38 ROYAL SOCIETY OF CANADA 
For mixtures of simple solutions, according to the above assumption, 
A the depression of the freezing-point will be represented by the expres- 
SION : 
A = [WN L'an — 1) ) + IGN, A + a, Gn, —1) ) + Be 
in which 1, 2, etc., denote the electrolytes, the m’s the number of ions 
into which the molecules of the respective electrolytes dissociate, the 
a’s the ionization coefficients in the mixture, the N's the concentrations 
(in gramme-molecules per litre) of the mixture with respect to the respec- 
tive electrolytes, and the M’s the depressions produced by one gramme- 
molecule or one gramme-ion of the undissociated and dissociated portions 
respectively of the electrolytes. 
In the following observations equal volumes of simple solutions of 
the two above-mentioned electrolytes, which have one ion in common, 
were mixed. As a molecule of HCl dissociates into two ions, and as 
H,S0, is regarded as breaking down into three ions, expression (2), since 
there is no change of volume on mixing, reduces to : 
Aen lee ao) Ae Mn: CL a PAIE INR ES 
where n, and n, are the concentrations of the simple constituent solutions. 
For the calculation of A by this expression, the n’s are known and the a’s 
are obtained by the modification of Prof. MacGregor’s method described 
below ; but what values the W's are to be regarded as having is doubtful. 
It was found for simple solutions of the electrolytes employed that the 
molecular depression varies with the concentration. This appears to 
indicate that the number of molecules and ions present affects the power 
which one molecule or one ion has of lowering the freezing-point, and it 
has therefore been assumed that in a solution made by mixing simple 
solutions of two electrolytes, the depression produced by a molecule or 
an ion of one electrolyte, which is surrounded by molecules and ions of 
this electrolyte and of the other electrolyte, would have the same value 
as if all the molecules and ions present were of this one electrolyte. Thus 
the W's of the above expression have been regarded as equal to the mole- 
cular depressions in simple solutions of the concentration N + MN. It is 
the applicability of expression (3) on this assumption that the present 
paper is intended to test. 
1 Trans. N.S. Inst. Sci., 10, 139, 1899-1900. 
