THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
103 
ionisation, which made Van ’t Hoff’s law (in a slightly modified form) an accurate 
expression of the relation between ionisation and dilution, down to twice decinormal 
solutions of KC1. This method of procedure gave for the radius of the hydrated ion 
an expression of the form 
r = rJl + B/r 2/3 )-\ 
which indicated that the average radius of the ion steadily increased with dilution, 
owing to increasing hydration of the ion, up to “infinite dilution. ' Whether the 
resulting expression for r did in fact represent the average radius of the ion was 
tested by a consideration of the density law which would thence result. The volumes 
of the ions would be proportional to r 3 , and it was found that a rational density 
formula could be constructed upon this basis which accurately corresponded with the 
observed densities of the solutions. 
In the present paper the necessary experimental determinations for applying the 
method to solutions of NaCl are given, together with some other determinations for 
collateral purposes, and the hypothesis is further tested by reference to other physical 
properties of solutions. These results are independently of some value, apart from 
the hypothesis by which they are reached, and it has been thought well to designate 
the function r, which, according to our view, expresses the average radius of the ion, 
by the term “ radion.” Whilst this term connotes our hypothesis, it may, if 
necessary, be merely considered as expressing a certain function of the dilution. But 
it has a further convenience, as it enables us readily to extend the conception to 
denote the average molecular radius of any group of ions or molecules, or even of the 
whole of the ions and molecules both of solvent and solute in any given solution. The 
utility of this extended conception will appear more clearly in the section relating to 
a consideration of ionic size with reference to the viscosity of a solution. 
The volume of the ion, according to our hypothesis, is proportional to the cube of 
the radion, and the volume of a pair of ions to the sum of the cubes. These cubes 
and their sums we refer to as “ ionic volumes.” But except where the context 
indicates the contrary, the term “ radion ’ may be taken as merely denoting the 
function 
r = rJl + Bh- 2 'r\ 
and the term “ ionic volume ” as denoting the cube of the radion or sum of the cubes 
of the radions, apart from the hypothesis as to size. 
As in our former paper, with reference to KC1, it is shown that the “ solution 
volume of NaCl solutions is a linear function of the ionic volumes. Hence the 
densities of KOI and NaCl solutions can both be accurately expressed by the same 
formula as simple functions of the radions. 
A theoretical consideration of the relation of the Hittorf migration numbers to the 
sizes of the ions is given, and it is shown that our hypothesis as to the influence of 
