Permeability 
141 
in general electrolytes with the highest diffusivity have the highest 
electrical conductivity. 
Mathematical formulae have been evolved to express these 
relations in the case of diffusion of non-electrolytes. Thus Sutherland 
(1905) and Einstein (1905, 1906) derived the formula 
N * 67 TYjp ’ 
where D is the coefficient of diffusion, R is the gas constant, T the 
absolute temperature, A T the Avogadro constant (that is, the number 
of molecules in one gram molecule), 77 the viscosity of the solvent, 
and p the radius of the diffusing molecules which are assumed large 
in comparison with those of the solvent. Sutherland showed, how¬ 
ever, that should the molecules of the solvent be large in comparison 
with those of the solute, the relation more nearly approximates to 
J;a. 
iv 47777/) 
Von Smolukowski (1906) obtained a similar expression but with 
a different constant, his formula being 
D = 64 RT _I_ 
27 N * 67777/) ’ 
A general confirmation of this formula experimentally has been 
made by Svedberg and Andreen-Svedberg (1909,1911) who could not, 
however, decide whether the constant in the equation of Einstein, 
Sutherland and von Smolukowski is 1 or 64/27. 
The relation between molecular size and coefficient of diffusion 
has been stated in another form by Exner (1867, 1874, 1877) for the 
case of gases. Exner’s conclusion is expressed by the equation 
dVm = k. 
where D is the coefficient of diffusion, M the molecular weight and 
k a constant. This relation has been extended to the case of non¬ 
electrolytes by Oholm (1910), who confirmed it experimentally for a 
number of sugars and other substances, and who used it to determine 
the molecular weight of dextrin from the coefficient of diffusion of the 
latter. A third formula has been proposed by Herzog (1910), namely 
Drj y/Mv = constant, 
where v is the specific volume and the other symbols have the 
signification already assigned to them. This relation is stated to hold 
for a number of non-electrolytes (Padoa and Corsini, 1915). 
