THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
129 
The above results are calculated as if the solution were fully ionised, the ionic 
volume for a pair of ions being taken as the sum of the volumes of the ions. Now, 
ionisation could only be complete for very dilute solutions, but we find that our 
formulae hold without sensible loss of accuracy nearly up to normal solutions for 
which the coefficient of ionisation is less than 07. This is a matter of some practical 
importance hereafter, as it is an indication that we can take the ionic volume of the 
un-ionised molecules as being approximately equal to the sum of the volumes of pairs 
of ions with radii given by the formulae obtained for the separate ions. This means 
that if we consider a pair of ions just after ionisation to be 
represented by a in the figure, we may consider a pair of 
ions just before ionisation to be represented by b. Hence, 
while a consideration of conductivities and mobilities only 
gave us a clue to the size of the ions themselves, the density formula indicates that 
in solutions of moderate dilution the volumes of the un-ionised molecules may be 
taken to follow approximately the same law. 
a- 
Part V.—Ionic Size in Relation to Viscosity. 
(a) Viscosity a Function of the Radions. —We discuss further on the general 
relation between the viscosity of a fluid and the sizes of the molecules of which 
it is composed. For the moment, it will suffice to say that it seems, <1 priori, 
probable that the change of viscosity caused by the introduction of foreign molecules 
VOL. CCVI.-A. 
s 
