MIXTURES OF ELECTROLYTES—MACGREGOR, 105 
solutions of the acids; and the calculated values were found to 
agree with those observed to within 0.5 and 0.2 per cent. respec- 
tively. So far as result is concerned, this forms a much more 
satisfactory test than those mentioned above: but the number 
of calculations is too small to exclude the possibility of accidental 
agreement. 
The calculation of the conductivity of a mixture of electro- 
lytes is so severe a test of the ionisation theory of electrolysis 
that I have thought it well to try its possibility on a larger 
scale, especially as a considerable body of material is available 
for this purpose in the observations of the conductivity of 
mixtures of solutions of potassium and sodium chlorides made 
by Bender*. The present paper contains the results of calcula- 
tions of the conductivities of mixtures determined experimentally 
by him. 
METHOD OF CALCULATION. 
In order to make such caleulations by Arrhenius’s method, it 
would be necessary to make a preliminary determination of a 
number of isohydric solutions of the two salts, and to restrict 
the calculations to very dilute solutions. They may be made 
however, without such preliminary experiments, and without 
such restriction, by employing a more general form of Arrhenius’s 
deduction. 
Two electrolytes, which have a common ion and are in a state 
of equilibrium in the same solution, may be regarded as occupying 
definite portions of the volume of the solution. If we apply the 
equilibrium conditions to the parts of the solutions occupied by 
the respective electrolytes, as well as to the whole solution, we 
obtain equations which, mutatis mutandis, are identical with 
those obtained by Arrhenius, as indicated above, for the iso- 
hydric solutions and their mixture. Thus. if in the equations of 
equilibrium given above, we take v, and v, to be the portions 
of the volume of the mixture occupied by the respective electro- 
lytes, and @, and «, to be their co-efficients of ionisation in the 
*Wiedemann’s Annalen, XXII, p. 197, (1884). 
