68 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 



COMPARISON OF DEVIATIONS FROM CONCENTRATION LAW. 



As in the case of the previous paper, it is interesting to compare the 

 deviations of the potentials given by various amalgamated metals from 

 the requirement of the simple concentration law. In order to make the 

 understanding of this matter more vivid, there are given together in the 

 following diagram the several curves showing the deviations of the various 

 potentials from the concentration equation. These lines are all drawn 

 upon the same scale and are arranged so that for any ordinate the atomic 

 concentration is identical. If the equation of Cady represented a complete 

 correction, it would reduce all the lines to the horizontal straight line 

 marked O. As a matter of fact only about three-quarters of the devia- 

 tions, on the average, are to be explained in this way ; and only thallium 

 and lead are brought nearer to the horizontal line than the uncorrected 

 curve for cadmium. 



These curves, therefore, not only give an excellent collective picture of 

 the behavior of these amalgams, but they enable anyone with a compara- 

 tively small expenditure of time to compute the potential which would 

 actually exist between two amalgams of the same metal between these 

 limits of concentration. The divisions in the direction of abscissae mean 

 in each case the doubling of the volume. Suppose one wished to deter- 

 mine the potential between an amalgam of a given concentration and that 

 of one-fourth its concentration. The place of the more concentrated 

 amalgam is found upon the proper curve and the second one will be just 

 two divisions to the right. The difference between the ordinates corre- 

 sponding to these two points will give the deviation from the exact gas 

 law for that particular combination. Accordingly the potential is to be 

 computed according to the following equation : 



,r=^(/w4) Arr 



in which ATT designates the difference between the ordinates just men- 

 tioned. If any dilution other than 2, 4, 8, 16 is desired the appropriate 

 point may easily be found from these and a table of logarithms, it being 

 borne in mind that each large division in the direction of abscissa; signi- 

 fies 0.30103 for Briggs's logarithms or 0.6932 for natural logarithms. The 

 scale of the curves here depicted is rather small for an accurate determi- 

 nation. Obviously the potential could hardly be found more nearly than 

 perhaps within the fiftieth of a millivolt, because the large divisions in the 

 direction of ordinates represent millivolts ; but this same principle might 

 be employed on a larger scale and with more accurate data to within any 

 degree of precision desired. 



It will be noticed that all the curves approach horizontally as the 

 deviation proceeds. It is clear that long before infinite dilution is reached 



