,

,

, all of which have the same major axis, but minor axes which increase in the ratios 1, 2, 3, 4 up to equality, in the circle (

), with the major axis. It is this multiplicity of orbits which predicts with beautiful accuracy the “fine-structure” of all of the lines due to atomic hydrogen and to helium.

Fig. 27—Bohr-Sommerfeld model of the hydrogen atom with stationary orbits corresponding to principal quantum numbers and auxiliary or azimuthal quantum numbers.