THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
133 
facts. Arrhenius proposed a formula of the form y = C m (‘ Zeit. f. Phys. Chem.,’ 1, 
285, 1887) to express the viscosity of a solution in terms of the concentration. For 
a mixture he proposed rj = Cr‘C 2 ra2 C 3 ™ 3 .... This formula in the case of KOI, where the 
constants for the two ions could be taken as approximately equal, reduced to the form 
y = C^G 2 2m \ In this form Euler (‘Zeit. f. Phys. Chem.,’ 25, 536, 1898) further 
investigated the matter. Neither of these formulae turned out to be of general 
validity. 
Gruneisen* (‘Wiss. Abh. der Phys.-Tech. Reichsanstalt,’ 4, 239, 1905) has 
elaborated a very accurate formula which takes the form 
^-T-dL 0 = Aa + B (1 — a) + Cm, 
m 
where a is the coefficient of ionisation. Gruneisen has given the constants A, B, 
and C for a large number of electrolytes, and the formula brings out the important 
fact that the equivalent viscosity increment for electrolytes has a minimum value at 
concentrations varying from normal to normal. But Gruneisen’s results stop 
short of furnishing a theoretical explanation of the facts. He observes (Inc. cit ., 
p. 250):— 
“ That the minimum found with electrolytes should result from experimental errors, 
I regard as impossible. The only doubt is whether it is peculiar to electrolytes. I 
held this idea at first, but further experiments are certainly desirable. This suggests 
the possibility that the phenomenon may be accounted for by the dissociation of the 
molecules. On this supposition, the increase of the equivalent viscosity increment at 
greater dilution would be most simply explained by assuming that the dissociation of 
the molecule always increases the friction of the solution .” 
Other observers who have theorised on supposed viscosity anomalies have tendered 
widely differing explanations. Arrhenius (‘Zeit. f. Phys. Chem.,’ 1, 296, 1887), 
referring to the lowering of viscosity, or so-called “ negative friction,” which results 
from the solution of certain substances, such as KC1, suggests that the lowering of the 
friction is a result of electrolytic dissociation. Euler (‘ Zeit. f. Phys. Chem.,’ 25, 
541, 1898) suggests that the change of viscosity in a solution consists of two 
components, first, an increase which is in inverse proportion to the mobilities of the 
ions, and, secondly, a component depending upon the compression (electrostriction) of 
the water through the electric charge of the ions. Wagner (‘ Zeit. f. Phys. Chem.,’ 
46, 871, 1903) controverts both these views, and adumbrates the view (based upon 
mixtures of alcohol, nitro-toluol, and other organic compounds) that the viscosity of 
a mixture depends upon the viscosity of its components, and that this will account for 
“ negative friction.” 
* Gkuneisen’s paper came to my notice whilst the present paper was in progress. His results afford 
strong confirmation to the hypothesis with which this paper is concerned, and a fuller reference is made to 
them later. 
