Here
and
represent the energy of the system before and after the emission.
If this law is assumed, the spectra do not give us information about the motion of the particles in the atom, as is supposed in the usual theory of radiation, but only a knowledge of the energy changes in the various processes which can occur in the atom. From this point of view the spectra show the existence of certain, definite energy values corresponding to certain distinctive states of the atoms. These states will be called the stationary states of the atoms, since we shall assume that the atom can remain a finite time in each state, and can leave this state only by a process of transition to another stationary state. Notwithstanding the fundamental departure from the ordinary mechanical and electrodynamical conceptions, we shall see, however, that it is possible to give a rational interpretation of the evidence provided by the spectra on the basis of these ideas.
Although we must assume that the ordinary mechanics cannot be used to describe the transitions between the stationary states, nevertheless, it has been found possible to develop a consistent theory on the assumption that the motion in these states can be described by the use of the ordinary mechanics. Moreover, although the process of radiation cannot be described on the basis of the ordinary theory of electrodynamics, according to which the nature of the radiation emitted by an atom is directly related to the harmonic components occurring in the motion of the system, there is found, nevertheless, to exist a far-reaching correspondence between the various types of possible transitions between the stationary states on the one hand and the various harmonic components of the motion on the other hand. This correspondence is of such a nature, that the present theory of spectra is in a certain sense to be regarded as a rational generalization of the ordinary theory of radiation.
Hydrogen spectrum. In order that the principal points may stand out as clearly as possible I shall, before considering the more complicated types of series spectra, first consider the simplest spectrum, namely, the series spectrum of hydrogen. This spectrum consists of a number of lines whose frequencies are given with great exactness by Balmer's formula
where