de_ 2_ 

 dz wee 



Hall Effect in a Binary Electrolyte. 469 



present C = ^(c); so that -7- = 0'(c) -7-. Eliminating -77- 



between this equation and (ii.) and between this equation 

 and (iii.), we obtain the equations 



_JL_HJ-5L(!0£M + a*L, . (vii.) 



w + u wee* (_ ?« J rt2' 



-7-= ; HJ+ < ^-^ +1 5--J-. . (Vlll.) 



dz coze u + v wee I v J dz 



w ... 2G<f/(c) , t T 2Gty'(c) , " M k , . , 



Writing h_a_z. + x = L, — — -f 1 = M, we obtain from 



w v 



(vii.) and (viii.) 



de _ 2 1 Mw — Lv H T ^! 



dz ~ wee L + M " m + u ' | 



or r • • • ( ix 



de we /r M XT T^7r 



T~ = T , M (LV — M.U)U. -7-. 



cte L + M 7 dx J 



For a completely dissociated electrolyte L=l, M=l, and 

 we get instead of equations (ix.) 



de 1 u — v T1 T cue . , . r c?7r .. . 



-7- = HJ = — (v — u)i± -7— . . (ix. a) 



dz toec.u-t-v 2 da: 



Comparing equations (v.) and (ix. a), we see that the final 



potential-gradient for a completely dissociated electrolyte is 



just one-half the initial gradient. 



de I dir 

 Let -77/ y- = D, and denote by U, V the velocities acquired 



under unit potential gradient by a gram-mol. of positive and 

 negative ionic matter respectively. Equation (ix. a) may 

 then be written 



D=i(V-U)H (x.) 



Van Everdingen * arrived at the equation D=- (V--U)H 

 for the stationary state in an electrolyte supposed to be very 

 slightly dissociated ; but he assumes in this case that the ionic 

 concentration docs not vary throughout the solution, an 

 assumption which is inconsistent with the equations (vii.) and 

 (viii.), and therefore appears to me to be erroneous. 



Equation (x.) may now be applied to the data obtained by 

 Bagard. He finds, for example, the following results. 



* Loc. cit. p. 207. 



