MIXTURES OF ELECTROLYTES—MACGREGOR. 103 
2. €., the amount of the common ion which is dissociated per unit 
of volume, must be the same in both constituent solutions. 
According to the dissociation theory, the specific conductivity 
of a mixture of two solutions of electrolytes 1 and 2, whose 
volumes before mixing were v’, and v’, respectively, which 
contained m, and n, gramme-equivalents of the electrolytes per 
unit of volume, whose combined volume after the mixture is 
p (¥1i+ v,), whose co-efticients of ionisation after mixing are 
@, and @2, and whose specific molecular conductivities at infinite 
dilution, under the circumstances in which they exist in the 
mixture, are wo1 and wx2, is given by the expression : 
1 
k=D(u, + U,) (ce, 21 VU, fol + O, Ne Ve oa) . 
Since in any case in which isohydric solutions are mixed without 
change of volume, 7,, v',,7, and v2 are known, @ and @, readily 
determinable, and p equal to unity, the specific conductivity can 
be calculated, provided we may assume that fo1 and woe have the 
same values in the mixture as in simple solutions. In the 
particular case in which equal volumes of the constituents are 
mixed without change of volume, the conductivity of the mix- 
ture becomes obviously the mean of the conductivities of the 
constituent solutions. 
Arrhenius has subjected the result referred to above to a 
number of tests. In one he determined by experiment several 
series of dilute aqueous solutions of different single acids, such 
that if any two of the members of the same series were mixed 
in equal volumes, the mixture was found to have a conductivity 
equal to the mean of the conductivities of the constituents. 
Regarding the solutions of each series as shewn thereby to be 
isohydric among one another, he calculated the concentrations of 
the ions in the various solutions by the aid of Ostwald’s obser- 
vations of the conductivity of acids. The following table gives 
the result, the numbers specifying the concentration of dissociated 
hydrogen (in mer. per litre) in the different solutions, and those 
