THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
141 
presence of a small fraction of the solute in the form of associated molecules. This, 
in our view, probably accounts for the observed viscosity values for NaCl in the 
neighbourhood of 6 per cent, coming out notably higher than the calculated values. 
It would be going too far from the purpose of this paper to follow up the con¬ 
siderations which are suggested by the view of the relation of viscosity to molecular 
size which is here presented. It must suffice to point out that to all the various 
speculative questions as to the meaning of “negative friction,” as to'the effect of 
dissociation in increasing or decreasing friction, and so on, this theory has but one 
reply_the change in viscosity in aqueous solutions under varying conditions is 
mainly dependent upon the change in the average molecular size which takes place, 
that is, to the change in the radions of the components of the solution. 
(q) Comparison with Gruneisen’s Results. —The important paper by Gruneisen, 
which came to hand during the progress of this paper, to which reference has already 
been made, tends strongly to confirm the propositions here advanced. Gruneisen 
oives viscosity measurements for some nineteen solutions of electrolytes, and finds 
that in all cases, as dilution increases, the equivalent viscosity increment comes to a, 
minimum, and then increases with further dilution. Lius is in accord with our 
results, according to which, as dilution takes place, ionisation at first diminishes the 
viscosity by breaking up the molecules and afterwards increases it, owing to the 
increase of the ionic radii with further dilution. 
Moreover, Gruneisen has dissected the equivalent viscosity increments due to the 
separate ions at infinite dilution, and has found values of the equivalent viscosity 
increments for hypothetical “ normal solutions ol the separate ions. for monovalent 
ions he finds that these viscosities may be approximately expressed by the equation 
p-l = -0-207+ 13-3 /I, 
where rj is the viscosity of a “ normal solution of ions ” and / is the mobility of such 
ions. The viscosity of water is reckoned as unity. 
This result is not exactly comparable with the present results, but an approximate 
comparison may be made. If r be the radion of the uncombined water, r' the radion 
of a set of ions of mobility /, /3 the fraction of unit volume of the solution occupied 
by 1 gram-molecule of the ions, we should have, according to our theory, for the 
viscosity of the hypothetical “ normal solution of ions, 
t? = C {(1 —/3) r + /3r'}. 
If r 0 be the radion of pure water, we should have r/„ = Cr 0 , and therefore, for the 
change in viscosity caused by the introduction of 1 gram-molecule of the ions, we 
should have (remembering that according to our theory r f = l/l) 
A 77 /C = (1 -P)r-r n + /3/l. 
