the Elementary Law of Hydrodiffusion. 527 



As, on the other hand, this gain of salt can also be repre- 

 sented by the value q I ~ ) dxdt, the following equation holds 

 \ot / o 



good as the expression of the salt-motion in the boundary 

 layer at x = 0: — 



For this layer must therefore, at every moment, 



BA hi ...... (2) 



^(^)„= 



for all values of t. In this case, therefore, a limit-equation is 

 valid which is analogous to the well-known one in the theory 

 of the conduction of heat. 



By applying the same manner of consideration to what takes 

 place in the motion of the salt in the lower boundary layer (in 

 contact with the anode), we get as a second limiting equation, 

 valid at every instant, 



hi (3) 



MBL- 



for all values of L 



If as the initial point of time that instant be taken in which 

 the galvanic current begins to pass through the solution, the 

 initial equation will have the form 



*=*« (4) 



for £ = and for all values of x. A solution which satisfies 

 equations (1), (2), and (3) is 



Ih » . (nir \ ~^ kt 



0=i— # + n2A„cos \-^-x\e L2 

 kq VL J > 



where n = 0, 1, 2 ... . 



There still remains so to determine the constant A n as to 

 satisfy the initial condition (4). From the equation for £=0, 



Ih 



Ih » . (nir \ 



r 



it follows that 



a IAL 



A °~*°~fy~2 

 and 



. 4 Ih L rnir\ 



