338 
MU. W. C. D. WHETHAil ON IONIC VELOCITIES. 
work consisted of a splendid series of determinations of the conductivities of salt 
solutions. Assuming that all the salt molecules dissolved are actively concerned in 
conveying the current, from simple notions of convection combined with Ohm’s law 
he calculated the relative velocity of the twm ions which would be necessary to give 
the observed conductivity. 
Thus (following Dr. Lodge’s abstract in the ‘B.A. Deport,’ 1886), let n® be the number 
of active molecules in 1 cub. centim., q the total charge of electricity of whichever kind 
possessed by the ions of each active molecule, and U the relative velocity with which 
the opposite ions are sheared past each other by a potential gradient, dvjdx; we shall 
then get from considerations of convection n^q\J for the intensity of cuiTent (or 
quantity of electricity conveyed per second through unit area normal to the flow), and 
from Ohm’s law h{dNjdx) for the same quantity, where k is the conductivity of the 
unit cube, therefore 
If N be the number of monad gramme equivalents of the active substance present 
in the unit cube, and r) the electro-chemical equivalent of hydrogen 
therefore 
therefore 
Whence the arithmetical sum of the opposite velocities of anion and kation {u and v) 
when urged by a slope of potential of one volt per centimetre through a solution 
containing N monad gramme .equivalents of active substance per cubic centimetre, 
and of specific conductivity k, is 
U = n -h = X-/N X '00010352 X 10® = 10352^YN centims. per second. 
In order to apply this to particular cases Kohlrausch assumes that all the 
dissolved salt is active, so that N is known from the strength of the solutions. The 
ratio iijv is taken from Hittorf’s migration experiments, and thus the absolute 
values of u and v can be obtained. 
Kohlrausch expresses his experimental results in terms of the specific molecular 
conductivity (he., h/N), and finds that for increasing dilution this tends to a limiting 
value. Thus, by drawing curves with N" (the reciprocal of the average distance 
N - = nhi ; 
7 3 NU 
y = h — — U = — 
' ax ^ rf 
k tlY 7 ] 
