THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 155 
changing size of the ions would be likely to affect it. A priori it seemed probable 
that the Hittorf transference numbers, and the viscosities of the solutions themselves, 
would depend merely upon the linear dimensions of the ions, whilst the densities of 
the solutions and the variations of effective molecular freezing-point depression and 
refractive power would depend upon the amounts of combined water, and therefore 
upon the cubes of the ionic dimensions. 
These cl priori considerations have, in fact, turned out to be justified, not merely 
qualitatively, but with considerable numerical accuracy, having regard to the difficulty 
of some of the approximations involved. We are able to express the Hittorf 
numbers, the densities, the effective molecular freezing-point depressions and the 
equivalent refractive power within the limits of experimental error, as simple functions 
of the radions, and to express the viscosities, with a fair approach to accuracy, not 
merely as a function of the radions of the solute, but also upon the extended 
conception of the radion as being simply proportional to the radion, or average 
molecular radius, of the whole solution. Our hypothesis has also enabled us to 
discover new relations which are independent of the hypothesis, viz., the fact that 
the Hittorf migration numbers are a linear function of (B + /r /j ) \ and the fact that 
the effective molecular freezing-point depression and the equivalent refractive power 
are linear functions of the solution volume. 
It is submitted that the above considerations justify the working hypothesis, that 
the function which we have named the radion, derived as above described, may in 
fact be taken to be a measure of the actual sizes of the ions. In any case, the radion 
turns out to be of fundamental importance in correlating the various phenomena of 
solution. 
APPENDIX. 
Note on the Yan ’t Hoff Law. 
Reasons for Supposing that the Van ’t Hoff Law with Index exactly § is an- Accurate 
Law for certain Binary Electrolytes with Monovalent Ions. 
1. A large number of such electrolytes follow the Yan J t Hoff law with close 
approximation over a considerable range of dilution. (See Bancroft, ‘ Zeit. Phys. 
Chem.,’ 31, 191, 1899, and for KC1 see Bousfield, ‘ Zeit. Phys. Chem.,’ 53, p. 268, 
1905, where diagram for KC1 is given.) 
For KC1 the value of the index is |4| for uncorrected a. 
2. In order to test the law with great accuracy, we ought to examine it over a range 
of dilutions so high that the viscosity is practically constant and the increase of ionic 
size (if any) is practically complete. In such a case we might expect to find the value 
of n practically constant and equal to f, if the Yan ’t Hoff law holds accurately. It 
is impossible to make such a test, owing to the fact that the error introduced by the 
uncertainty as to the correction for the conductivity of the solvent, multiplied by the 
x 2 
