134 
MR. W. R. BOUSFIELD : IONIC SIZE IN RELATION TO 
One matter of great importance has been established in relation to viscosity, viz., 
that it is an “ additive ” property. This is due,' in the first instance, to the work of 
Reyner (‘ Zeit. f. Phys. Chem.,’ 2, 744, 1888) and Wagner (‘ Zeit. f. Phys. Chem.,’ 
5, 46, 1890), and finally has been placed on a very firm foundation by Gruneisen 
( loc . cit.). 
( c ) A priori Considerations leading to a Genered Viscosity Formula. —The results 
obtained in section ( a) appear to point to the simple view that the viscosity of a 
solution is in the main merely a function of the number and size of its component 
molecules. We there saw that the change of viscosity of a liquid could be approxi¬ 
mately expressed in terms of the size and number of the molecules of the solute 
introduced, both in the case of simple salts and of mixtures. But the viscosity of 
the solvent itself should be capable of similar expression. According to Stokes’ 
theorem, the resistance to a very small sphere moving in a viscous medium is propor¬ 
tional to its radius. A priori this would lead us to the hypothesis that the viscosity 
of the medium itself would be proportional to r, in the case of a simple homogeneous 
medium consisting of molecules of radius r. Furthermore, this, in conjunction with 
the result which appears in section (a), suggests the hypothesis that the viscosity of 
a heterogeneous medium, consisting of molecules of radii r 1} r 2 , r 3 , ..., in proportions 
m i, m 2 , m 3 , ..., could be expressed as 
C 1 m 1 r 1 + C 2 m 2 r 2 + . . 
r \ = --. 
m 1 +m 2 + ... 
In the general case, the different sorts of molecules might have different coefficients 
of friction, so that the constants C l5 C 2 , C 3 would have different values. But, in the 
case of aqueous solutions, supposing the ions and molecules to be sufficiently hydrated, 
we should have, both in the case of water molecules and molecules of the solute, the 
friction of water on water. We will confine ourselves to this case and take the 
constant as the same for the different molecules, so that our expression would be 
simply 
y = C tnir/Sm. 
This would possibly exclude the case of H and OH ions, which are possibly little, it 
at all, hydrated. In case of molecules differing much from the spherical form either a 
special coefficient of friction would have to be assigned to them, or their radion would 
have to be taken as their largest or some mean dimension. 
The numbers m u m 2 might be regarded as expressing either the relative numbers 
of the various molecular species or their relative amounts reckoned by the total 
volumes occupied by each species in the solution. In some cases it will make no 
difference which view we adopt, in others it may make a serious difference. It is 
easier to work with relative volumes, and we find that such a volume relation holds 
for the changes of viscosity of mixtures of normal KC1 and NaCl solutions. We 
shall therefore adopt this alternative in order to test the hypothesis, bearing in mind, 
