TN AQUEOUS SOLUTION, AND THE EXISTENCE OE COMPLEX IONS. 
coiTectly represented l)y c {u v) c' {v' ~ ?>), the nui^ierator in tlie above 
fraction is determined by a measnre]nent of concentintion change, and the amount of 
this will depend on the type of complex that is formed. 
If u, V, and v' represent the velocity of that quaiitity (jf matter which carries 
I unit charge of electricity, u and v rvill 1)e associated with the passage frojii one part 
of the solntion to another of single equivalents, but this is not the case with v'. If 
m is the mnnber of monad anions into 'which the complex would fall if completely 
dissociated, tlien the clunige in concentration that would be produced by the 
movements of the complex is proportional to mv' ; hence the increase in concentration 
at the anode is proportional to (c — c') v + c'mv\ and the Hittorfian 
rr + c' {mv' — v) r + oi(mv' — v) 
^ r {n, -)- t) + (' ( v — r) u + V + «( r — i’) 
where a = c jc, or the rati(') of complex to total anions. 
Now since, as we have before remarked, v' is probably less than u, the denominator 
becomes diminished, and urdess /h is very small, niv'^ r, and so the numerator 
increases with formation of complexes, or tlie anion transport numl)er as determined 
in this manner increases with formation of complex anions, that is, Avith concentration, 
and the change is in the opposite direction if complex cations are present. If the 
aboA'e equation is put into the form 
f 4 ci{v' — V) + xv' (m — 1) 
^ r 4- « (v' — v) + ‘ic ’ 
it is seen at once that for the case > 1 it is only necessary that a v {m — 1) should 
be > u, a relation AAdnch is fulfilled if either a or m is A^ery large. In the case 
of the cadmium and zinc salts the anions are probably more complex than in the 
magnesium group. 
For the relation of the coefficient of ionization to g AA^e haA^e the folloAving. Let us 
define by the coefficient of ionization the ratio of total cations or anions to the total 
number of molecules ; then, if c is the ionic concentration of the cations and n the 
total concentration, cjn = x. 
The conductiAuty of the solution is 
\ z= e (c {ii -\r v) — c ( v — v') ), 
= ec [(rt v) — a [ v — v')~\. 
For any other concentration 
Xi = eCi [(m + v) - a, {v — F)]. 
T 2 
or 
if - = a. 
