142 
MR. W. R. BOUSFIELD : IONIC SIZE IN RELATION TO 
Gruneisen’s expression, for the purpose of comparison, may be written 
A rj = —a + b/l. 
But according to our vieyq the value of (3 differs for each ion, and hence Gruneisex’s 
expression, in which a and h are given constant values for all monovalent ions, could 
only approximately represent the general result, and in fact it does not profess to do 
more. But the important point is that Gruneisen’s empirical result, which brings out 
the equivalent viscosity increment of a “ normal solution of ions " as approximately 
a linear function of the reciprocal of the mobility, is in complete accord with and so 
far confirms the general theory of ionic sizes herein set forth.* 
Part VI.—Toxic Size in PiElatiox to Freezixg-poixt Depression. 
(a) General Considerations. —As is well known, the so-called “ molecular" freezing- 
point depression, which is normally nearly constant for dilute solutions of non- 
electrolytes, varies with the concentration in the case of dilute solutions of 
electrolytes, and tends at great dilution to a value which is for binary electrolytes 
about double the value for a dilute solution of non-electrolytes. This may partly be 
attributed to the ionisation of the electrolyte, upon the theory that the ionisation of 
a molecule of a binary electrolyte breaks up one molecule into two ions, each of which 
ions produces the effect of a molecule in the depression of the freezing-point. 
Hence, if 
A = observed freezing-point depression, 
N = gram-molecules of solute per LOGO grammes of solvent, 
a = ionisation coefficient, 
the effective number of gram-molecules per 1000 grammes of solvent is N(1 — a) + 2Na, 
that is to say, N (1 +«). 
Hence, upon this theory, the true molecular freezing-point depression is A/N (1 + a), 
instead of A/N, the ordinary so-called molecular depression. In order to distinguish 
the fraction A/N (1 + a) it will be convenient to refer to it as the “ effective molecular 
freezing-point depression,” or more shortly by the initials E.M.D., since upon the 
ionisation theory N (1 -fa) is proportional to the actual or effective number of molecules 
present. 
When we have evaluated the E.M.I). for any electrolyte, we still find it not 
constant but variable with the concentration, and it is probable that this variation is 
intimately connected with the varying ionic volume of the solute, which represents, 
upon our hypothesis, the varying amount of water in combination with the ions. 
* Gruneisen’s relation for divalent ions is ?/-l = -0'207 + 24/Z. This appears to indicate that 
divalent ions have a different coefficient of friction from monovalent ions, possibly because they are not 
approximately spherical. 
