588 RICE 



ART. L 



In [592] p is a function of t, and so Hs a function of p and we 

 have 



da{t) dt(v) 



and the right hand side by a well-known proposition of the 

 differential calculus is equal to 



da(p) 



V 



dp 



The reader whose acquaintance with mathematical technique 

 may be limited should not regard these remarks as idle comments 

 on mere mathematical "niceties." Actually, if the method 

 suggested were more widely used, and not merely in thermo- 

 dynamic texts, it would conduce to clarity of exposition and 

 consequent ease of understanding on the part of the reader. 



S3. Alternative Method of Obtaining the Results in This Section. 



Total Surface Energy 



The methods by which Gibbs arrives at the results of this 

 section are easy to follow and eminently physical. It may not 

 be out of place, however, to obtain them by a more analytical 

 method which will also help to illustrate the remarks just made. 



Thus the energy of the whole system consisting of two phases 

 and surface of discontinuity with n components is a function of 

 the variables 77, v, s, mi, 1712, . . . nin, since 



€ = tri — pv -{- as -\r Mi^i + M2W2 . . . + finmn* 

 and 



de = tdr] — pdv + ads + iJ-idmi + fi^drn^ . . . + fJ-ndnin. 



We should write the functional form which represents the energy 

 in these variables as e(r], v, s, mi, m2, . . . ) but actually, with the 

 assumption of a practically plane interface, we have an equation 



p'{t, Ml, M2, . . .) = p"{t, m, /i2, . . .) . 



* See Gibbs, I, 240. 



