154 
MR W. R. BOUSFIELD: IONIC SIZE IN RELATION TO 
ordinary value of a, there exists a linear relation between log D and log U, leading to 
a relation of the form K = D/U", where n is for various electrolytes nearly but not 
quite two thirds. (See Appendix.) 
This suggested that if we could find a suitable correction for a, which is usually 
taken as X/A, the Van’t Hoff dilution law would turn out to be an exact relation for 
dilute solutions of binary electrolytes such as KC1. 
The materials for such a correction were sought in. the known fact that the viscosity 
of the solution produced aberrations in the mobilities of the ions, but viscosity 
differences alone were inadequate to give an account of such aberrations. 
Kohlrausch’s observations on the temperature coefficients of the ions had already 
led him to the general view that the ions must be considered to be water-coated. 
This water combination necessarily altered the sizes of the ions, and it was considered 
that the joint effect of changes of viscosity and changes of size might adequately 
account for changes in the mobility. 
To reckon these effects quantitatively, Stokes’ theorem as to the motion of a small 
sphere in a viscous medium was available, and though the actual motion of the ions 
through an electrolyte under the influence of a potential gradient is probably 
extremely erratic, it was thought that, nevertheless, the effect of size and viscosity 
upon the average rectilinear drift under the influence of the electro-motive force might 
be amenable to exact treatment, just as the average rectilinear drift itself can be 
accurately calculated. 
Assuming, then, that the aberrations of the mobilities which made the Van’t Hoff 
law inexact were due to such causes and could be dealt with in this way, corrections 
were applied to the mobilities, and corrections for a were calculated, the nature of 
which was determined by the Stokes theorem, and the amount of which was 
determined by the Van’t Hoff law (expressed in terms of the hydration h instead of 
the volume V of the solution). 
The result of this process was to give us the expression * 
r = r x (1 +B/ff 2/3 ) -1 
for the relation betwen the radius of an ion and the dilution of the solution. 
Up to this point, if one may compare small things with great, the process followed 
is similar to that of the astronomer who sought to locate the position of a new planet 
by considering the irregularities produced in the movements of the old ones. In that 
case the result could be tested by turning a telescope to the spot indicated by the 
calculations. 
In the present case the result could only be tested by considering how far the 
hypothesis as to the changing sizes of the ions owing to the changes in the amount of 
water combination could be rationally related to the various physical phenomena of 
solutions, and how the quantitative results were functionally related to existing data. 
In the case of each set of phenomena it was, necessary to consider a priori how the 
