SURFACES OF DISCONTINUITY 535 



the n + 1 variables tjs = tVs> Ti = nii^/s, T2 = mz^/s, etc. 

 By means of the n + 1 equations which express t, mi, M2, etc. 

 as functions of the n + 1 quantities 77s, Ti, r2, etc., we can 

 theoretically express 77s, Fi, r2, etc. as functions of t, mi, M2, etc. 

 In consequence a, which is also, as we have just seen, a function 

 of the former set of n + 1 quantities, can be expressed as a 

 function of the second set, viz., t, /xi, 1x2, etc. This functional 

 relation between a and the new variables t, ni, jU2, etc. is referred 

 to by Gibbs as "& fundamental equation for the surface of dis- 

 continuity." Now the values of the potentials jUi, 1x2, etc., are 

 themselves determined by the constitution of the phases or 

 homogeneous masses separated by the surface of discontinuity; 

 so we see that o- is itself ultimately dependent on the constitu- 

 tion of the adjacent phases and the temperature (unless any of 

 the potentials relate to substances only to be found at the 

 surface). Furthermore, as we know, the pressures p' and p" in 

 these phases are also determined by the temperature and the 

 potentials. Since by equation [500] 



pf _ p" 



Ci + C2 = , 



it follows that the curvature of the dividing surface is also 

 dependent on the temperature and the constitution of the 

 phases separated by it. 



14- Derivation of Gibbs' Adsorption Equation 



Suppose the constitution of the phases suffers a change so 

 that a new equilibrium is established at a temperature t + dt, 

 with new values of the potentials in the phases equal to mi + dyn, 

 H2 + dn2, etc. This will involve changes in the surface energy, 

 entropy and masses to values e^ + de^, rj^ + drj^, mi^ + dnii^, 

 rriz^ + dm2^, etc., and the surface tension will alter to o- + da. 

 The equation [502] still holds for this neighboring state of 

 equilibrium, so that 



e^ + de^ = {t-\- dt) (tjS + drjs) + {(T + da) (s + ds) 

 -f- (jLii + c?jui) (mi^ + drui^) + etc. 



