46 SECTIONAL ADDRESSES. 
dilution, Milner was able to calculate the freezing-point depression of an 
electrolyte at different dilutions, assuming that it was completely 
dissociated. He did not, however, attack the problem of conductivity. 
Another ten years elapsed without further progress until a discussion 
at Zurich in 1921 of the ingenious, but erroneous, theory devised by 
Ghosh attracted the attention of Debye to a field that was entirely new to 
him. That lucky accident tempts us to speculate on the potential value 
of a doubtful hypothesis, for how would the problem stand now if Ghosh’s 
papers had not seen the light of day @ 
Debye, who at the time did not know of Milner’s work, found a simple 
mathematical solution of the problem by applying Poisson’s equation to 
the relation between the average potential and the density of charge at 
any point in the sphere surrounding the central ion, and he showed that 
the distribution of the charge in the ionic atmosphere depends on the 
square root of the concentration; thus, explaining why such diverse 
properties of solutions as activity coefficients and equivalent con- 
ductivities are functions of c?. With the collaboration of Hiickel, the 
whole problem was attacked in detail, and in 1923 they succeeded in 
calculating the effect of the ionic atmosphere on the mobility of the ion. 
The conductivity of a solution depends on the number of ions that it 
contains and on their mobility. The classical theory of Arrhenius con- 
siders the effect of ionic dissociation on the former factor, whilst the 
Debye-Hiickel theory considers the effect of the interionic forces on the 
latter. 
When an ion moves under an external potential gradient, it has to 
build up continuously a fresh atmosphere in front of it while the atmo- 
sphere behind it has to die away, but since the ionic atmosphere takes a 
finite time to form or disperse, there will always be an excess of ions of the 
opposite sign in its rear, and consequently it will be subject to a retardation 
due to the dissymmetry of the atmosphere, which depends on the velocity 
with which it is moving. Further, as ions of opposite signs are moving in 
opposite directions and as both carry with them a certain amount of 
solvent, the viscous resistance to the motion of the ions will be greater 
than if the solvent were at rest. Thus, both these effects reduce the 
mobility of the ion below its value at infinite dilution, and Debye and 
Hiickel arrived at the following equation for the variation of the 
equivalent conductivity of a z-valent binary electrolyte in a solvent of 
dielectric constant D at a temperature T, 
NG rien Ne _ { K, 
No | OT: 
K, pe 
mt apaiad | VBE - cl ET 6) 
in which the first and second terms on the right-hand side are the dis- 
symmetry and viscosity terms respectively, K, and K, are universal con- 
stants, w, and w, are valency factors, and 6 is the average radius of the 
ions. This reduces to 
RES EV Mere a eee ee 
which is identical in form with the empirical equation of Kohlrausch. 
Comparison with experimental results shows that the coefficient of c? in 
