the Conductivity of Solutions of Double Salts. 513 



paper *, though the data are somewhat meagre for the 

 purpose, and the results must therefore be used with caution. 

 Having obtained the requisite data in the ways indicated, we 

 have calculated the amounts by which the conductivities of 

 the alum solutions should differ from the arithmetic means 

 of the conductivities of their mixture constituents, if no double 

 salt were present as such ; and we find that for solutions of 

 KAI(S0 4 ) 2 and of KCr(S0 4 ) 2 of dilution 12 litres per gramme- 

 molecule, the molecular conductivity should be less than the 

 arithmetic mean of the molecular conductivities of the mixture 

 constituents by about 0*4 and 0'7 per cent, respectively. 

 Jones and Mackay found that for these solutions the molecular 

 conductivity was less than the arithmetic mean by 2*6 and 8*8 

 per cent, respectively. Assuming that the available data are 

 sufficient for the calculation, it is obvious not only that the 

 conclusion of these observers with respect to the chromium 

 alum seems to be substantiated, but that in the case of the 

 potash alum also the result is such as w r ould be accounted for 

 by the existence of double salt in solution. 



The same observers determined the ionization coefficients 

 in the mixture constituents of a series of solutions of sodium- 

 aluminium alum also, as well as the differences between 

 observed and volume mean conductivities of the alum solu- 

 tions. We have calculated the differences on the assumption 

 of no double salt in solution in the case of this alum, although 

 the data are much less satisfactory than in the former case, 

 with the result that for a solution of the same dilution as 

 above the actual conductivity should be greater than the 

 arithmetic mean by (very roughly) 2 per cent. This particular 

 solution was not examined by J ones and Mackay, but from the 

 observations given it would appear that its actual conductivity 

 is less than the arithmetic mean. While the conductivity 

 would be greater than the arithmetic mean if there were no 

 double salt in solution, it is found to be less ; and it is in this 

 direction that it would be affected by the association of some 

 of the molecules. 



The possibility of determining what the ionization co- 

 efficients in a solution of double salt w T ould be, if none of the 

 molecules were associated, suggests obviously that in investi- 

 gations of the kind under consideration, we should abandon 

 the volume mean method of study, and, instead, should calcu- 

 late what the conductivity of such a solution would be on this 

 assumption and compare the result with the observed con- 

 ductivity. 



* Phil. Mag. [5] xli. p. 276 (1896;.. 



