﻿Molecular Thermodynamics. 639 



Appendix III. 



The form of the cofficients in {S6) suggests an alternative 

 method of meeting the practical difficulty of slow convergence 

 of the J series, which will be preferable in many cases 

 'though not always) to that already given on account of its 

 very attractive simplicity — both formal and practical. 



Extending (85) to the fourth term 



(l s — S s - a x h + \aJ l s) = (/ — £ — a x k + \aji) 



= =(-lV l l 4 +4 a l 2a 2-i^l«3-9«2 2 +i«4) ~ - 3 Vl 4 ' ' ( 119 ) 



we have for the coefficients of the Jm-series, 



h = t; , 3 = (?+3*/7+/F) j (120) 



t 2 =(t 2 + h); 7 4 =(" 4 +6" 2 /7+2A 2 + 4i/7+") ) 



and on comparing this with (59) it is at once seen that if 



we write C for ( C + p Jm V> then 



J u J 3I =/^-l\=fC'+AC' 2 + IC' 3 + FG' 4 . . (121) 

 Also (but less c obviously), if 



G S ~c ' 



we find 



Rlogr s -J s = Rlogc/-J7, . . . (122) 

 where 



-J s ' = UC'(t s + h s C'+K s G ,2 + l s C' 3 ). . . (123) 



These " concentrations w (c s \ C) have no simple physical 

 significance, though they will approximate roughly to the 

 4; true " concentrations of the earlier analysis. They are, 

 however, a great practical convenience, since the series in 

 (121) and (123) will clearly converge "practically" in few 

 terms so long as the expansions of a s and a (in ascending 

 integral powers of the total " true " concentration) do so, 

 that is, as we have seen, up to very high concentrations. 



Now, supposing either that we can neglect G (thus 

 making, tentatively, the assumption of perfect solution), or 

 that we can separate G from J in our measurements, then 

 solvent-separation data will give us Jm and solute-separation 



