648 Dr. S. R. Milner on the 



which, while only approximately correct, does not seem to- 

 lead to any serious error in its results — the number of silver 

 ions passing upwards through a square centimetre of any 

 cross section of the tube per second may be expressed on the 

 theory developed by .Nernst and Planck by the equation 



• RTU/ dc\ _ / dd>\ 



where U is the ionic velocity of the silver ions, and ( j^\ 



/ d6\ ^ ^ 



and (— -jM are the rates of decrease of the concentration 



and the potential respectively in going up the tube. 

 Equation (3), which in the general case of a mixture of 

 nitric acid and silver nitrate leads to very complex results, 

 degenerates in two cases into the ordinary law of diffusion ; 

 namely, when the concentration of the nitric acid is zero, and 

 when it is very large compared with that of the silver nitrate. 

 In the latter case, which is that realized in the present experi- 

 ments, practically no potential-difference is set up in the 

 electrolyte due to the variation in the concentration of the 

 silver ions, and the actual slope of potential becomes simply 

 that given in terms of the current by Ohm's law, i. e. 



_dcf>_Cp 

 dx " A ' 



where p is the specific resistance of the solution. Conse- 

 quently the second term on the right of (3) may be made as 

 small as we please and negligible in comparison with the 

 first by sufficiently increasing the concentration of the nitric 

 acid, and thereby diminishing the specific resistance of the 

 solution. To avoid complexity we need only consider the 

 case in which the concentration of the nitric acid is sufficiently 

 great for this approximation to apply, and write (3) in the 

 form 



RTU/ dc\ 

 e {-dJ l±) 



c = - 



This expresses the ordinary law of diffusion, the coefficient 

 of diffusion of the silver ions beino- 



n RTU 



D =~T~ (5) 



By substituting in (2) the value of c x=0 given by (4) we 

 have 



(- d JL) = C L_ 



• (6) 



