THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
135 
however, that this is merely a tentative selection from the alternatives. Hence, if 
A, A> As, represent the total volumes occupied in the solution by each species of 
molecules, we propose to represent the viscosity of the solution as 
77 = CZ/3r/Z(3. 
In order to simplify matters, we shall always take S/3 = 1 , so that A, A, A> ••• 
will be the fractions of the total volume of the solution occupied by each species of 
molecules, and the expression becomes 
77 = C Z/3r. 
(d) Extended Conception of the Radion.— The conception of the radion as the 
average molecular radius of any set or sets of molecules, basing the average on a 
volume reckoning, will greatly simplify the hypothesis. We adopted the term 
“ radion ” as a convenient contraction for the radius of the ion , which we supposed 
to be an aggregate consisting of the ionic nucleus and water molecules. The 
expressions which we obtained for the ionic radius in terms of hydration, which were 
of the form 
r = rj l+B/r 2/3 )-\ 
clearly indicated that the radius so derived must be an average radius, since the 
hydration h is a continuously varying magnitude, whilst the actual numbers of 
molecules must be whole numbers and must vary per saltum. We may now 
generalise the conception of the radion and use the term to indicate the average 
radius of any group of molecules. Suppose, then, we have a liquid containing a 
volume A of molecules of radius r 1} a volume A °f molecules of radius r 2 , and so on, 
the radion of this liquid, taking the average on a basis of volumes, would be 
R = ZPr/Z/3. 
If we always consider a unit of volume so that Z/B = 1 , and therefore A, A, ••• are 
the fractions of the total volume occupied by each set of molecules, then we have for 
the radion, or average molecular size, simply R = Zfir. 
It follows also that if r x , r 2 , r 3 , ... be the radions of different volume fractions 
A, A> A ••• °f the liquid (instead of the radii of the ultimate molecules) the radion of 
the liquid is still expressed as R = Z/3r. 
(e) The General Viscosity Formula. —The general viscosity formula for aqueous 
solutions in which the coefficients of friction between the molecules may be taken as 
constant throughout, to which we were led by d priori considerations, was 77 = C Z/3r. 
The conception of the radion enables us to express this simply as 77 = CR, where R 
is the radion of the whole solution. Also if the liquid be composed ol various 
composite constituents having radions r x , r 2 , r 3 , ... for the respective volume fractions 
A, A, A. •••> the viscosity of the separate fractions (if they could be separated) would 
