332 
PEOFESSOR 0. MASSON ON IONIC VELOCITIES. 
tlie ionized state, or (wliich is tlie same thing) that fraction of the total time during 
which, on the average, any given dissolved molecule is ionized and that the relation 
of the tvo 7 'king velocity U (or V) to the running velocity ttu (or ttv) is therefore similar 
to that which holds between the average speed of a train for its Avhole journey, 
including stoppages, and its actual average speed between stations. Briefly, U = ttxu 
and V = TTXV. 
The values of u and v are not necessarily c[uite the same for the same ions in 
different strengfhs of solution, for the running s]3eed, apart from stoppages, may be, 
and almost certainly is, affected Ijy the concentration. Nor can it be assumed that 
all ions ai'e equally affected in this manner : more probably each has what may be 
called its own frictional coefficient. In other woi'ds, the value of the ratio ujv for any 
given electrolyte may be expected to show some variation according to the strength 
of the solution, though in dilute solutions these variations may practically vanish. At 
extreme dilution tlie maximum values and are attained. Here, also, x attains 
its maximum value 1 ; so that 
= TTU^ and V,, = ; 
or the v'orkine; and ruimino’ velocities are identical. 
The history of the study of ionic velocities divides itself naturally into three 
chapters. The first may be called the Hittorfian chapter, the second the Kohlrauschian, 
and the third may be associated rvith the names of Lodge and Whetham. 
Hittore, and those who have since adopted his well-known method, studied the 
changes of concentratif)n in the neighbourhood of the electrodes and deduced from 
U A' . . . . . u 
these the lutios =7-and ^, or (which is the same thing;) the ratios —— and 
U -t- A^ U -f- A^ ’ ^ V 
V , 
y—. These ratios, generally called the transport numbers of the cation and anion, 
may l)e conveniently represented in the sequel by the symbols 1 — p and/.). They 
represent respectively the cation share and the anion share of the current. 
The classical work of Kohlrausch consists essentially in the measurement of 
current and })otential difterence in an electrolytic cell of known dimensions, and con¬ 
taining a uniform solution of an electrolyte of known concentration. Thus all the 
values in the general equation, as given above, can be observed except x (r q- v), 
and this can be calculated if the truth of the equations be assumed. From this 
value of X iii + v) and the value of —-—, as detei’inined by Hittorfian methods, the 
separate values xu (= U/tt) and xv (= V/tt) for any given concentration may also be 
calculated. Further, 1 jy working with various strengths of solution up to extreme 
dilution, x is eliminated and Woo + t’=o obtained. But here it is obviously impractic¬ 
able to determine the Hittorfian ratio by experiment; so that a certain assumption is 
necessarv in calculating the separate values of Ux, and I'x. This assumption is that 
* Compiu'e AViietjiam, ‘Phil. Trans.,’ A, 1893, p. 340. 
