426 UNPUBLISHED FRAGMENTS. 



We may avoid ' hedging ' in regard to B by using the differential 

 equation (2). We may simply say that this equation holds for 

 changes produced by varying the quantity of (D), when y D is small. 

 It is not limited to changes in which t is constant, for the change 

 in fi D due to t appearing in (1) (both explicitly, and implicitly in B) 

 becomes negligible when multiplied by the small quantity yj>. 



The formula contains the molecular weight Jf D , and if all the 

 solutum has not the same molecular formula, the y D must be under- 

 stood as relating only to a single kind of molecule. 



Thus if a salt ( 12 ) is partly dissociated into the ions Q and ( 2 ), 

 we will have the three equations 





The three potentials are also connected by the relation 



which determines the amount of dissociation. We have, namely, 



M.B. + M 2 B 2 - M IZ B 12 + ^ log 2 = 0, 



7l2 



which makes constant, for constant temperature and solvent. 



Vl2 



I may observe in passing that this relation, eq. (1) or (2), 

 which is so fundamental in the modern theory of solutions, is some- 

 what vaguely indicated in my " Equilib. Het. Subs." (See [this volume] 

 pp. 135-138, 156, and 164-165.) I say vaguely, because the coefficient 

 of the logarithm is only given (in the general case) as constant for a 

 given solvent and temperature. The generalization that this coefficient 

 is in all cases of exactly the same form as for gases, even to the details 

 which arise in cases of dissociation, is due to van't Hoff in connection 

 with Arrhenius, who suggested that the " discords " are but " harmonies 

 not understood," and that exceptions vanish when we use the true 

 molecular weights. At all events, eq. (2) with (98) (E.H.S.) gives for 

 a solvent (S) with one dissolved substance (D), 



m , At 



If we integrate, keeping t constant and also ju. 8 (by connection with 

 the pure solvent through a semi-permeable diaphragm), we have van't 

 HofTs Law, 



, At 



