100 Prof. J. Gr. MacGrregor on the Relation of the Physical 



conclusion should thus have beeu that the difference, if any, 

 between the surface-tension of a mixture and the volume-mean 

 of those of its constituents was within the limits of his experi- 

 mental error. He might even have concluded, however, that 

 there was probably such a difference in the case of Sodium 

 and Potassium Chlorides ; for in all the mixtures of solutions 

 of these salts which he examined, the volume-means of the 

 values for the constituent solutions were found to be less than 

 the values for the mixtures. 



The above expression (5) will vanish if the constituents ^ of 

 the mixture are isohydric, i. e., have states of ionization which 

 do not change in the mixing ; and it will vanish in that case, 

 whatever the values of the other quantities involved in the 

 expression may be. When the constituents are not isohydric 

 the condition of its vanishing will be 



n 2 (l^ — &!)(«! — a/>i 



It is obviously improbable that in any case in which this con- 

 dition may be fulfilled the numbers of gramme-equivalents 

 per litre in the constituent solutions will have a simple relation, 

 such as 1:2, 4:3, &c. 



The conclusions drawn by Bender and Bruckner from 

 their observations on density, thermal expansion, electrical 

 conductivity, and viscosity, viz. that there is such a simple 

 relation in the case of all "corresponding" solutions, so far 

 as the properties mentioned are concerned, is thus inconsistent 

 with the possibility of expressing the values of these properties 

 in terms of the state of ionization. 



Both Bender* and Bruckner f obtained their results from 

 numerous series of observations, in each of which a solution 

 of given concentration of one salt was mixed in succession, in 

 equal volumes, with a number of solutions of different con- 

 centrations of a second salt, having one ion in common with 

 the first. The values of the property under consideration 

 were determined both for the simple solutions and for the 

 mixtures and the arithmetic means of the values for the con- 

 stituents of the several mixtures were found. Curves were 

 then plotted with molecular concentrations of the simple solu- 

 tions of the second salt as abscissae, and the observed values 

 for the mixtures and the arithmetic means of the values for 

 the constituents, respectively, as ordinates. The " corre- 

 sponding " solutions were indicated by the points of intersec- 

 tion or contact of these curves. In all cases the curves for 



* Wied. Ann. xxii. (1884) p. 184, and xxxix. (1890) p. 89. 

 t Ibid. xlii. (1891) p. 293. 



