68 ROYAL SOCIETY OF CANADA 



that, therefore, the concentrations of ions are functions of the dilution 

 only. Hence we have 



(c) from the relation of dissociation to dihition, 



» 1 



What the functions involved in these equations are, may be determined 

 from measurements of the specific molecular conductivity of sufficiently 

 extended series of simple solutions of the respective electrolytes. 



We have thus four equations for determinino- the four vmknowji 

 quantities involved, viz.. a^ a.,, Fj, V2. 



These equations may be most conveniently solved by a graphical 

 process. Draw curves from the experimental data just referred to, having 

 as abscissa^ the concentrations of ions for simple solutions of 1 and 2, 

 respectively, and as ordinates N^ and No times the corresponding values 

 of the respective dilutions. Then select two points, one on each curve, 

 which have the same abscissa, and which have ordinates the sum of 

 which is equal to v. Multiply the values of the ordinates of these points, 

 read otf on the scale on which the}" would represent dilutions, by the 

 common value of the abscissa, and we have the values of a-, and a.,. 



If the solution have been formed by the mixing of two simple solutions, 

 and especially if the constituent solutions had equal volumes and were so 

 dilute as to undergo no appreciable change of volume on mixing, the 

 graphical process is very easily carried out.' 



Arrhenius'' has shown that the conductivity of a complex solution, 

 containing two electrolytes with one ion in common, may be calculated 

 by, fir.st. making sufficiently extended series of observations to determine 

 what simple solutions of the two electrolytes are isohydric with one an- 

 other (i.e., do not change in their state of dissociation on being mixed), 

 and, secondly', finding by the aid of these observations, and bj^ a series 

 of approximations, of what two isohydric solutions the complex solution 

 might be formed by mixture. Isohydric solutions were recognized as 

 such by the equality of the specific conductivity of a mixture of equal 

 volumes of them, to the mean of their specific conductivities. The iso- 

 hydric constituents of the complex solution having been determined, its 

 conductivity was the mean of their conductivities. The method was ap- 

 plicable only to solutions so dilute that there was no ap])reciable change 

 of volume on mixing. 



' For a detailed account of tliis graphical process see Trans. Nova Scotian Inst. 

 Sci., vol. ix., p. 107. 



- Wied. Ann., x.\x., p. Ti (1887). 



