72 IONIZATION OF COMPLEX 
dilutions, of which the intercept T X, between the curves A and 
K, is bisected by RS, W being the point of bi-section. Let T Y 
cut Bin U. X and U are the points required. For they have 
the same abscissa O Y, and their ordinates, X Y and U Y, are 
such that 
N, 1 
OO Se ee = oN we as 
mm 2 WY XN, 
Then a= OVX Yerand jase—J0.Y.., UY: 
The second and third of these methods involve less arith- 
metical work, and are less liable to error, than the first, and the 
second does not require the procedure by inspection which is 
required by the third. The second is therefore the most satis- 
factory. But the limited area of co-ordinate paper frequently 
gives the third a practical advantage. 
Only such portions of the curves A, B, C,D, E, need be drawn 
of course as may be seen by inspection to be required for the 
purpose in hand. 
Determination of the concentration, when the required 
ionization is given. 
The determination of the concentration which must be given 
a complex solution in order that it may have any required state 
of ionization, is of importance as facilitating the conducting 
of research based on the dissociation theory of electrolysis. 
It is not sufficient for the determination of the concentra- 
tion which the solution must have with respect to the two 
electrolytes, that the required ionization coefficients a, and a, 
should be given, because they are not independent. For a given 
value of a, the regional ionic concentration of electrolyte 1 has 
a determinate value, which may be found by plotting a curve 
for simple solutions of 1, with ionization coefficients as ordinates. 
and ionic concentrations as abscissee. The regional ionic con- 
centration of electrolyte 2, must by equation \1) be the same as 
that of electrolyte 1; and since it is thus determined, the ioniza- 
tion coefficient, a,, can have but one value which may be found 
by the aid of an ionization-coefficient-ionic-concentration curve 
