MIXTURES OF ELECTROLYTES—MACGREGOR. 107 
If we employ the symbol V to represent the dilution (v/n Vv’) 
we may write the above equations as follows :— 
ue Ny 
v LRRD) Bee eee ete (3) 
vy, So a Re eee Neha. (85 
I determined @, and «, from these equations by the following 
graphical process :—Equation (3) was employed by drawing, from 
experimental data, for simple solutions of electrolyte 1, a curve 
having values of the concentration of the ions («/V) as abscissee 
and corresponding values of the dilution (V) as ordinates. This 
curve was drawn once for all, and was used in all determinations. 
The curve embodying equation (4) had to be drawn anew, (or 
rather such portion of it as was necessary), for each mixture 
examined. In the case of a mixture of solutions containing 
m, and ”, gramme-molecules per unit volume of electrolytes 
1 and 2 respectively, the curve had as abscissee the concentrations 
of ions of a series of simple solutions of electrclyte 2, and as 
ordinates, since Bender’s mixtures were mixtures of equal 
volumes, n,/7, times the corresponding values of the dilutions, 
Were the mixtures under consideration mixtures of unequal 
volumes, n,v,'/n,v, times the values of the dilutions would 
have to be used as the ordinates. Equations (1) and (2) were 
applied by finding, by inspection, two points, one on each of the 
above curves having a common abscissa (@,/V,=@,/V,) and 
. . VW . ’ : 
having ordinates (V, and ies V. respectively) of such magni- 
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