THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
105 
and at present* unknown, and hence a consideration of ionic sizes at 18° C. in relation 
to osmotic data at another temperature might lead to error. But it seemed probable 
that the ionic sizes at different dilutions might have the same relative, values at 18° C. 
and 0° C., and in the absence of other data it was decided to use these. 
Defining the “ effective molecular freezing-point depression ” as the ordinary 
so-called molecular freezing-point depression divided by (1 + a), where a is the 
ionisation, and denoting it by the letter D, it was found that D was a linear function 
of the ionic volume, and that it could be expressed both for KG1 and NaCl as 
D = 1-86 + 0(1. —1„), 
where I„ stands for the ionic volume at the given dilution and l r for the ionic volume 
at infinite dilution, the value of the constant C being nearly the same for both 
substances. 
In addition to the confirmation thus afforded to our view as to the fundamental 
importance of the radion in the theory of solutions, we are further led to a useful 
formula for obtaining by extrapolation the value of the molecular freezing-point 
depression at “infinite” dilution. For this purpose we are able to dispense 
with our hypothesis, and obtain from it a new result quite independent of it— 
one of the recognised tests of the validity of a hypothesis, though not a con¬ 
clusive one. 
We saw that the solution volume was a linear function of the ionic volume, and we 
have now the effective molecular freezing point-depression also as a linear function of 
the ionic volume. Hence the effective molecular freezing-point depression should be 
a linear function of the solution volume, and in this case the reference to ionic sizes 
which correlated the two sets of phenomena can be dispensed with. In order to test 
this matter, measurements of the densities of KC1 and NaCl solutions at 0° C. were 
made. This is a little above the freezing point of dilute solutions, but it was 
considered to be near enough to make the desired comparison. Density measure¬ 
ments were made upon solutions of strengths of lr, - x \, normal, and empirical 
formulae (based on the lines of the rational formulae for 18° C.) were constructed to 
obtain the solution volumes at the concentrations at which Jahn’s freezing-point 
determinations were made. 
The result was that the effective molecular freezing-point depression both for KC1 
* In my former paper I attempted to calculate the variation of ionic size with temperature by reference 
to the conductivity temperature coefficients of the ions at infinite dilution which were given by 
Kohlrausch. I have, however, since come to the conclusion that these results are unreliable. 
Kohlrausch’s values were largely based on determinations of the conductivities of normal 
solutions. Dissociation being incomplete in such solutions, any variation of conductivity due to change 
of ionisation with temperature would be included in his temperature coefficients and might entirely 
vitiate the deductions which I drew. This portion of my former paper must therefore be withdrawn, and 
I propose to pursue the matter further experimentally. 
VOL, CCVI.-A. 
P 
