286 Prof. J. G. MacGregor on the Calculation of 



It will be seen that in the case of the more dilute solutions 

 Nos. 1-17 and 19, the differences, which are in all cases less 

 than 1 per cent, and for the most part considerably less, are 

 one half positive and one half negative ; and that whether the 

 solutions are arranged in the order of conductivity or in the 

 order of mean concentration, they exhibit quite a sufficient 

 alternation of sign to warrant the conclusion that they are 

 due, chiefly at least, to errors in the observations and the 

 graphical portion of the calculations. 



In the case of the stronger solutions, Nos. 16-18 and 19-22, 

 the alternation of sign has disappeared. In the weakest solu- 

 tions of these two series the differences are positive and small; 

 but as the concentration increases, the differences become 

 negative and take increasing negative values, the negative 

 difference having its greatest value in No. 22, which is a 

 mixture of a strong solution of NaCl with a saturated solution 

 of KC1. The tendency towards a negative difference as the 

 concentration increases may be recognized also in Nos. 11 

 and 15 ; and it is perhaps worth noting that, while the mean 

 value of the positive differences is slightly greater than that of 

 the negative differences up to a concentration of 1 gramme- 

 molecule of salt per litre, the mean negative difference is the 

 greater for higher concentrations. 



It is manifest from these results that for solutions of these 

 chlorides containing less than, say, 2 gramme-molecules per 

 litre, it is possible to calculate the conductivity very exactly, 

 but that for stronger solutions the calculated value is less than 

 the observed. 



This excess of the observed over the calculated conduc- 

 tivities shows one or more of the assumptions implied in the 

 mode of calculation to be erroneous. It would seem to be 

 probable that the error is at any rate largely due to the 

 assumption that the molecular conductivity of an electrolyte 

 at infinite dilution is the same whether it exists in a simple 

 solution or in a mixture, and that the discrepancy is thus due 

 to the effect of mixing on the velocities of the ions. The 

 mode of calculation assumes that in the mixture the con- 

 stituents are not really mixed, but lie side by side so that the 

 ions of each electrolyte in their passage from electrode to 

 electrode travel through the solution to which they belong 

 only. They must rather be regarded, however, as passing in 

 rapid alternation, now through a region occupied by one 

 solution and now through a region occupied by the other* 

 The actual mean velocities of the ions in the mixture will 

 therefore probably differ from their values in a solution of 



