Molecular Thermodynamics. 621 



will affect the quantities c 0l c 02 etc. only indirectly and 

 relatively slightly, or in other words will produce only 

 second-order variations in c 0l c . 2 



In the second place, since X m 0l c 0l is constant (unity), it 

 is clear on examining (51) that the effects upon ^ of varia- 

 tions o£ c 0l Cq 2 . . . . are throughout more or less mutually 

 compensatory. 



In the case of 2c 0l \ogm c 0v for instance, we note that 

 the mutual compensation will be greatest when c 0l c 02 . . . are 

 of similar order. When, however, this is far from the case, 

 and any of them, c 0l (say) approaches either of the extremes 

 zero or l/m , then, since the relative magnitude of the effect 

 on yjr of a variation in c 0l may be estimated as 



d lo p- Cq [ c °i 1o S ~ l ° C °J = % [log m c 0l + 1] , 



we see that this is small whether c 0l approaches zero or l/?» . 



Finally, the "general terms" (which may depend some- 

 what on c 0l , c 02 . . . .) are themselves small when Cj c 2 . . . . 

 are not large, so that altogether it is dear that the effects 

 upon -\jr of variations in c 0l , c 02 .... are relatively small, that 

 is, second-order effects. 



That is, variations in cj, c 2 . • • . will produce only third- 

 order variations in ^. 



From the general form of this argument we must expect 

 of course that special cases will be producible in which it 

 does not hold, but, in general, we are able to conclude that 

 it is possible by means of the modification given in this 

 section to go a surprisingly long way without complete 

 knowledge of the molecular constitution of the solvent. 



Naturally' the most general case will require complete 

 knowledge of the constitution of the phase for accurate 

 treatment, but even then the grouping of equation (51) may 

 be found convenient, concentrations being referred to the 

 mass of the whole " solvent," rather than to the numerical 

 quantity of one molecular form of the ic solvent.' 5 The 



derivatives - JC and ^~ obtainable from (51) are of course 



obvious. 



Returning to the equations (53) we see that they depend 

 on m in respect of the term \og(l + m^2,Ci). 



Expanded, this term takes the form 



riioXci [ 1 — ^m 2ci -I- ] . 



