340 
MR. W. C. D. WHETHAM ON IONIC VELOCITIES. 
carefully to consider the data on which it is based. The only objection which can be 
raised is to the assumption that all the molecules are active, and on this the accuracy 
of the results deduced apparently depends, for if we suppose only a part of the salt 
tp be active, it seems necessary to allow a greater ionic velocity in order that the same 
current may he carried. Now the work of Arrhexius, Van’t Hoff, Ostwald, and 
others, gives very strong evidence that only a certain fraction of the number of 
dissolved molecules are active (whatever we may assign as the cause of this activity), 
and it seems to have been generally supposed that this was quite inconsistent with 
Kohlrausch’s hypothesis (see Lodge, ‘ B. A. Beport,’ 1886, p. 391, et seq.). 1 have 
shown, however, that by examining the matter a little more closely the two ideas can 
be reconciled. The proof has already been published (‘Phil. Mag.,’ July, 1891), but 
it will be convenient to reproduce it here. 
Suppose that the ratio of the number of the active to the whole number of 
molecules, which measures the “ ionization ” (to use Professor Fitzgerald’s convenient 
name), represents in reality the fraction of each second during which each molecule 
is on the average active. Each molecule is iii turn active, but at any instant only a 
certain fraction of the whole number of molecules are active. (In terms of the disso¬ 
ciation hypothesis this ratio measures the “mean free time” of each ion.) As far 
as statical effects, such as osmotic pressure are concerned, this is, of course, equivalent 
to supposing a certain fixed fraction of the whole number of molecules to be active, 
but when we consider the velocities of the ions the case is different. 
Kohlrausch gets the relative veloctity of the ions from the relation 
= u + V = hjm ; 
but if we suppose that only of the molecules are active, we should apparently 
have to put Ug = knim to get the same current through the solution, which would 
give Ug = wUi. 
But this Ug represents the actual velocity of the ions while they are active (or 
“free”), and if we take a dynamical view of the ionization equilibrium, they are 
active only for part of their time. While inactive (or “ combined ”) they have 
no relative velocity, and so their average velocity for any long time is Ijn^^ Uo = Ui 
—the same as in Kohlrausch’s hypothesis. The view that all the salt is active 
supposes a uniform ionic velocity—the view above detailed supposes a series of rests 
interposed with a series of intervals during which the ion is moving forward with a 
velocity which is, while it lasts, on the average =nUi; but the final result is the 
same, tXie.effective velocity is Up 
We can, therefore, combine Kohlrausch’s theory with the supposition that some 
of the molecules present in the solution are inactive, the result being that the presence 
of the inactive or non-electrolytic molecules, which decreases the molecular con¬ 
ductivity of the solution, shows itself by diminishing the effective velocities of the 
ions. 
