THE PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS. 
157 
a = X/A), the values of x and y calculated therefrom and the values of Ay/Ax In 
diagram XIII. are set out the values of Ay/Ax—\ as ordinates, upon the values of a 
as abscissae. Each value of Ay/Ax belongs to a value of a intermediate between the 
two values of a from which it is reckoned. As this intermediate value is uncertain, 
each value of Ay/Ax— f is set out twice, i.e., to say upon the two values of a which 
lie one on each side of it. It will be seen from the diagrams that when a = 1, 
i.e., at infinite dilution, the extrapolated value of Ay/Ax—% is in each case zero, i.e., 
dy/dx = f accurately. 
This enables us to say that in the region of dilution where change of viscosity 
and ionic size become negligible the Van ’t Hoff law holds accurately for KC1 
and NaCl. 
If we were to follow out the same process for (say) acetic acid, we should find that 
the limiting value of dy/dx was accurately J, i.e., we should get Ostwald’s law. 
3. Ostwald’s law, with its accurate index, can be easily derived from the law 
of mass action. There is, therefore, reason to suppose that the Van ’t Hoff law 
should also be capable of being based upon the law of mass action, which would 
necessarily give us, for high dilution, some definite and exact value for the index, 
since the index is the ratio of certain small numbers of molecules, which are necessarily 
whole numbers. In the former paper (see ‘ Zeit. Phys. Chem.,’ 53, p. 266, 1905) this 
matter was discussed, and a hypothesis was set out upon which the law of mass action 
gives the Van’t Hoff law with exact index. This hypothesis may be unsound, but 
it shows the possibility of -basing the Van ’t Hoff law upon the law of mass action 
when the nature of the equilibrium between the molecules of solvent and solute 
is better understood. 
Morgan and Kanolt (‘ Journ. Amer. Chem. Soc.,’ 26, p. 635, 1904) have arrived 
