Properties of Aqueous Solutions to their State of Ionization. 109 



in the same way, amount to *0 3 1, or about 0*5 per cent, of 

 (P ap — F bp )/n. A proved independence of p at this dilution 

 would be more satisfactory. 



Observations at such extreme dilutions, in the case of 

 most properties of solutions, are probably impracticable. 

 But they are fortunately unnecessary for the settling of the 

 question under consideration. For if the values of the 

 ionization-constants for any property have been obtained as 

 above from observations over a range extending to great, 

 though not necessarily extreme, dilution, the values so ob- 

 tained may fairly bo assumed to apply very approximately to 

 much greater dilutions ; and from the values of l a + l p , h + lp, 

 h + lq, h + lq, &c., thus obtained, it may readily be determined 

 whether or not J a — l b is independent of the ions p, q, &o. 

 Unfortunately, Kohlrausch and Hallwachs's observations on 

 density are not sufficiently numerous for this purpose. 



The Determination of the Ionization- Constants for the 

 Free Ions. 



The values of the constants l a , 4> lp, &c. may probably, in 

 some cases at least, be determinable in the following way. 

 The experiments just referred to would give l a +■ l p , h + l p , &C, 

 as well as k ap and k bp , &c. If now, guessing at the value of 

 l p , we find the first three terms of (12) to be negligible at 

 dilutions at which P a & and V bp can be determined with suffi- 

 cient accuracy, a determination of these quantities will give 

 the value of laa ap — ha bp ; and if a ap and a bp be known with 

 sufficient accuracy, la, l b . and l p may then be found. It would 

 of course be necessary to check our guess at the value of l p by 

 substituting the value found in expression (12) and seeing 

 whether or not with this value the first three terms would be 

 negligible. 



The accurate determination of the ionization-constants for 

 the various properties of a variety of solutions would form 

 valuable material to serve as a basis for theory. I may 

 therefore express the hope that observers who are so fortunate 

 as to have the necessary instruments of precision at their dis- 

 posal may be led by this paper to make the requisite 

 observations. 



Phil. Mag. S. 5. Vol. 43. No. 261. Feb. 139 



