48 Prof. J. G. MacGregor on the Relation of the Physical 



These coefficients were obtained from Kohlrausch and 

 Grotrian's and Kohlrausch's observations of conductivity at 

 18° C* In obtaining them I took the specific molecular con- 

 ductivity (referred to mercury) at infinite dilution to be 

 1216 x 10- 8 for KOI, and 1028 x 10~ 8 forNaCl,not being aware 

 at the time that Kohlrausch had given 1220 and 1030 respec- 

 tively as more exact values. Nevertheless, to save labour I 

 have used the above values of a in the calculations of this 

 paper, having satisfied myself by a re-calculation in one case 

 that no appreciable difference in the results would be pro- 

 duced by the employment of more exact values. It will be 

 noticed that in one or two cases the above values of <x are 

 obviously a little out ; but they would seem to be sufficiently 

 accurate for my purpose. I did not foresee the extent of the 

 calculations, or I should have determined all the values of a . 

 required at the outset, and checked them by comparison with 

 one another. 



I have determined the ionization-constants (k and Z) in all 

 cases in which more than two observations of a property on 

 solutions of sufficient dilution were available by the method 

 of least squares. The constants thus determined and used in 

 the calculations are tabulated below. In all cases the avail- 

 able observations had been made on solutions of such great 

 concentration that the values of the constants obtained cannot 

 be regarded as exact ; but the calculations may serve as a 

 test of the general applicability of the expression referred to 

 above. The only available observations, so far as I know, on 

 solutions of sufficient dilution for the determination of the 

 ionization-constants and the limits of concentration within 

 which the above expression is applicable, are those by Kohl- 

 rausch and Hallwachs f on the specific gravity of dilute 

 solutions, from which two of my students have undertaken to 

 determine the density-constants for the salts and acids exa- 

 mined. 



With regard to the observations which I used in deter- 

 mining the various ionization-constants, the following state- 

 ments should be made : — 



Bender's determinations of density (t. e. specific gravity 

 referred to water at 4° C.) were made at 15° C, but were 

 readily reduced to 18° by the aid of his observations on the 

 thermal expansion between 15° and 20° of the same solutions. 

 According to his statement, the fourth place of decimals in his 

 values may be in error by + 2 or +3. The density of water 

 was taken to be 0*99863. 



* Wied. Ann. vi. (1879) p. 37, and xxvi. (1885) p. 195. 

 f Wied. Ann. liii. (1894) p. 14. 



