158 
MR. W. R. BOUSFIELD: IONIC SIZE IN RELATION TO 
at a similar result, based upon the law of mass action, with a wholly different 
hypothesis as to combination of ions and water molecules. 
Again, this hypothesis may not be accurate, but it strengthens the view that the 
Van’t Hoff law can, in some way, be based on the law of mass action, which would 
give an exact instead of an approximate index. 
The above sets of considerations point to the view, that if a, the coefficient of 
ionisation, be corrected for viscosity and ionic size, the Van ’t Hoff law would hold 
accurately in the lower range of dilution. It is found that such a correction can 
be made by the aid of Stokes’ theorem, according to which the velocity of trans¬ 
portation is inversely proportional to the linear dimensions of the ionic complex, 
which gives the ionic size as a simple function of dilution. 
The relation above indicated should be expressible by the equation 
when 1 - a is small. This equation can be compared with the relation 
h(l -a) 2 /a 3(1+ ”> = C . . . 
( 1 )< 
Since for considerable dilution h is proportional to 1 /to, the relation may be written as 
(1 - o)I*p = Bm 1 ' 2 .(2). 
This is the relation given by Kohlrausch as an empirical result (‘ Sitz. Akad. Wiss. Berlin,’ 1900, 
p. 1006). It is shown by him to hold with great accuracy from decinormal to infinite dilution for a series 
of nine binary electrolytes with monovalent ions, and is used by him to deduce the values of A x . 
As equation (1) is thus established as an adequate empirical relation, we may use it by a reverse process 
to examine the more exact relation which the diagram indicates when the curve is prolonged. 
Equation (1) may be written 
3 log - - 2 log —— = log C 4- 3n log a. 
a 1 - a 
Using Napierian logarithms and writing y, for the modulus of common logarithms, 
and we may write the relation as 
By differentiation we get 
x , 
- = 
h y , h 
- -, = log- 
1 - a fi a 
3 y - 2x = log C + 3pn log a. 
dy p _ n A 1 da. 
dx 5 ’ a' dx 
(3), 
(4). 
Also from (3) we get by eliminating the variable h and differentiating 
p da. 
a' dx 
-a), 
whence by substituting in (4) and writing 
dy 
I-*-* '-“-ft 
we obtain the equation 
2 = nf3(±-z) 
(5). 
This, then, is the more exact equation of the curve which has been indicated as a straight line in the 
diagram on p. 157. The curve starts from the origin, and has a horizontal asymptote. 
To compare the constants with Kohlrausch’s figures, we note that 
p = § (1 + n), or n = - 1. 
