468 Dr. F. Gr. Donnan on the 



The stationary condition then gives the equations : — 

 co 2 e 2 c 0TT d7r coec de iiWt dc , ^n.rfC A ... N 



— 7— M 2 H— + — - W ^ + — T- +Cxltt -- =0, . (11.) 



2 due '2 dz 2 dz dz 



co 2 e 2 c » TT d7r coec de , vR^ rfc , n-r, ± dQ A .... . 



—r—v'Rj — V-J- +^7" -T- +GR* 7 - =0. . 111.) 



2 eta- 2 ds 2 rf^ (te 



Elimination of -=- and -r- from the equations (i.), fii.>, and 



(iii.) leads to the result 



de 2 u — v T t T R£ u — v dc .. , 



-j- = HJ • — . . . . (iv.) 



dz coec u + v coec u + v dz 



It is to be observed that equation (iv.) holds for the variable 

 as well as the stationary state, because although during the 

 variable state the left-hand members of equations (ii.) and 

 (iii.) are not zero, they are always equal to each other. 



Accordingly for the initial phenomenon, before any appre- 

 ciable concentration-gradient occurs, we obtain, putting c = c 



and — =0, 

 dz 



de 2 u — Vjjj f .„ dir ,' 



= — HJ = G>e(v — m)H-i-, . . (v.) 



dz coec u + v v ax 



or, integrating, 



whence 



2 u-« Bi 



CO€Cn u + v d 



(vi.) 



where e = total difference of potential measured in direction of 

 positive «z-axis, d= thickness measured in direction of mag- 

 netic field, and i = primary current-strength. So that we 

 obtain for the constant of the initial Hall- effect the value 



2 u — v 



const. = . 



coec u-\-v 



In order to further investigate the stationary state, we shall 



suppose that the equilibrium-equation required by the laws of 



electrolytic dissociation is everywhere satisfied. This amounts 



to supposing that the processes which adjust this equilibrium 



proceed very much more rapidly than any of the other changes 



occurring in the system. In the uncertain state of knowledge 



concerning the equilibrium-equation it may be written for the 



