622 Mr. Bernard Cavanagh on 



As a first approximation we may neglect all but the first 



term of this series, and in ^- clearly we may neglect even 



the first term in comparison with log c s . Thus we obtain the 

 equations 



^==M o (0 M + RSc l )+2wi(^i-Rlogc 1 )+RMo2^ af '/z(c 1 c a ...) 



. . . (54) 

 .and thence 





(55) 



— from which m is completely eliminated so that no know- 

 lodge of the constitution of the solvent is assumed. 



In this first approximation we have neglected ^m %Ci in 

 comparison with unity. 



Now, for example, taking m for water as roughly 36. we 

 see that in half-molar solution the error involved in this first 

 approximation is about one per cent. 



It is clear that at or above tenth-molar concentration we 

 ■ought to proceed to a further degree of approximation by 



including in ~^- the first term and in ^-X the second term 



O n s t O^VIo 



of the expansion of log (1 -f m %c{) . We thus get the 

 .equations 



^± =rf, s _R (logc s -m S Cl -2^#V 



. . . (56) 



in which, it is seen, 7J7 only enters in the form of small 

 correction terms, so that, until considerable concentrations 

 are reached, a quite approximate idea of m will suffice. 



These equations (56) may profitably be substituted for 

 equations (55) at and above tenth-molar concentration. 

 Whether the inclusion of a further term of the expansion of 

 loo- (l-\-mQ%Ci) would be of any value (except possibly in 

 certain special cases) is very doubtful, particularly when, as 

 in this section, we are considering associated or polymerized 

 solvents, for at reallv considerable concentrations the third- 



