228 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 
change, we shall have as the value of the property for the 
mixture, assuming no change of volume on mixing, 
Un 
Vy $V, 
P=P,+(k,0 = a,')n4 at l,a,'n1) + (ke = a,!)No +140!n9)——9— (4) 
a 
Ve 
the n’s being numbers of gramme-equivalents per unit volume 
of the original simple solutions, and @' and @,! being the 
ionization-coefficients in the mixture. As the values of the k’s 
and /’s have been determined above for sodium and potassium 
chloride for a number of properties, and, as I have shown in my 
paper on the “ Conductivity of Mixtures,” cited above, how the 
ionization-coefficients after mixing may be determined, it should 
be possible to predict the values of these properties for mixtures 
of solutions of these salts. 
The following tables show that this can be done. The 
ionization-coefficients were determined in the way described in 
the paper referred to. The constants k and J employed in the 
calculations were those determined above. The observations 
were made by the authors whose determinations for simple 
solutions were used above; in fact in most cases it was the 
solutions of the tables given above which were mixed. The 
limits of experimental error are thus of about the magnitudes 
mentioned above in each case. All remarks made above with 
regard to the reduction of observations to 18° C., the values of 
the property for water, ete., apply also to the mixtures. In all 
cases, except that of surface-tension, the solutions mixed were 
mixed in equal volumes. Unfortunately, Bender made no 
observations on the refracting power of mixtures. 
