158 ON THE DEPRESSION OF THE FREEZING-POINT 



Professor MacGregor's equations so as to express them in terms 

 of regional conductivities and concentrations. 



In the case of mixtures of three electrolytes the transformed 

 equations are as follows : 



I.. _ f*i /,. _^i /,. , r v 



"'i "'a u Iv 3> \P) 



7^+ ^- + ^- = 1. (7) 



k,=f ! 



.(8) 



=/ 



where 1, 2, and 3 denote the electrolytes, the k's the specific 

 conductivities of the electrolytes in the regions which they 

 respectively occupy in the mixture, (these conductivities having 

 the same values as in simple solutions of equal concentrations), 

 the juoo's the specific molecular conductivities at infinite dilution, 

 the N's the concentrations of the mixture with respect to each 

 electrolyte, and the C's the regional concentrations, which in the 

 case of dilute solutions are the concentrations of the constituent 

 isohydric solutions. 



We have thus six equations for the determination of three 

 k's and three C's. 



These equations can be solved by a graphical process. In 

 the first place the values of the specific conductivities of elec- 

 trolyte 2, (& 2 ), are multiplied by the constant 5*1, and those of 



/*oo2 



electrolyte 3, (7c 3 ), by i. Equations (8) are now employed by 



ftw 3 



drawing curves having as abscissae the values of the specific 

 conductivities, and the corresponding values of the concentrations 

 as ordinates. Three points are now found by inspection, one on 

 each curve, having a common abscissa, according to equations (6) 



