Section 115. Summary of the Transference Numbers. 325 



from the reduction of the nitric acid around the cathode. It is in fact 

 very probable that both the larger variations and the greater magnitude 

 of the cathode values are due to this cause. In spite of this source of 

 error it is to be noted that the mean cathode value exceeds the mean anode 

 value by only 0.9, 0.6, and 1.1 per cent, respectively, in the case of the three 

 more concentrated solutions. Taking into account the fact that almost 

 all other errors affect the two results in opposite directions we believe the 

 final A. D. values give a fair measure of the probable precision of the 

 final results, which is from 0.2 to 0.3 per cent for the 0.06 to 0.007 

 normal nitric acid solutions. 



In the case of the 0.002 normal solutions of both acids the divergence 

 of the cathode and anode mean values is much greater, and it seemed 

 best to assign an equal weight to each without reference to the value of 

 its average deviation ; for the divergence probably arises in the main from 

 a slight contamination of these very dilute solutions during the experi- 

 ment, which would affect the cathode and anode values oppositely and 

 about equally. The final A. D. values, which expressed as percentages 

 are 0.7 per cent for the nitric acid and 1.0 per cent for the hydrochloric 

 acid, are again a fair measure of the maximum error of which there 

 is any reasonable probability. 



of it of the water corresponding to the hydrogen and oxygen evolved ; and at the 

 cathode it had been decreased by the weight of the transferred nitric acid. 



By considering the effect of this on the result, it will readily be seen that when 

 any acid of equivalent weight a, transference number n, and original content c in 

 equivalents per gram of solution is electrolyzed as in this case with the production 

 of hydrogen and oxygen, and the calculation is made as above (multiplying the 

 total weight of the portion by c) then the anode transference-number should be 

 increased by the fractional amount (a 9)c/ and the cathode transference num- 

 ber should be increased by the fractional amount ac. In this case, with the strong- 

 est (0.058) normal solution, the corrections, applied (since a = 63, n = 0.156, and 

 c = 0.000058) are +0.03 per cent on the anode value and -j- 0.36 per cent on the 

 cathode value. With the 0.0184 normal solutions the corrections are one-third of 

 these percentages. 



The corresponding correction was not applied by Noyes and Sammet to their 

 results with hydrochloric acid. It would have the effect of increasing their final value 

 at 0.05 normal (165.69) by just 0.17 per cent (to 165.96), while at the lower con- 

 centrations the correction would be scarcely appreciable. 



A more simple way of calculating transference numbers from the experimen- 

 tal data is to refer the initial content to the weight of water present instead of to that 

 of the whole solution, and to calculate correspondingly the weight of water in the 

 portion after the electrolysis by subtracting from its total weight the weight of solute 

 found in it ; but even then a correction must be applied to the anode portion for the 

 water electrolyzed out of it. The present basis of all such transference determinations 

 is of course the assumption that the water itself does not migrate. 



