10 ROYAL SOCIETY OF CANADA 
APPLICATION TO THE CALCULATION OF THE DEPRESSION IN MIXTURES. 
The observations made by Messrs. Archibald and Barnes of the 
depressions in mixtures make it possible to apply a more severe test to 
the applicability of the above expression for P. For if it holds for the 
various series of simple solutions, the depression, A, of complex solutions 
containing two or more of the above electrolytes, should be calculable 
by means of the expression : 
= k, I—a,) n, + an, + hk, (1—a.) n, + 1, a, n, + &c., 
in which the constituent electrolytes are represented by 1, 2, &c., the 
concentrations of the solution with respect to them by n,, n,, &c., their 
ionization coefficients by a,, a, &c., and the ionization constants, deter- 
mined by the observations on the simple solutions, by k,, k,, L,, L,, &e. 
It is not to be expected of course that the depressions of the mixtures 
will be calculable with the same degree of accuracy as in the case of the 
simple solutions ; for the ionization constants have been only approxi- 
mately determined, and the ionization coefficients cannot be so accurately 
determined for complex as for simple solutions. But they ought to be 
at least approximately calculable within the concentration range, 
throughout which the above expression for 6 holds for simple solutions of 
all the constituent electrolytes. 
The tables given below show how closely the depressions for the 
mixtures examined can be calculated. But in order to facilitate a 
judgment as to the success with which the predictions have been made, 
they should be prefaced by a few remarks on the determination of the 
ionization coefficients. In the case of the potassium and sodium sulphate 
solutions Mr. Archibald used my method of finding the coefficients ; but 
in the chloride and acid solutions Mr. Barnes used a modification of that 
method, devised, with much ingenuity and insight, in order to save the 
labour involved in making long series of observations of conductivity or 
in the reduction of long series already made by others. For this purpose 
instead of employing curves obtained by plotting concentration of ions 
against dilution, which have rapid curvature in the region of moderate 
dilution, he employed conductivity-concentration curves which are much 
flatter ; and for the drawing in of these curves he trusted to a compara- 
tively small number of observations. Now in drawing in a curve 
through a small number of points there will be a tendency to give 
the curve between successive points either too much or too little 
curvature ; and in determining ionization coefficients by the aid of 
successive portions of such a curve, the coefficients may be expected to 
be affected by an error varying in magnitude in a periodic manner, The 
