﻿626 Mr. Bernard Cavanagh on 



Comparison with experimental data expressed in "esti- 

 mated" concentrations will thus give (A«), (A/8), (A7), 

 and (AS), and hence also (A7') and (A3') [from (74)]. 

 This will give « , /3, 7", and 6", and we can then at once 

 get 7 and 8, for it is easily shown that 



S"={34 2^(A a ) + ;3[(A/3) 2 +(A«)']}. . . (75) 



This procedure being available when a and [3 are large, 

 the highest concentrations, for which four-term expansions 

 of a and u s suffice, fall within the scope of the results given 

 here and it has been seen that these concentrations are high. 



In considering (62) in the sequel, it is understood that 

 this special procedure will be resorted to where necessary, in 

 which case (Aa) etc. will replace « etc. in the coefficients 

 ti, ti, etc. 



Main Result of the Analysis. 

 Having now completed the analysis we may conveniently 



use M , C, c s , in place of M(/, C, c s ', for the "experimental" 

 quantities, since the corresponding " true " quantities will 

 but seldom have to be considered. 

 If, then, we write 



}■ 



(76) 



J M =HC»(* 1 + * S |CI.+ *,C s + *4C i ) 

 _ J S =EC fa' + t,'Q + h'C 2 + * 4 'C 3 ) 

 (62) takes the form 



7: !■••;■■ ("> 



g=*.-Elog*+J. + G.J 



and, in fact, if, corresponding to Gr, we write 



= * M + 2^„ (78) 



J=J M + %J S - • (79) 



= -EC 2 (^ + ^ 2 C + ^3C 2 + i/ 4 C 3 ), . • (80) 

 (77) can be condensed to 



^=<^ + RSc,(l-logc,) + J + a, . . (81) 



which is perhaps the simplest and most concise expression 

 of the main result of the analysis of this and the preceding 

 papers. 



