A.—MATHEMATICS AND PHYSICS. 27 
The reciprocal nature of this relationship between the series spectrum 
of an element and its atomic structure will be evident. Ina case where 
the series spectrum of an element is not known a knowledge of it 
may be obtained by determining the energy levels in the atoms of this 
element independently. This can be done after the manner of Moseley 
and Franck and Hertz by causing atoms to emit limited portions of its 
spectrum under bombardment by electrons of selected speeds. 
Tn illustration of the foregoing it may be pointed out that empirically 
determined spectral relationships obtained in a study of the radiation 
emitted by such elements as hydrogen and helium have enabled us to 
determine with some precision the constitution, structure, and stationary 
states of the atoms of these comparatively simple elements. Moreover, 
explicit and definite knowledge of the temporary modifications that 
can be impressed upon the structure of the normal atoms of these ele- 
ments has been acquired through spectral relationships established by 
observations on the fine structure of these spectral lines, and by a 
study of the resolutions of these lines obtainable through the application 
of external electric or magnetic fields. 
Stationary States—Quantum Conditions. 
To illustrate the manner in which stationary states are defined on 
Bohr’s theory we may take the simple case of an atom of hydrogen 
which consists of a nucleus with charge +e and an electron with 
charge—e. It is known that the frequencies of the series spectra of this 
element are given with great accuracy by the generalised Balmer 
formula 
SERS. PENS ibe | Sets ae) 
nol ew 
where n" and »’ are two integers and K is the well-known Rydberg 
constant. From this formula we see that all the spectral terms are of 
the form K/n’, and it follows at once that the energy corresponding to 
the various stationary states of the atom of hydrogen must be given by 
Kh/n? with n having all possible integral values. 
Now it can be shown that when an electron describes an elliptic 
orbit about the nucleus of a hydrogen atom the major axis of the orbit 
described is inversely proportional to w the work required completely 
to remove the electron from the field of the nucleus. The major axis 
2 2 2 
is, in fact, given by Qa—°% . If, therefore, we take a= Fe we have 
w v 
determined for the hydrogen atom a set of clearly defined stationary 
states consisting of a series of elliptical orbits for which the major 
axis takes on discrete values proportional to the squares of the whole 
numbers. Transitions from one to another of such a set of stationary 
states will suffice on Bohr’s theory to account for all the lines in the 
Series spectrum of atomic hydrogen. 
In the early development of Bohr’s theory it was noted that for 
, 2 2 
each value of 1 in the equation 2a=—s it was possible to have a 
= 
