SOLUTIONS.—M ACGREGOR. 73 
for electrolyte 2. Thus any one of the quantities a,,a,, and 
the common regional ionic concentration, which is of course 
equal to the total ionic concentration of the whole solution, 
being given, the others may be found, if we have sufficient data 
as to the conductivity of the simple solutions. 
Even if the ratio only of the ionization coefficients is given, 
the state of ionization is in many cases completely determined. 
For as 
ft aes 
— 3, 
NG \ 2 
a, Vi 
we have ee 
a, Ve 
and the dilution-ionic-concentration curves are frequently of 
such forms that a given value of V,/V, corresponds to a definite 
value of V, and V 
curves. 
>» Which may be found by inspection of the 
Some datum in addition to the state of ionization is there- 
fore requisite, if the concentration of the solution is to be fully 
determined. It may be the concentration with respect to one 
of the electrolytes, or the ratio of the concentrations with 
respect to the two, or the total concentration, or any such func- 
tion (the conductivity for example) of the concentrations with 
respect to the two. If the state of ionization is not fully given, 
an additional datum is obviously required. 
(1.) Given the required state of ionization and the concen- 
tration with respect to one electrolyte : to find the concentration 
with respect to the other.—A and B (Fig. 3) being the dilution- 
ionic-concentration curves, OY is given; and N, being also 
given, we have only to find N,/N, in order to determine N,. 
From Y draw YT parallel to the dilution-axis, cutting A and 
B in X and U respectively. Draw the line RS parallel to the 
axis of ionic concentrations and distant from it by 1/(2.N,). Let 
RS cut YT in W. Cut off WT equal to X W. Then TY/UY 
will be the value of N,/N,. (The curve E in Fig. 3 is of course 
not required.) 
(2.) Given the required state of ionization and the ratio of 
