THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
I 39 
which reduces to 
- = R — r, where R = n + r 2 —« — + - ^ 2? 1 . 
ym(Y 1 + V 2 ) Vi + V 2 
R is of course (vide equation ante) the radion of the solute, and the equation, when 
written in the form 
r )/C = 7- + ymI„(R—r), 
is seen to be identical with the general equation (17) before given. 
In the following tables are set out the values of R and 77 , calculated from the above 
expressions, together with the necessary data for the calculations. The ionic data 
are taken from Tables XIII. and XIY. The values of a are obtained by setting out 
the corrected values of a (given in Table IX.) on a large-scale curve and taking oft 
the values for the different values of m. The observed values of the viscosities are 
the same as in Tables XIX. and XX. The values of y used for the calculation were 
0-032 for KC1 and 0-030 for NaCl. These are mean values calculated from the 
separate sets of figures for the two salts. The value of r, the radion of the 
uncombined water, is taken as 0"01946 in both cases. The value of C was worked 
out from these two sets of figures and the mean value 0‘54 was obtained, as before 
mentioned. 
Considering the various slight inaccuracies involved in the approximations above 
detailed, the correspondence between observed and calculated values appears to be 
sufficiently close to support the general character of the hypothesis as to the relation 
between the radions of the various species of molecules and the viscosity of the 
solution. The two sets of viscosities are calculated from the same formula, with 
'practically the same constants, the only difference in the constants employed being 
that the factor y is taken as 0-032 for KC1 and 0"030 for NaCl. 
It must be borne in mind that the purpose was not to construct an accurate 
empirical formula, which is fairly easy where plenty of constants are available. But 
in the cases examined the simple formula 17 = CSfir is found to be adequate to 
express, with a near approach to accuracy, the viscosities of the solutions up to 
normal strength in the case of KC1 and 5 per cent, in the case of NaCl, showing that, 
with such aqueous solutions, the viscosity depends mainly upon the average size of all 
the molecules present. 
The departure of the calculated values from the observed values for the NaCl 
solutions at about normal strength may be partly due to our approximations breaking 
down before normal strength is reached. But we are more inclined to attribute this 
departure to a cause which was considered in Part III. (c) of this paper. With an 
autolytic solute, it is probable that there is some association of the molecules of the 
solute in more concentrated solutions. In the case of KC1, with its comparatively 
small ions and molecules, this does not appear. But in the case of NaCl, with its 
larger hydrated molecules, the radion of the solute might be notably increased by the 
T 2. 
