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



them and Kohlrausch's corresponding values as ordinates, 

 and drawn a smooth curve through the points. By the aid of 

 this curve I determined the correction b of the table given 

 below. The correction is, of course, a more or less doubtful 

 one ; for it is not certain that the observations on mixtures 

 suffered from the same unknown source of error as the obser- 

 vations on simple solutions. It seems probable, however, 

 that they did ; and the results of the table given below would 

 appear to render it almost certain. __ . .; * 



It may bo well in one case to give an example of the mode 

 of calculation. We may take for this purpose the mixture of 

 solutions containing 1 grm .-molecule of salt each. It is 

 found by the graphical process that the value of a/V for this 

 mixture is 0*718 grm.-molecule per litre, and that the 

 dilutions of the mixture are 0*937 and 1*063 litre per grm.- 

 molecule for the NaCl and the KC1 respectively. The den- 

 sities of the constituent solutions were l - 0444 and 1*0401 

 respectively, and that of the mixture 1*0422. The expansions 

 per unit volume between 15° and 20° C. were 0*0013569 and 

 0*0012489 respectively. The values of the conductivity at 

 infinite dilution I took to be 1028 and 1216, according to 

 Kohlrausch's observations. Hence the conductivity of the 

 mixture, 



,_1 2 x 1-0422 /lx 0-718x0-937x1028 1 x 0718 x 1-063 xl216 \_ 809 , 2 

 2* 20845 \ 1 +06 x 0-00136 + 1+0 6x000125 / 



Bender's observed value (he used the same standard as 

 Kohlrausch) was 814. To this a correction of about —3 

 must be applied to make the observation agree with the 

 others of the same series (correction a), and a correction of 

 about —3 to make it comparable with a calculated value 

 based on Kohlrausch's data (correction b). Bender's reduced 

 result is thus 808, which differs from the calculated value by 

 1*2 or 0*15 per cent. 



Results of the Calculations. 



The following Table gives the results of the calculations ; 

 the second and third columns containing the numbers of 

 grm .-molecules per litre in the simple solutions at 15° C; the 

 fourth column, Bender's observed values of the conductivities 

 of the mixtures; the fifth and sixth, corrections a and b referred 

 to above ; the seventh, Bender's reduced values ; the eighth, 

 the calculated values; and the ninth, the excess of the calcu- 

 lated values over those observed, expressed as percentages 

 of the latter. 



