160 Dr. J. Shields on the Relative Strengths 



the square roots of the electrolytic dissociation-constants. 

 But the dissociation-constant is arrived at from the equation 



m 2 7 



==k, 



(1 — m)v 



in which m is the degree of electrolytic dissociation or the 

 ratio of the molecular conductivity at any given dilution, v, to 

 that at infinite dilution. Now, when m is very small, the 

 above equation becomes 



V 



or, when the dilution for different acids is the same, 



m 2 k 

 nil 2 "" k Y ' 



i. e. the electrolytic dissociation ratios are as the square 

 roots of the dissociation-constants, or directly as the ratios of 

 distribution. 



According to Guldberg and Waage's law (as enunciated by 

 Julius Thomsen), the ratios of distribution are as the square 

 roots of the velocity-constants. If we call K the velocity- 

 constant in the hydrolysis of aqueous salt-solutions, then */K 

 becomes the measure of the dissociation ratio, or the relative 

 strengths of the two weak acids are as \/JL : i/Kj. 



To apply this method to a few specific cases, we may 

 obtain the necessary data in my former paper on hydrolysis 

 in aqueous solutions of salts of strong bases with weak 

 acids (Phil. Mag. [5] xxxv. p. 365, 1893). It was there 

 pointed out that when potassium cyanide, for example, is 

 dissolved in water it is partially decomposed into free acid 

 and free base, and the following equilibrium takes place : 



KOH + HCN-^- KCN + HOH, 

 from which we get the equation 



KOH x HCN=K(KCN x HOH), 



where K= — of the more general equation, 

 c i 



Cl (KOHx HON) =c 8 (KCJSrx HOH), 



in which c x and c 2 are the velocity-coefficients in opposite 

 directions (Guldberg and Waage, Journ. f. pr. Chem. [2] 

 xix. p. 69,1879). 



In the present case, however, we desire to study the for- 

 mation of the salts or the ratio of distribution of the base 



