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 :— 
je) Ps fee SE a Oa etd. 6 
; Hoo 9 Hoo 3 me (8) 
N, NG No oS. 
C, + Te == Ue ag) Das Se Se se CE) 
| 1 (C3); 
ka=To (Co) (crtrtttttttetetes (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 yo’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 
cease 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, (k,), are multiplied by the constant Poot and those of 
wo 2 
electrolyte 3, (k,), by ae Equations (8) are now employed by 
o3 
drawing curves having as abscissee 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), 
