The first measurements of the kinetic energy of the electrons emitted from hot bodies were made by myself, partly in collaboration with Dr. F. C. Brown, in 1907-1909. The completed experiments were practically confined to platinum as a source of emission, largely on account of technical difficulties experienced with other materials. These experiments showed that the velocity distribution among the emitted electrons was in close agreement with Maxwell’s law of distribution for a gas, of molecular weight equal to that of the electrons, in thermal equilibrium at the temperature of the source. This applies both to the component of velocity normal to the emitting surface and to that in a perpendicular direction. In the simple unidimensional case, where the cathode and anode form parallel planes of indefinite extent, the current,
i
, which flows against a retarding potential, V, depends only on the normal velocity component, and with Maxwell’s distribution is given by
i
=
i
0
exp. ( —
α
V), (1) where
α
=
e
/
k
T,
e
being the electronic charge,
k
the Boltzmann constant, T the absolute temperature, and
i
0
the current when V = 0. The inverse of the factor
α
is in fact a measure of the energy with which the electrons are ejected from the surface. The experiments showed that, with platinum under a very considerable variety of conditions, the exponential equation was obeyed with considerable accuracy. The average of eight determinations of
k
/
e
by this method agreed with the theoretical value to within a fraction of 1 per cent., although the individual determinations differed from the average by almost 20 per cent.These variations were undoubtedly large, and in excess of expectation from any obvious source of experimental error. At the same time, these experiments were subject to a number of defects such as might arise from (1) inequalities in the temperature of the source, (2) unsatisfactory methods of determining these temperatures, (3) the difficulty of realising a truly plane surface of hot metal, and (4) the presence of the electric and magnetic fields caused by the electric currents used in heating the source. In view of these and other known sources of uncertainty, the foregoing experiments, as a whole, were taken to indicate that the electrons emitted from platinum under the conditions to which the tests were subjected, possessed a velocity distribution in accordance with Maxwell’s law.
Pickup Probability of Sediment under Log-Normal Velocity Distribution