144 Proceedings of the Royal Society of Edinburgh. [Sess. 
It follows that the acquired angular momentum 
Ar 
Aw = li 
eM 
and, since h is a constant of the dimensions of angular momentum, the 
frequency v is either equal to eM/A or is a numerical multiple of it. Also, 
since e is constant, v oc M/A. 
How is the rotational energy JAco“, which is communicated to the wheel 
by the bombarding electron, converted into an oscillatory form ? When 
Professor Whittaker reaches this point in the development of his argument, 
he leaves the model and compares the system to a Hertzian oscillator or 
‘‘ condenser in the act of discharging.” It should, however, be remembered 
that his “ magnetic current ” — which is set up by a non-elastic encounter^ — 
is a current established in one direction. Such a current is equivalent to a 
charged condenser simply, not to a condenser undergoing Hertzian oscilla- 
tions. Obviously a condenser with the charge oscillating from + to — in 
each plate would be equivalent to a magnetic current ” undergoing 
reversals of corresponding frequency. To make the comparison to a 
Hertzian oscillator valid, we must have the wheel execute angular 
oscillations, and this implies that when it is displaced from its initial 
position a restoring moment is called into being, so that the angular 
impulse which it receives as the electron passes through the system sets 
up oscillations like those of the balance-vzheel of a watch. The single-line 
spectra of Franck and Hertz show that these oscillations are sensibly 
isochronous. 
In accounting for them it seems preferable not to drop the model at 
this stage. For in the model — as I have described it — there are essentially 
two magnetic systems in any atom : a central 
one forming what is here called the wheel, and 
another around it, which may for distinction be 
called the ring. (For simplicity of description 
we may coniine the consideration to one plane.) 
Thus in the figure we have the ring system 
ABCD as well as the wheel system W. Each 
may be taken as rigid, but there is freedom of 
relative rotation in the plane of the figure, 
except for the control exerted by magnetic forces 
between the two systems. These forces make the systems take up a 
position of equilibrium as sketched, because the outer poles of the wheel 
have the same name as the inner poles of the ring. When an electron 
passes through and escapes, it gives an impulse producing relative angular 
