﻿622 Mr. Bernard Cavanagh on 



series of symmetrical expressions of the form 

 (M^+M„S, a ), (M s *Z Sl + M S2 % 2 ), (M^ + M^J, etc., 



where x sx and 7c S2 stand for the limiting values Lt % Sl 

 and Lt a?„. 0->0 



The same procedure exactly, however, can be applied to 

 the more general case (52), but becomes, of course, more 

 complex and laborious as the number of solvates is increased. 

 There can be little doubt that the maximal values of the 

 coefficients remain of the same order of magnitude so long as 

 'Gx s n , etc., are minor quantities as they will be in general ; so 

 it will be assumed in what follows that u s can be expressed 

 in the form (53), and (49) will be used in roughly estimating 

 the ranges of validity of the results we shall obtain. 



The Integrated Linear Terms. 

 We can now evaluate the quantity 



\*d\og(l + mC) or L s (l_ ai a4-a 2 C 2 -a 3 C 3 )dC, 



e=0 ' c=0 



and, subtracting logl^ 3 -j-m C! (as evaluated in previous 

 -paper), obtain 



-log(J + ,-„c)+J|^og(l + mC) 



c = 



=«iO + ie,O s + ^ 8 G» + ^0* . (54) 

 where 



*i = : (*s — %) , H = (y.s - a x fi s -f a 2 a So — a s ) , ] 



e 2 = (& — «i a s + a 2) > e± = (^ ~ <h Js + a 2 fi s - a z a So ) ) 



and (37) now appears in the more practical form ; 



—^7 = <£m + RC (1 - foC + Ja 2 C 2 - ia 3 C 3 ) + Gr M 



(55) 



dM ' 



^=^-R[logc s + ^C + ^ 2 C 2 + ^ 3 C 3 + ^ 4 C 4 ]+G s 



(56) 



Introduction of " Experimental " Concentrations. 



We have now to introduce the " experimental" concentra- 

 tions (cs, C) in place of the "true" concentrations (c s , C) 

 in the exuressions we have obtained. 



