10 McBAIN 



I', and Cdig' respectively, in a solution of potassium cadmium 

 iodide ; and «, b, c, d, their concentrations expressed as gram- 

 equivalents per cubic centimeter. Three of the mobilities, viz. : 

 M, V, zif, may be taken as known ; and among the four concen- 

 trations there must exist the relation 



a + d = c -\- d 



so that four of the eight symbols, u, Vy w, x, a, d, c, d, repre- 

 sent unknowns. Four experiments giving four independent 

 relations involving these four are therefore necessary in order 

 to determine the concentration of each of the ions, and the 

 mobility of Cdl/. Such, for example, are the following : 



1. The specific conductivity x may be determined ; by Kohl- 

 rausch's law 



au -}- dv -}- cw -\- dx =^ X. 



2. The quantity of potassium which enters the cathode com- 

 partment during the passage of one faraday through the solu- 

 tion may be determined ; it is aujx equivalents. 



3. Similarly, the net gain of cadmium in the anode compart- 

 ment per faraday, is {idx — bv)lx equivalents. 



4. And the gain of iodine at the anode per faraday r 

 [c2v -\- 2^x)/x equivalents. 



These are not the only experiments, however, that might be 

 employed. By means of E.M.F. measurements, for instance, 

 the concentrations b or c might be determined ; t-he freezing 

 point gives a -\- }^b -i- c -{- d, etc. The experiments thus furnish 

 more equations than unknowns, and the surplus may be used to 

 check the theory. This has been done in my paper ' in which 

 the concentrations were calculated from transport measurements 

 and one E.M.F. determination; the results so obtained are in 

 accordance with the conductivity and freezing points. 



It may be remarked that when the number of analytical com- 

 ponents among the ions of a solution is represented by «, the 

 migration of the ii-ih may be calculated from those of the 

 remaining « — i by means of the stoechiometrical relations. 

 Hence agreement between the directly measured migration of 

 the «-th component and the calculated value is the best proof 

 that unsuspected ions (due to hydrolysis, for example) have not 

 been overlooked. 



' Zeit. f. Elektrochem., //, 961 (1905). 



