Polarization at a Metallic Anode. 647 



the mobility of the silver ions. The polarization, V, or the 

 potential-difference between A and B excluding the current- 

 resistance fall of potential between them, may, by the theory 

 of the concentration-cell, be expressed in terms of this con- 

 centration and that. c 1} at the surface of B. When the nitric 

 acid is in considerable excess, its effect is to practically annul 

 any potential-difference in the solution itself due to the 

 different concentrations of the silver ions at A and B, and 

 the polarization will consequently be simply the difference in 

 the two potential steps which exist at the surfaces of the 

 two electrodes. On the theory of Xernst it will be given by 

 the expression 



V= RT c 



e c x 



in which R is the gas-constant, T the absolute temperature, 

 and e the charge carried by a gramme-ion of silver. 



If the current passing through the cell be C, whiah may 

 be any arbitrary function of the time, the number of gramme- 

 ions of silver dissolved per second at the anode will be C/e. 

 Patting A for the sectional area of the tube and of the 

 electrode, and c for the number of gramme-ions of silver 

 passing upwards per second through a square centimetre of 

 the cross section of the tube, we must consequently have 



for the whole of the silver ions dissolved must pass immediately 

 upwards through a cross section of the tube imagined 

 indefinitely close to the electrode. c x = is thus a known 

 function of the time. Before the current is put on, the 

 concentration of the silver ions is everywhere c l9 and this 

 value is maintained permanently at the end of the tube 

 by reason of the large volume of solution in which the tube 

 i- immersed. The problem of the polarization is consequently 

 reducible to the determination of c x=u , the concentration of 

 the silver ions at the surface of the anode, in a process 

 of diffusion of the ions up the tube which is subjected to 

 the above conditions. 



The differential equation of the motion of the silver ions is 

 not. however, strictly that expressing the ordinary law of 

 diffusion, for in addition to the diffusional process the ions 

 are urged upwards by the electrical forces in the electrolyte 

 which are called into play. If we make the usual assumption 

 rhat the silver nitrate i> completely dissociated, and that the 

 osmotic pressure of it< ions obeys the gas law — a supposition 



