ii8 
THE QUANTUM 
[vin. 5 
difficult to justify apart from the fact that it leads to the desired 
result hv — U. We find, however, that this assumption is in 
complete agreement with the generalized form of the quantum 
theory proposed by Wilson and Sommerfeld, and now commonly 
accepted. In the present case we have only one degree of freedom 
to consider, and the quantum condition for action is 
2 <pTdt = nh 
. 8 :14 
where T represents the kinetic energy, n is an integer, and the 
integration is to be extended over a complete period. We may 
identify the kinetic energy, T, with the electromagnetic energy 
%Li 2 where i is the instantaneous value of the discharging current. 
If we call q the instantaneous value of the charge on one plate of 
the condenser, we may write 
q — ¿cos^/VLC), 
The action is 
L \ iHt — e —\ sin 2 - dt 
J C J VLC 
= p- x nVLC = £ 2 \/L/C x n . . 8 :16 
Introducing the quantum condition, with n — 1, we obtain 
Whittaker’s relation 
thus justifying the assumption which he makes. 
Sir Alfred Ewing has discussed the conversion of rotational 
energy into the oscillatory form in a somewhat different way 
from Whittaker, using a more complex type of model (see 
opposite page), such as he had previously employed in his explana 
tion of magnetism. 
“ How is the rotational energy -|Aco 2 , which is communicated 
to the wheel by a bombarding electron, converted into the 
oscillatory form ? When Prof. Whittaker reaches this point in 
the development of his argument he leaves the model and com 
pares 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 oscillations. Obviously a con 
denser with a charge oscillating from -f to — in each plate would 
be equivalent to a ‘ magnetic current ’ undergoing reversals