Polarization at a Metallic Anode. 663 



further consideration. Equation (26) can obviously not hold 

 at very small times, when it would give values for the current 

 verging on infinity. The actual current must, however, start 

 from the value C = E/R , where E is the applied E.M.F., 

 and R fl the resistance of the circuit, and since the integration 

 to be carried out in (23) extends from the instant £ = 0, the 

 substitution in it of (26) would be inadmissible. We may 

 easily modify the empirical equation so as to make the 

 current start from the correct initial value by writing it 



C=B-Mog(*-r-T) (27) 



where r is a small and suitably chosen time such that 



B-61ogT=C (28) 



If t is sufficiently small this equation does not differ materially 

 from (26), except when t is very small. 



To obtain the polarization we substitute in equation (23) 

 the value for C or / (0), 



C=/(0)=O before and at the instant = 0. 



=B-Mog lo (0 + r) -s 



a, ( after the instant 



=G„-51og, ^Iby (28) j = 0; 



and we have 



f s/i=df(o)dO = cv7-6io gl0 *f y£=£ dff, 



where the first term represents the effect of the sudden 

 increase of f(0) from to C at t = Q, and the second that 

 of its gradual decay. 



A— timing that r is negligible with respect to t, the right- 

 hand ^ide may be evaluated as 



sfti C -61og 10 ^ + 2olog, *(l-log e 2) 1 



C being the value of the current at the time t substituted 

 from (2#J. Consequently by (23) 



v RT i ) 1 2 C+.-267& , 1 

 represents the polarization at any time. 



