,
, etc., we get the well-known Balmer series of hydrogen. If we put
or
we obtain respectively the ultra-violet and infra-red series. We shall assume the hydrogen atom simply to consist of a positively charged nucleus with a single electron revolving about it. For the sake of simplicity we shall suppose the mass of the nucleus to be infinite in comparison with the mass of the electron, and further we shall disregard the small variations in the motion due to the change in mass of the electron with its velocity. With these simplifications the electron will describe a closed elliptical orbit with the nucleus at one of the foci. The frequency of revolution
and the major axis