78 On the Concentration at the Electrodes in a Solution. 



values found at the beginning of the experiment were again 

 approximately attained. The experiments in which the 

 solution was stirred were performed on different days to 

 those in which no artificial stirring took place. It will be 

 seen that in cases where otherwise over 60 per cent, of the 

 equivalents given off would have consisted of hydrogen, the 

 hydrogen could be made to disappear altogether. When a 

 current-density was employed which would reduce the copper 

 to zero in about O035 of a second, the stirrer could not make 

 the hydrogen disappear altogether, but only decrease during 

 the first minute to the extent to which it would have 

 decreased if no stirring had been going on, owing to natural 

 convection alone, after three minutes. 



Summary of Results. 



An equation (No. 8) has been derived and rigidly proved 

 or calculating the concentration at the electrode of a solution 

 of a single salt from which the metal is being deposited under 

 the conditions that (1) the solution is contained in a cylin- 

 drical vessel bounded by the electrode ; (2) that no convection- 

 currents occur ; and (3) that the diffusion of the salt obeys 

 Fields law and its transport values are constant. This formula 

 can be made the basis of a method for roughly determining- 

 diffusion coefficients. 



In the case of mixtures, it is possible to arrive at limits for 

 the concentration; and it has been experimentally proved 

 (1) that hydrogen always appears at the electrode of an acid 

 solution of copper sulphate in which no currents of liquid 

 are taking place, between the limits of time for the concentra- 

 tion to go down to zero ; and (2) that the time when it 

 appears differs only slightly from that calculated by equa- 

 tion 16, which is the same in form as equation 8. It seems, 

 therefore, that this formula can be taken as a sufficient 

 empirical expression for the concentration at the electrode of 

 a mixture too. 



Lastly, the great part played by convection-currents in 

 determining the ratio of the two constituents given off at the 

 electrode of an acid copper- sulphate solution has been shown, 

 it having been proved experimentally that by artificial 

 stirring hydrogen can be made to disappear altogether in 

 cases where it would otherwise have presented over 60 per 

 cent, of the equivalents carrying the current from the 

 solution to the electrode. 



The experiments described here have been carried out 

 entirely in the laboratories of Prof. P. F. Frankland and 



