512 Prof. J. G. MacGregor and Mr. E. H. Archibald on 



dilute (all the a's equal to unity), or (2) the solutions are 

 isohydric («/—-«! and aj — a 2 both equal to zero), or (3) the 

 change of ionization and other quantities involved are 

 appropriately related to one another. It will be obvious 

 that in experimenting on solutions of double salts of moderate 

 dilution these conditions of the valid application of the volume 

 mean criterion cannot in general be applied. 



Jones and Mackay* are the only observers in this field who 

 have recognized this difficulty ; and while still employing the 

 volume mean method, they have endeavoured in one case 

 to meet it. In studying solutions of potassium-aluminium 

 alum and of potassium-chromium alum, they determined 

 the ionization coefficients of series of simple solutions of 

 the three sulphates involved, by means of freezing-point 

 observations, and found that for equi-molecular solutions 

 of the aluminium and chromium sulphates they have ap- 

 proximately the same values. They assumed that the dif- 

 ferences between the actual and the volume mean con- 

 ductivity in these alum solutions, so far as they might be 

 due to ionization, would therefore be the same for both ; 

 and from the fact that much greater differences were found 

 for the chromium alum than for the aluminium alum they 

 concluded that in solutions of the former double salt existed 

 as such. 



The assumption thus made may be shown to have been 

 justified, in its result at any rate, by a calculation of what the 

 differences would be if no double salt existed in solution. For 

 this purpose the fi^ 's and the «"s of the above expression 

 must be determined. The former may be found from the 

 determinations of ionization coefficient and molecular con- 

 ductivity made by Jones and Mackay ; for the molecular 

 conductivity at infinite dilution is very approximately the 

 ratio of the latter to the former. Thev were found in this 

 way to be 1412, 759, and 763 for iK 2 S0 4 , iAl 2 (S0 4 ) 3 , 

 and £Cr 2 (S0 4 ) 3 respectively, when expressed in terms of 

 10 — 8 times the conductivity of mercury at 0° G. The value 

 for ^K 2 S0 4 at 25° C. (Jones and Mackay's temperature) calcu- 

 lated from Kohlrausch's data is about 1465. The values 

 which the ionization coefficients would have in the alum 

 solutions, on the assumption of the presence of no double mole- 

 cules, may be determined from the values of the ionization 

 coefficients of the simple solutions observed by Jones and 

 Mackay, by the method described by one of us in a former 



* Zoc. cit. 



