124 
MR. W. R. BOUSFIELD: IONIC SIZE IN RELATION TO 
The value of these equations considered merely as empirical extrapolation formulae, 
quite apart from the theory on which they are based, is clear. Putting h — x, they 
give us for the values of the Hittorf numbers at infinite dilution the figures 0'5055 
and 0’610 respectively, and these are undoubtedly the numbers which must be obtained 
by extrapolation from the data given by Kohlrausch. But in Kohlrausch’s 1900 
paper ( loc. cit.) he states, without giving further data, that he takes the value of the 
migration number for KC1 as 0"503. 
This paper is still the standard paper for the most accurate values of the con¬ 
ductivities of binary electrolytes with monovalent ions. The great accuracy of the 
values of X is shown by their correspondence both with Kohlrausch’s empirical 
formula and with the formula given in this paper—the modified Van ’t Hoff law 
with the corrected coefficient of ionisation. Kohlrausch gives the values of the 
separate mobilities at infinite dilution as 
K, / = 64-67, Na,/ = 43-55, Cl, Z = 65*44, 
and the values of A at infinite dilution as 
KC1, A = 130-10, NaCl, A = 108-99. 
The Hittorf numbers which correspond to these mobilities should be 
*» = BAr = 0' 5 °30 and = 0-6006. 
Both of these diverge seriously from the actual values obtained by extrapolation 
from the data formerly given by Kohlrausch, especially the number for NaCl, which 
is 0‘6004 as against 0 - 610. It might be well to reconsider the values of the 
mobilities of the separate ions, in the light of the above given extrapolation 
formulae, unless it turns out that Kohlrausch had more accurate but unpublished 
data in his possession in 1900, since these numbers are of such fundamental impor¬ 
tance in the theory of conductivities. 
(f) Deduction of Hydration Numbers and Values of Radions and Ionic Volumes. 
—It remains now to deduce the hydration numbers for our present purpose. 
Comparing the expressions for n 2 above given with equation (12) above set out, 
the KC1 equation gives us for the Cl ion the value B 2 = 3‘65, and the NaCl equation 
gives us for the Cl ion the value Ih = 3'54. This is on the hypothesis that the 
values of the Hittorf numbers at infinite dilution are 0 - 5055 and 0‘610 respectively. 
We shall assume, however, that Kohlrausch has data at his disposal which justify 
his taking the figure for KC1 at 0’503 instead of 0-505, which makes the velocities 
of the K and Cl ions more nearly equal, and we shall provisionally fix the hydration 
number for (I at the value 3"5. We then deduce the values for the K and Na ions 
from the equation 
BA + 
