52 ROYAL SOCIETY OF CANADA 
DETERMINATION OF THE JONIZATION COEFFICIENTS IN A MIXTURE. 
For the calculation, by expression (3), of the depression of the freez- 
ing-point of a mixture of the two electrolytes, having an ion in common, 
the ionization coefficients, a, and a,, involved in this expression, have 
been obtained by the foliowing method. 
Professor MacGregor ' has shown how to obtain equations sufficient 
for finding the ionization coefficients in a mixture of this kind, and how 
to solve them by a graphical procedure. I have pointed out in a former 
paper * that by throwing these equations into other forms they may be 
solved with little trouble, even in cases in which but few observations of 
the conductivity of simple solutions of the electrolytes in the mixtures 
are available. The transformed equations are as follows : 

J4 © 1 2, 
Ko k, ; : : ; 5 : : 6 
: AM (6) 
NE VN, 
Pi (CO), COCR SMe fee rr 
REG), | kul) palatal a 
where 1 and 2 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 solu- 
tions of equal concentrations), the ’s the specific molecular conduc- 
tivities at infinite dilution, the V’s the concentrations of the mixture with 
respect to each electrolyte, and the (’s the regional concentrations. If 
there is no change of volume on mixing, these k’s and Os are the conduc- 
tivities and concentrations of the isohydric constituent solutions. 
These equations can be solved graphically. Equation (8) is employed 
by drawing a curve having as abscissæ the values of the specific conduc- 
tivities (4,) and corresponding values of the concentrations (C,) as ordin- 
ates. Before equation (9) is used, the values of the conductivities (4,) 
are multiplied by the constant ae 

Re and these new values are plotted 
against the corresponding concentrations (C,) to the same scale on the 
same co-ordinate paper as employed for equation (8). In the present 
instance these two curves were drawn from the data given in Table III. 
From these two curves one finds by inspection two points, one on each 
curve, having a common abscissa, according to equation (6), and ordin- 
1 Trans. Roy. Soc. Can., (2), 2, 69, 1896-1897. 
2 Trans. N.S. Inst. Sci., 10, 124, 1899-1900. 
