th stationary state:
A comparison between the motions determined by these equations and the distinctive states of a Planck resonator may be shown to offer a theoretical determination of the constant
. Instead of doing this I shall show how the value of
can be found by a simple comparison of the spectrum emitted with the motion in the stationary states, a comparison which at the same time will lead us to the principle of correspondence.
We have assumed that each hydrogen line is the result of a transition between two stationary states of the atom corresponding to different values of
. Equations (8) show that the frequency of revolution and the major axis of the orbit can be entirely different in the two states, since, as the energy decreases, the major axis of the orbit becomes smaller and the frequency of revolution increases. In general, therefore, it will be impossible to obtain a relation between the frequency of revolution of the electrons and the frequency of the radiation as in the ordinary theory of radiation. If, however, we consider the ratio of the frequencies of revolution in two stationary states corresponding to given values of