Polarization at a Metallic Anode. 653 



If we now substitute in (20) for F(f) its value in terms of 

 the polarizing current given by (6), and the value of D given 

 in (5), we get 



. 2 8 r C y/i^Tr 



r 2 2, O r <J S/t-t r ^ 



v. 



where ©VC is the sudden increase in the current at the time 

 t rj and the summation includes all the variations which have 

 occurred since just before the instant £ = 0. Substituting 

 this value of c x= o in(l), we obtain finally for the polarization 



Y ~**\ 1+ itt3mr\- ■ (22) 



In the case in which the current undergoes a continuous 

 variation as well as sudden ones we may write 



c=f(t)=( f f(0)tw, 



Jo 

 and using (21) instead of (20), we get 



P s/'T^0f{0)d0^ 



Both (22) and (23) are useful forms, and from them the 

 polarization may be calculated absolutely in any given case. 

 To obtain numerical values we must express all the 

 quantities involved in terms of C.G.S. units. We have 



R = 8'32 x 10 7 ergs per degree C. 

 T=291at 18° C. 



e = [)654 electromagnetic units per gramme-ion 

 for a monovalent ion such as silver. 

 Hence RT 1Q _ 8 RT 



' e l ° ge '' = '4343 ~ ]o &°* volts ' 

 = •0576 log 10 ci- volts. 



An accurate estimation of the value of U, the effective 

 ionic velocity of the silver in the nitric acid, offers some 

 difficulty, but for our present purposes it is simplest to 

 neglect the possible effect on its value of incomplete dissoci- 

 ation of the silver nitrate and to take it as the same as that 

 in a very dilate solution of a silver salt in water. Kohlrausch 

 and Holborn (Lekvermogen der Electrolyte, p. 200) give for 



Phil. Ma,,, s. *;. Vol. 9. No. 53. May 1905. 2 X 



