A number of interesting results can be obtained from this correspondence by considering the motion in more detail. Each harmonic component in expression (22) for which
is an even number corresponds to a linear oscillation parallel to the direction of the electric field, while each component for which
is odd corresponds to an elliptical oscillation perpendicular to this direction. The correspondence principle suggests at once that these facts are connected with the characteristic polarization observed in the Stark effect. We would anticipate that a transition for which
is even would give rise to a component with an electric vector parallel to the field, while a transition for which
is odd would correspond to a component with an electric vector perpendicular to the field. These results have been fully confirmed by experiment and correspond to the empirical rule of polarization, which Epstein proposed in his first paper on the Stark effect.
The applications of the correspondence principle that have so far been described have been purely qualitative in character. It is possible however to obtain a quantitative estimate of the relative intensity of the various components of the Stark effect of hydrogen, by correlating the numerical values of the coefficients