IN AQUEOUS SOLUTION, AND THE EXISTENCE OF COMPLEX IONS. 
107 
explained 1)Y the supposition that in more concentrated solutions oidy a certain pro¬ 
portion of the molecules are employed at any instant in the carriage of the current, 
and that with increasing dilution tire proportion of active molecules increases until 
finally all are dissociated, or ioiiized. 
The molecular conductivity of a solution is equal to the sum of the actual 
velocities of the 2 ions nndtiplied by the quantity of electricity carried Ijy 1 monad 
ion ; this is equal to 9G,450 coulombs. At infinite dilution /x^ = e('/. -T -r), at 
other dilutions p,, = jr, e{u -f- r) = e(U + V), and hence x = p where x is tiie 
coefficient of ionization, or tlie proportion of ions (cations or anions) to total 
molecules. Provided that the specific velocities are independent of the concentration, 
the actual average velocities at any concentration are U = xu and V = xv, u and v 
are the specific ionic velocities, or the velocities with which the ions move under a 
driving force of 1 volt per centimetre. The ionic velocities of Kohlrausch are 
obtained from these by multiplication 1)y e. In all cases the relation U -f- V 
X [u ii) holds good. 
Here, as iii the case of the transport number, it is found that it is only salts of the 
sim})lest type—as, for example, the chlorides and nitrates of the alkali metals—that 
agree well with theory; salts of the alkaline earth metals and of dyad and triad 
metals generally present the difficulty that they do not give values for the specific 
ionic velocities, which are tlie same when calculated from the measurement of different 
salts of the same metal. 
The idea of measuring directly the velocity of ionic movement by tlie o1)servatlon 
of a boundary originates with Lodge (‘ Brit. Assoc. Reports,’ 1880, 389), who, in a 
large ninnher of experiments, endeavoured to follow the movement of certain ions by 
their reaction with chemical indicators; thus the passage of the Cl ion through a 
tube filled witii gelatine, was traced l)y a faint cloudiness caused by its combination 
with a very little silver salt, which was placed there to mark the progress of the 
anion. Similarly the passage of the H ion through a gelatine solution was Indicated 
by the discharge of the colour of a very faintly alkaline solution of phenolphthalein. 
In other experiments the 2 >oint at which 2 ions travelling from opj^osite ends of tlie 
same tube formed a precipitate, was considered to divide the tnlie in the ratio of the 
resj^ective velocities of the 2 ions. Of all these ex})eriuients only that in which the 
H ion was measured gave results in agreement with those of Kohlrausch. 
Tills has been shown Ijy Whetham and Masson to be due to a faulty assumption 
as to the distribution of jDotential in the circuit. 
Kohlrausc:h, in his calculations of the alisolnte velocity, reduces the velocities to 
that conditioned by a jDotential fall of I volt jier centimetre, assuming that the 
velocity is jiroportional to the driving force. A knowledge of the j^otential fall is 
therefore necessary before any just conclusions can he drawn from the observed 
velocity of a margin. 
In any solution maintained at constant temjierature the resistance and hence also 
r 2 
