CALCULATION OF PRELIMINARY RESULTS WITH ZINC. 35 



concentrated amalgam is compared with a weak amalgam, as in cell I d ; 

 and least when two weak amalgams are involved, as in cell II f ; in one 

 case of the latter kind, I c, the sign of the Dtt has actually been reversed. 



To exhibit the results graphically, the following plan might be adopted: 

 Consider an imaginary series of cells, all having for one electrode a standard 

 amalgam, A 3 , containing 1 gram atom of zinc in the volume V 3 , and for the 

 other electrode different amalgams formed by diluting a given volume of A 3 

 to the new volumes Vn, Vn', Vn" Plot the magnitudes of V as abscissae 

 and the potentials of the corresponding cells as ordinates ; two curves, one 

 for observed and the other for calculated potentials, result. The distance 

 they intercept on any ordinate measures Dtt for the cell which is defined by 

 the position of that ordinate. 



Plotted within a reasonable compass, these curves will not be sensitive 

 enough to exhibit fully the accuracy of the work, since some of our poten- 

 tials are known to 1 part in 5,000. If, however, the common logarithm of 

 the concentration ratio is plotted as the abscissa and Dtt as the ordinate, 

 a very compact and sensitive curve can be drawn (figure 6). 



Amalgam No. 3, the strongest used in the work, is taken as the standard, 

 and all the others referred to it. As a matter of fact No. 3 was never 

 actually compared with No. I, but the calculated concentration difference 

 was so slight that the point ( 1 ) can be interpolated without danger ; its ab- 

 scissa is 0.00375 ! an d then its ordinate will be 0.0000 1. The measurements on 

 amalgams derived from No. 1 start at that point as from an independent 

 origin. In this way all the data so far obtained are made comparable. 



The use of this curve is now easily extended to predict Dtt for any cell 

 containing two amalgams, A m and A , of known concentration. 



Let tt 1 = potential calculated for cell A 3 .->A m . 

 7r 2 =r potential calculated for cell A 3 ->A n . 

 7r 3 = potential calculated for cell A m ->A n . 

 Then 



ir 1 Dtt 1 = potential observed for cell A 3 ->A m . 

 7r 2 D-n-o = potential observed for cell A 3 -= A n . 

 7r 3 D-rr 3 = potential observed for cell A m ^>A n . 

 Now ir 1 + 7r 3 = 7T, as proved before. 



Also (71-! Dir^ -f- (ir 3 Dir 3 ) = (?r 2 Dtt 2 ) for the same reason. 

 Therefore, Dtt 1 -f- Dir 3 = Dn 2 and Dir 3 = Dir 2 Dtt 1 . 



