222 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 



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 I) 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 available 

 observations had been made on solutions of such great concen- 

 tration 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, as 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 Kohlrausch and 

 Hallwachs* 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 examined. 



With regard to the observations which I used in determining 

 the various ionization-constants, the following statements should 

 be made : 



Bender's determinations of density (i. 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. 



Bender's determinations of thermal expansion are for the 

 interval between 15 and 20 C., and will therefore be sufficiently 

 nearly proportional to the coefficients of expansion at 18 for 

 my purpose. He considers that they may be in error by 2 in 

 the sixth place of decimals. On plotting his observations, how- 

 ever, it becomes obvious that they do not all attain this degree 



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



