134 
MR. B. I). 8TEELE ON THE MEASUREMENT OF IONIC VELOCITIES 
represented by %l and y, and the ionic concentration by c, then for the transport 
number we have 
CV V 
c {u + r) i! + v' 
For any otlier total concentration n the mobilities are Wj and and the ionic concen¬ 
tration Cj : 
pn = 
0^1 
Cl («! 4- ri) 
«i + i\ * 
In order that 2^» should he greater than p> it is necessary either that t'l increase 
faster than that diminish faster than Vj, or that decrease and Vy increase 
with increase of concentration ; the latter case may he excluded from its great 
improhal)ility. Further, since in all cases the fluidity of a solution decreases with 
addition of salt, it is not probable that the ionic mobility will he greater in tlie more 
viscous solution.'^ 
Assuming, then, that no increase in or i\ takes place, for a variation in p 
must decrease very Jiuich more rapidly than y,. To take the case of barium chloride, 
the anion transport number changes between n = O'Ol and n = 2'0 from 0'56 
to 0'66. 
In the dilute solution 
in the stronger solution 
u — 
u, = 
0-44 
0-34 
0-66 
V = 0786 V, 
= 0-514 y, 
and hence 
u 
= 1-53 
or between these concentrations u has diminished in velocity I’oS times as much as v. 
For calcium chloride a similar calculation gives the relation 
Uj ri ■ 
Such a large difference in the influence of concentration change on the actual velocities 
of the two ions seems hardly to be expected. 
It is also difficult to explain by any change in u and i’ the fact that if we consider 
solutions up to O’l N of potassium nitrate and chloride and barium nitrate and 
chloride, in the case of the three former no change in 2^ occurs ; whilst for the latter 
* The coiidusioiis of Jahn (‘Zeitsc-hrift fiir Pliys. Cheni.,’ 33, 545, 1900; 35, 1, 1900) point to the 
N 
fact that with increasing concentration, up to the velocity of the ions increases in solutions of potassium, 
sodium, and hydrogen chloride, the ratio of the velocities, however, remaining constant. (See also 
AltKHENirs, ihki., 36, 28, 1901, and Sackuu, ‘ Zeit. fiir Electrochemie,’ 1901, No. 34.) 
