THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
153 
given by Dinkhauser,* the values of the equivalent refractive power as given by 
him, together with the values calculated from the linear relation 
An/m = 0-01643 —0-0215V,. 
It will be seen that the difference between observed and calculated values nowhere 
exceeds more than a unit in the last place of decimals, from a concentration of 
one-tenth normal to five times normal. 
It may be noted that we have here a clue which may enable us to obtain the ionic 
volume in concentrated solutions.! In dilute solutions we have shown that the ionic 
volume, as derived from the radions, is a linear function of the solution volume. It 
seems probable that this linear relation persists through concentrated solutions, and 
that the solution volume may therefore enable us to calculate accurately the ionic 
volume in concentrated solutions. But we cannot follow up this clue in the present 
paper. 
Table XXXI.— NaCl. 
TO. 
o-l 
0-25 
0-5 
0-75 
1-0 
2 
3 
4 
5 
V s . 
An/m 
observed. 
An/m 
calculated. 
Difference. 
0-2831 
0-01035 
0-01034 
+ 1 
0-2888 
0-01023 
0-01022 
+ 1 
0-2960 
0-01008 
0-01007 
+ 1 
0-3016 
0-00994 
0-00995 
- 1 
0-3071 
0-00982 
0-00983 
-1 
0-3235 
0-00946 
0-00947 
-1 
0•3350 
0-00922 
0-00923 
-1 
0-3461 
0-00898 
0-00899 
- 1 
0-3567 
0-00876 
0-00876 
+ 
Part VIII.— Concluding Observations. 
Let us now briefly review the main course of the argument, as developed in this 
and the former paper, in relation to our fundamental hypothesis. 
As our starting point we took the Van ’t Hoff dilution law, which we may express 
by saying that if D represents the concentration of the dissociated portion of a solute 
and U the concentration of the undissociated portion, reckoned by means of the 
* Dinkhauser gives the values of A p/m, where Ap is the difference of the density p of the solution 
from the density p 0 of water at the same temperature, and to is the concentration. The solution volumes 
can he calculated from the expression 
I/I 10_ * 2 3 4 5 \ 
\ to ‘ E ) 
where E is the weight of a gram-molecule of the solute. 
t It would be more accurate in concentrated solutions to use the term molecular volume instead of 
ionic volume, but unfortunately the term molecular volume has been already misapplied to indicate the 
product of the solution volume by the weight of a gram-molecule—a use which has led to much confusion 
of ideas. 
VOL. CCVI.-A. 
X 
