﻿Molecular Thermodynamics. 245 



of the solvent enters into the "general" terms it does so 

 only through the quantity D, and if this is the dielectric' 

 constant of the solution in bulk it can be. measured and so 

 determined as a function of c s without considering the corre- 

 sponding variation in the constitution of the solvent, or the 

 way in which the latter exerts its effect on D. 



If, as is probable at the less extreme dilutions, D is not 

 the experimental or " bulk " dielectric constant, but a certain 

 statistical-average quantity of a peculiar kind, then its varia- 

 tion is, at least partially, not due to a variation in the solvent, 

 but directly to variation of c s as in the first case above. 



Clearly from the preceding it would theoretically be pos- 

 sible iu such a case to determine from comparison of theory 

 with experiment whether the effect of c s on D was direct or 

 indirect or in what proportion both, but it might not be 

 practicable owing to the smallness of the effects to be 

 measured. 



Note on the " Gibbs Fundamental Relation." 



Consider any property it of a homogeneous substance or 

 phase, which is determined in magnitude by the composition 

 of the phase and the quantity of substance considered. 

 In view of the homogeneity it must then be proportional to 

 the quantity of substance when the composition is fixed. 



Such properties are (at constant temperature and pressure) 

 U and V, the total-energy and volume, Q or (U + pY), 

 which might be called the "reversible heat content," and 

 any thermodynamic potential such as entropy, free energy, 

 Gibbs' " chemical potential," or Planck's yjr, which may all 

 be expressed (at constant temperature and pressure) as func- 

 tions of the quantities ]M\ M 2 .... of the constituents which 

 suffice, under the conditions considered, to produce the 

 phase. 



We can show, as Planck does in the case of i/r, that for 

 any such property it, 



- = SM W • • • • • («) 



for if e be some infinitesimal fraction and we remove (eMj) 



of the first constituent, clearly it is diminished by eMx ^rr- . 



Removing simultaneously the same fraction of the total 

 quantity of each constituent we diminish w, in all, by 



SeMx^r^-, or eSMj— ^. But, in so doing, we have 



