at the Electrodes in a Solutu 



73 



From the results obtained in the foregoing part of this 

 paper, the electrolytic evolution of hydrogen from an acid 

 solution of copper sulphate is explained in the following 

 manner. The concentration of the copper goes down to 

 practically zero with great rapidity, as shown by the formulae, 

 when current- densities are employed which are considerably 

 larger than those used in the preceding experiments. After 

 this, diffusion no longer brings sufficient copper to the elec- 

 trode to carry the current, and hydrogen is given off too in 

 ever increasing quantity, until either the concentration of its 

 ions has gone down to practically zero, or convection-currents 

 bring new liquid to the electrode from which copper alone is 

 again deposited. It will thus be seen that convection-currents 

 play as great a part in the determination of the ratio of the 

 two constituents as any of the other conditions of the ex- 

 periment, and always have the effect of diminishing the 

 relative quantity of hydrogen given off. 



A lower limit of this quantity, when sufficient convection 

 takes place, is thus always per cent.; and the question might 

 be asked, Is there an upper limit when we employ a given 

 current-density, and use a large quantity of electrolyte ; and 

 what is its magnitude ? I do not propose to discuss this 

 question fully, but only to point out that, owing to the fact 

 that convection-currents always have the tendency to diminish 

 the production of hydrogen, such an upper limit can for all 

 practical purposes be taken as represented by the relative 

 quantity of hydrogen produced in a solution in which no 

 convection-currents whatever interfere, at the time when the 

 concentration of both copper and hydrogen ions at the cathode 

 has gone down to practically zero. It is also possible to see 

 from the formulae given which are the main influences that 

 determine this limit, by determining the lengths of time 

 during which copper only and during which mainly hydro- 

 gen have been given off. They are, in the first place, the 



relative magnitudes of the expressions - — — for the hydro- 



1 lie 



gen and the copper ions, and, to a smaller degree, the relative 

 values of the ditfusion-coefficients of sulphuric acid and copper 

 sulphate. 



I have discussed this question in view of some experiments 

 that have been quite recently performed by Toepffer*, a short 

 account of which will be found in the Zeitschrift fur physi- 

 kalische C/iemie, xxx. p. 570. He deposited alloys of iron, 

 cobalt, nickel, and zinc from mixtures of several of their 

 salts, with the result that when his so-called low current- 

 * Fully described in his thesis kindly sent me by the author, 



