THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
137 
In this case the value of C makes no difference to our results. The water radion 
is not required, as we can take the radion of the u'hole of each solution , before mixing, 
as the basis of our calculation, thus accounting for the total number of molecules 
both of solvent and solute. The constant is here introduced as illustrating the 
procedure in the more complex case. Care must be taken to distinguish between 
the radion of a salt solution as a whole, and the radion of the salt in solution. 
In the following table are set out the observed values of the viscosities for the 
mixtures, and the values calculated from the equation 77 - 0'54 2/3r, where fi 2 are 
the fractions of KC1 and NaCl respectively in unit volume of the mixture. 
Table XXII.-—Viscosities of Mixtures of KC1 and NaCl Normal Solutions, calculated 
from their Radions. 
Pi. 
P* 
1 ] observed. 
7 / calculated. 
Difference. 
1 
0 
0-01037 
0-01037 
+ 
0-75 
0-25 
0-01063 
0-01063 
+ 
0-5 
0 - 5 
0-01088 
0-01090 
_ 2 
0-25 
0-75 
0-01116 
0-01117 
-1 
0 
1 
0-01143 
0-01143 
+ 
Let us now apply the equation to the general case of a salt in solution. Let r be 
the radion of the uncombined water in the solution (which may be different from the 
radion of water itself). Let r f be the radion of the hydrated solute (comprising 
both ions and molecules). Let /3 be the total fraction of unit volume of the solution 
which is occupied by the hydrated ions and molecules of the solute. Then 1 —/3 will 
be the fraction which is occupied by uncombined water. Then the equation 
77 = Cl/3 r takes the form 77 /C = (1 —/3) r + /3/, or 
,/C-r-=/3 (/-»•) ..(17). 
This may be regarded as the fundamental viscosity equation for a simple salt 
solution. It may be noted that if we take r as the radion for pure water, we have 
its viscosity 77 = Cr, so that for solutions so dilute that the value of the water radion 
is not sensibly changed by the addition of the solute we may say 
S77 = C /3 (r'-r), 
which indicates that if the radion of the solute is less than that of water 877 is 
negative. This is in fact the case for KC1, the solutions of which have a less viscosity 
than water. Cases of “ negative friction ” therefore are readily explicable upon the 
present hypothesis. 
So far the matter is simple, but in applying the above equation in practice we 
VOL. COVI.—A. 
T 
