. r )26 Prof. H. F. Weber's Researches on 



interval of the concentration, varies scarcely perceptibly 

 with the concentration. The concentration used in the follow- 

 ing experiments possessed such high values, and the differences 

 of concentration produced were kept within such narrow limits, 

 that the value of n could not vary more than a fraction 

 per cent. 



In order to ascertain the connexion subsisting between the 

 concentration z in any layer at the depth x below the upper 

 electrode after the lapse of time t from the commencement of 

 the current and these two variables x and t y let us start from 

 the hypothesis that, if the action of the galvanic current at all 

 influences the progress of the diffusion, this influence asserts 

 itself only in the numerical value of the diffusion-constant k. 

 (I may here remark that a trial of the correctness of this 

 hypothesis, mentioned further on, showed that the galvanic 

 current passing through the solution simultaneously with the 

 diffusion did not in any way perceptibly influence the latter.) 

 The variable concentration z has then first to satisfy the 

 partial differential equation 



t-*=*|| a) 



Moreover z has to satisfy two limiting conditions, the form of 

 which is first to be developed. This development may be car- 

 ried out for the one boundary surface of the salt-solution at 

 x = 0:— 



From the boundary layer in contact with' the upper elec- 

 trode (the cathode), of the infinitesimal thickness dx, the gal- 

 vanic current of intensity I carries away during the element 

 of time dt the quantity of salt hldt, if the symbol h be put for 

 the constant 2*48(1— n)e. If the values of the differential 

 quotient of the concentration in the direction of x for the place 



# = be denoted by l^— ) , (^2) , then the expression of 



the quantity of salt brought by the diffusion-current, during 

 the same time, to this layer, through its lower boundary sur- 

 face, from the deeper-lying layers, is 



where q signifies the cross section of the diffusion- vessel. The 

 quantity of salt gained by the infinitely thin boundary layer 

 during the time-element dt is therefore 



