148 THE QUANTUM [ X<5 
that structure within the atom which may be regarded as the 
origin of the quantum magnetic tubes. 
Consider the case of an atom consisting of a positive core 
and a negative electron. There are two possibilities presenting 
themselves. The core of the atom may be a magneton, or the 
negative electron may be a magneton. 
Without entering into a discussion of these alternatives, it 
will be sufficient for our present purpose to assume that the 
magneton is closely associated with an integral number of quan 
tum tubes of frequency v T . As in Bohr’s theory, the electron is 
supposed to describe an orbit about the nucleus, the size of the 
orbit and the frequency being determined by the usual quantum 
relations. For simplicity we shall consider the case of a massive 
nucleus, which may be regarded as at rest. 
Let n denote the number of quantum tubes linked with the 
orbit and also passing through the magneton, and n T the num 
ber of quantum tubes associated with the magneton which are 
not linked with the orbit. 
Then, in accordance with the principles discussed in the 
earlier portion of this chapter, the electrokinetic energy of the 
system in its initial state is given by 
T = \njiv r + \nh{y -f v r ) . . . io : 46 
Denoting the corresponding quantities in the final state by 
accented letters, we have, similarly, 
T # = \n r 'hv/ + \n'h{y' + v T ') . . . 10 :47 
To proceed further we have to make some specific assumptions 
with regard to the frequencies. In the first place, we assume 
that the frequency v r remains unchanged in passing from the 
initial to the final state, and we identify this frequency with that 
of the emitted radiation. 
In systems which emit hydrogen-like spectra the kinetic 
energy is numerically the same as Bohr’s W. In his theory the 
kinetic energy in the new orbit is greater than that in the old, 
but the amount of potential energy set free is exactly twice the 
change in the kinetic energy. Consequently, an amount of 
energy is available for radiation which is equal to the change 
in the kinetic energy. This is 
T' — T = §[(w/ + n') — (n r + n)]hv r + \n'hv' — \nhv 10 : 48 
We now assume that in the change from one state to the other 
one quantum tube has been liberated from the magneton, and 
put 
\hv T — T' — T 10 : 49 
Hence 
\hv T — l[{n T ' + n') — (n T + n) ]hv r -f- \n'hv' — \nhv 
10 :50