at the Electrodes in a Solution. 57 



It is of importance to know by how much the value of 



"2/ 



y differs when determined by either the one or the other of 



K 



these equations. This calculation does not offer sufficient 



interest to give it in detail, we shall therefore only state the 



i 2 t 

 result that the ratio of the difference between ^ calculated 



by (11) or calculated by (8) is given sufficiently accurately 

 by the expression 



2x0'047 c -c 



1- 1284 s ria ' 

 which for values of 



Co=0 . m6 ^S^l\ and c=0, 

 cm/ 



the only ones employed in the experiments, amounts to about 

 2J per cent., i.e. K, calculated by (8), is 2J per cent, smaller 

 than calculated by (11). 



In concluding these remarks it must be mentioned that, 

 according to Wiedeburg's * careful investigation of the 

 diffusion of copper sulphate, this does not accurately follow 

 Fick's law, the diffusion-coefficient decreasing slightly with 

 increasing concentration. A thorough examination based 

 upon Wiedeburg's law would, however, lead beyond the 

 scope of this paper. 



(b) Application of Equation (7) to a mixture of Copper 

 Sulphate and Su/phuric Acid. 



As has already been stated, we shall in dealing with mix- 

 tures be obliged to confine ourselves to obtaining upper and 

 lower limiting values for the concentration at the electrodes, 

 which will enable us to follow the real values in broad lines 

 in their dependence on initial concentration and current 

 density. Great accuracy in these values will not be required, 

 and we shall be justified in wholly neglecting influences 

 which only slightly affect the results. We shall thus suppose, 

 that in a mixture of copper sulphate and sulphuric acid, the 

 diffusion of the former is not affected by the presence of the 

 latter. 



We first proceed to determine limits for the flow F, defined 

 by Fdt being the quantity of copper brought by diffusion in 

 the differential of time to each unit of surface of the electrode, 

 when copper alone is being deposited on it. Using the same 



* Wied. Ann. xli. p. 075. 



