MIXTURES OF ELECTROLYTES MACGREGOR. 107 



If we employ the symbol V to represent the dilution (v/n v) 

 we may write the above equations as follows : 



$-- -a) 



,2, 



which in the case of mixtures of equal volumes becomes 



= <K (V,) ................... (3) 



I determined a 1 and 2 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 abscissae 

 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 

 %! and n 2 gramme-molecules per unit volume of electrolytes 

 ] and 2 respectively, the curve had as abscissae the concentrations 

 of ions of a series of simple solutions of electrolyte 2, and as 

 ordinates, since Bender's mixtures were mixtures of equal 

 volumes, n 2 /n l times the corresponding values of the dilutions. 

 Were the mixtures under consideration mixtures of unequal 

 volumes, W a t; 9 / /'ji 1 v 1 / times the values of the dilutions w r ould 

 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 (<*i/V 1 = 9 /V 8 ) and 



having ordinates (V x and V 2 respectively) of such magni- 



