found in the Applications, Chapter XII. A critical 

 inspection of the two formulae, Gibbs' and Thomson's, shows 

 that they are not so similar as one imagines. We have already 

 mentioned that the assumptions made concerning the dilute 

 nature of the solution places a limitation on Thomson's result 

 not ostensibly present in Gibbs'. Added to that, it is possible 

 that the mathematical restrictions imposed by the neglect of 

 higher powers in the expansion of the exponential function may 

 place a further restriction on (17) which is more severe than 

 that necessitated by the physical assumption concerning dilu- 

 tion. Thomson actually makes no quantitative application of 

 his formulae — indeed in those days there were no data available ; 

 he draws from it just the same broad qualitative conclusions 

 which can be inferred from Gibbs' result. If the presence of a 

 solute lowers the value of the surface tension, so that da/dc or 

 da/dp is negative, then T is positive by Gibbs' equation and 

 p' < p by (16), which we can write in the form 



