108 
AFR. R. I). 8TEELE OX T?TE MEASUREMENT OF TOXIC VET.OCTTTES 
the potential fall depends on the concentration; any changes in which, that mar take 
})lace during electrolysis wdll condition corresponding changes in potential fall. The 
([uestion of concentration changes and the movements of these during electrolysis is 
discussed by Kohlrausch (‘"VAhed. Ann.,’ vol. G2, 209, 1897), in wdiose calculations it 
is assumed that the electrodes are far removed from the part of the .system under 
consideration ; the effects of ordinary diffusion are also not dealt with. 
If w^e consider the case of electrolysis in a long narrow^ column of liquid, and 
neglect tlie movements that take place in directions at right angles to the length of 
the tube, dealing only with those in the direction of the axis, Kohlr.\u.sch’s general 
ecpiation takes the form 
0c . 0 /«C\ 
dt ^ 0r \ /U, / ’ 
wTere c is the ionic concentration of one species of ion (cation), that of the anion being 
necessarily tlie same ; 
i is the current density ; 
X is the length of the tube ; 
u is the velocity of the cation who.se concentration is c : 
[JL is the molecular couductivity of the solution, if r is the velocity of the anion 
and 
IJi = {u + v) c ; 
tlien 
KC U 
/X 'II + V 
(1 -P) =P\ 
wliere }■>' is fke cation transport number, and the equation takes tlie form 
^ / 'A 
OC .0/1 . o/> oc 
fit ^ a. ^ ^ 0f ' 
From this it follows that a change in concentration can be brought about only in the 
case that there exists an initial concentration change, dcxlx, together with a change in 
tran.sport number wuth change in c ; when the solution is originally homogeneous no 
variation in c is caused even if p' varies wuth c. If, how'ever, the solution is not 
originally of the. .same concentration throughout, a portion, .s% of the .solution being, 
perhaps, more dilute than the remainder, then if dp'/dc = 0, or if there is no 
variation in transport number, ,s remains stationary, “ as many ions leave the section 
as enter it.” 
If dp'jdc is positive, that is, if the cation transport number increases with increasing 
concentration, then moves in the direction of the current. 
If dp'/dc is negative, the movement is in the opposite directiou, 
A .sharp margin between a concentrated and a dilute solution of the same .salt is 
