282 Prof. J. Gr. MacGregor on the Calculation of 



greater dilutions, where the curvature is most rapid. I there- 

 fore obtained interpolation formulae, by means of which I 

 drew in the latter parts of the curves, expressing «/V in the 

 case of each salt in terms of the reciprocals of powers of V. 

 These formulae, having no permanent value, need not be given 

 here. The table of results below shows that they were accu- 

 rate enough for the purpose in hand. 



As Bender measured the specific gravities of both his 

 simple solutions and his mixtures, his paper affords the neces- 

 sary data for determining the change of volume on mixing. 

 Such change will have a double effect on the calculated con- 

 ductivity : (1) it will affect the value of a as determined from 

 the curves, and (2) it introduces the factor p in the final com- 

 putation. In the case of Bender's solutions, though in some 

 cases they were nearly or quite saturated, the first effect was 

 so small as to be much less than the error incidental to the 

 graphical process, and I did not therefore take it into account. 

 The second effect was also very small ; but as in some cases 

 it was nearly as great as Bender's estimated error, I took it 

 into account in all cases. 



While Kohlrausch's solutions had at 18° C. both the con- 

 stitution and the conductivity specified in his tables, Bender's 

 solutions had at 15° the constitution and at 18° the conduc- 

 tivity ascribed to them. I found that it did not appreciably 

 affect the values found for a x and « 2 to take the concentra- 

 tions at 15° as being the concentrations at 18° ; but that this 

 approximation was inadmissible in calculating the conduc- 

 tivity, as in some cases it made a difference of about the 

 same magnitude as Bender's estimated error. Hence in the 

 calculation I took the values of n ± and ?i 2 to be Bender's 

 values multiplied by the ratio of the volume of the solution 

 at 15° to its volume at 18°. As Bender measured the thermal 

 expansion of his solutions, his paper affords the necessary data 

 for this correction. 



The conductivities given by Bender as the results of his 

 observations are the actual results of measurements, and are 

 thus affected by accidental errors, which in some cases are 

 considerable. In order that his measurements may be 

 rendered comparable with the results of calculations, these 

 accidental errors must, as far as possible, be removed. I 

 therefore plotted all his series of observations on coordinate 

 paper, drew smooth curves through them, and estimated as 

 well as I could in this way the accidental errors of the single 

 measurements. The correction thus determined is referred 

 to in the table on p. 285 as correction a. 



Bender himself draws attention to certain differences be- 

 tween his observations of the conductivity of simple solutions 



