108 Prof. J. G. Macgregor on the Relation of the Physical 



of volume on solution, by Pontgen and Schneider for com- 

 pressibility, and bv Jabn for the electromagnetic rotation of 

 the plane of polarization. 



Applying the above expression, we have for the difference 

 in the values of a property per unit of molecular concentration, 



(Pap — Fbp)/n = k a p{l— a ap ) —h P (l — abp) + lp{<*ap — abp) + Ua ap — l b a bp ,(12) 

 and at infinite dilution 



(Pap-? bp )/n=la-h (13) 



Had the experiments referred to been all carried out at extreme 

 dilution, as were those of Kohlrausch, afterwards extended 

 by Loeb and Nernst*, the evidence would be quite satisfactory. 

 But in general they have been made at only moderate dilution, 

 and it is obvious from (1.2) that the approximate independence 

 of the common ion on the part of (P ap — Pj p )/w, may be quite 

 consistent with considerable variation in l a — h, It is clear that 

 the first three terms of (12) may readily mask any variation 

 in the last two, and that, if the last two did not vary, l a — l b 

 could not in all cases be the same. 



That no satisfactory conclusion can be drawn from experi- 

 ments of this kind, unless conducted at extreme dilution, 

 may be shown roughly in the case of density by the aid of 

 the results obtained above. For we may assume that the 

 ionization-constants for density obtained above will not be 

 very different from those which would be derived from 

 observations made at greater dilution f. We know from 

 Kohlrausch and Hallwachs's observations that if ap and bp 

 represent NaCl and ^Na 2 C0 3 respectively (Pap— F bp )/n will 

 have the value O0139 for solutions containing *005 grm.- 

 equivalents per litre, and that for NaCl and HC1 it will have 

 the value 0*0235. We may assume that for EaCl and KC1 

 it will be about 02 From the values of k for these salts we 

 find the first two terms of (12) to be "0 3 64. If we assume l n 

 to have half the mean value of I for NaCl and KC1, the third 

 term will amount to — *0 4 98. The first three terms thus 

 amount to about "0 3 54, or say 4 per cent, of the value of 

 (P fli j — Tb P )/n. Thus, observations of the kind referred to, for 

 density, could give no satisfactory result, even if conducted 

 at this very great dilution. At a dilution of '001 grm.- 

 molecules per litre, the first three terms of (12), calculated 



* Ztschr.fiirphys. Chemie, ii. (1888), p. 948. 



t Mr. E. H. Archibald, one of iny students, tells me that for magnesium 

 sulphate, Kohlrausch and Hallwachs's data give £=-05663 and / = -066887. 



