230 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 
It will be noticed that in the case of the third mixture of 
the density and thermal expansion series (the same mixture) 
the differences are comparatively large; but it is obvious from 
the data of the fourth column in these series that the ionization- 
coefficients have not been accurately determined for mixtures of 
about the concentration of the one referred to. With these 
exceptions the agreement between observed and _ calculated 
values is satisfactory, the differences being either well within, 
or at worst on, the limit of observational error, up to mean 
concentrations of about 1.5. The determination of the ioniza- 
tion-coefficients was especially difficult in the case of the 
surface-tension observations, because Rother mixed equal 
weights of his simple solutions, not equal volumes. Neverthe- 
less, in all except the strongest of these mixtures, the differences 
are probably not beyona the limits of experimental error, 
Obviously, alternation of sign is not to be expected in these 
calculations. 
RELATIVE VALUES OF A PROPERTY FOR A MIXTURE AND FOR 
ITS CONSTITUENTS : “ CORRESPONDING ’ SOLUTIONS. 
As change of ionization in general occurs on mixing two 
solutions, it follows from (3) and (4) that the value of a pro- 
perty for a mixture of two solutions having one common ion 
will differ from the volume-mean, (v,P,+v,P,)/(v, + vg), of its 
values for the constituents by the amount 
(U, =e a (aa, \ ee a (ai eee .-4(5) 
Vi + Ve Uzt U2 
The name of “corresponding” solutions has been given to 
solutions for which this quantity vanishes. In general it will 
obviously have a value, though that value may be small. 
In most eases this conclusion is borne out by experience. 
But Rother has coneluded from his observations that, in the 
case of surface-tension, throughout a wide range of concentra- 
tion, solutions of all concentrations are “corresponding.” Were 
this the case it would throw serious doubt on the possibility of 
expressing surface-tension in terms of state of ionization. If, 
