128 Proceedings of the Royal Society of Edinburgh. [Sess. 
barding electrons are set free from a heated body and are caused to acquire 
a suitable velocity by passing through a space in which there is a measured 
drop of electrostatic potential. When their velocity is less than a certain 
limit, there is no visible radiation from the atoms of the gas. When the 
velocity is increased, by bringing the drop of potential up to a certain 
value Vq, radiation of a single definite wave-length begins to be emitted. 
When the velocity is further increased (by raising the potential drop 
beyond V^), the same definite wave-length, and no other, continues to be 
emitted ; until finally, when the velocity is raised above a second and 
generally much higher limit, ionisation sets in and a many-lined spectrum 
is produced. The relation of Vq to the frequency v of the monochromatic 
radiation which the atoms continue to emit until they are ionised — that is 
to say, until the bombardment becomes strong enough to knock electrons 
out of them — is found to satisfy the quantum condition 
cYq = hv, 
where e is the charge of an electron and h is Planck’s constant. Thus with 
mercury vapour it is found that a potential drop of 4’9 volts is required 
to give the bombarding electrons velocity enough to make the atoms of 
mercury emit any radiation. When the potential drop is raised to that 
value, they are observed to give out monochromatic light with a wave- 
length of 253672 A.U. When the potential drop is further raised, the 
same single-line spectrum continues to be emitted until the potential drop 
is 10 2 volts, when the many-lined spectrum appears. The suggestion 
made in this note deals, first, with the conditions under which the encounter 
is elastic, giving rise to no radiation ; and, second, with those under which 
a single-line spectrum is produced, when the bombarding electrons have 
sufficient, or more than sufficient, kinetic energy to upset a stable group- 
ing of the electrons in the atom, but have not enough energy to deprive 
the atom of any of its electrons. In the second case, after the encounter 
has taken place the parts of the atom again assume a stable grouping, but 
with oscillations that give out a train of electromagnetic waves. 
The model can reproduce such effects, and in doing so it goes some way 
towards reconciling quantum theory with ordinary dynamics. 
Phys. Soc., vol. xxxiii, p. 13 ; Horton and Davies, Proc. Roy. Soc., 95, A, p. 408 ; Phil. Mag., 
June 1921 ; Horton and Bailey, Phil. Mag., Oct. 1920 ; Moliler, Foote, and Stimson, Phil. 
Mag., July 1920. 
(Issued separately April 27, 1922.) 
