Hall Effect in a Binary Electrolyte. 



467 



e = quantity of electricity travelling per gram-equi- 

 valent of ionic matter , 

 a) = valency of each ion, 

 H= magnetic field-strength, 

 t = temperature (absolute). 

 We shall suppose the laws p = cRt and P = CfU to hold for 

 the solution in question, although this is not essential. We 

 have furthermore 



J=- 



dir 



(i.) 



Now an ion with a positive charge coe moving with a velocity 

 V in the positive direction of axis of x will be acted on by a 

 force in the positive z direction equal to ft>eVH ; so that the 

 force in this direction on a positive gram-ion is given by 



— w 2 e 2 wH— , whence it has a component velocity in the same 



dir 

 direction amounting to — ft) 2 eV 2 H-^. By similar reasoning 



the velocity of a negative gram-ion in the positive z direction 

 dir 



is 



*2„2 



eVH 



doc' 



Expressing quantities of matter in mols., we can now draw 

 up the following list, which takes into account all the fluxes 

 of matter occurring in the solution. 



1. Quantity of positive ionic matter tra- 



versing per unit time unit section 

 perpendicular to axis of z in positive 

 direction of this axis, due to pondero- 

 motive forces arising from the mag- 

 netic field. 



2. Corresponding quantity of negative 



ionic matter. 



3. Flux of positive ionic matter in same 



direction due to potential-gradient 

 along z-axis. 



4. Corresponding flux for negative ionic 



matter. 



5. Flux of positive ionic matter in same 



direction due to osmotic gradient. 



6. Corresponding flux of negative ionic 



matter. 



7. Flux of undissociated salt in positive 



z direction due to osmotic gradient. 



o) 2 e 2 c 9TT dir 

 2 dx 



(0 2 6 2 C 0TT dTT 



2 dx 



wee de 

 2 dz 



coec de 

 2 dz' 

 Rt do 



2 dz 

 Ride 



V 2dz 



-gbJ9. 



dz 



