certain definite wave-length in the medium, the period of the ray absorbed from a beam of circularly polarized white light will not be the same when the polarization is right-handed as when it is left-handed. "Thus," wrote Tait, "what was originally a single dark absorption-line might become a double line."
The effect anticipated under different forms by Faraday and Tait was discovered, towards the end of 1896, by I. Zeeman.[1] Repeating Faraday's procedure, he placed a sodium fame between the poles of an electromagnet, and observed a widening of the D-lines in the spectrum when the magnetizing current was applied.
A theoretical explanation of the phenomenon was immediately furnished to Zeeman by Lorentz.[2] The radiation is supposed to be emitted by electrons which describe orbits. within the sodium atoms. If e denote the charge of an electron of mass m, the ponderomotive force which acts on it by virtue of the external magnetic field is e ['i.K], where K denotes the magnetic force and r denotes the displacement of the electron from its position of equilibrium; and therefore, if the force which restrains the electron in its orbit be κ2r, the equation of motion of the electron is
.
![{\displaystyle m{\ddot {\mathbf {r} }}+\kappa ^{2}\mathbf {r} =e[\mathbf {{\dot {r}}.K} ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae010bb35db995575c86bc591faabf77f4a7f19)
The motion of the electron may (as is shown in treatises on dynamics) be represented by the superposition of certain particular solutions called principal oscillations, whose distinguishing property is that they are periodic in the time. In order to determine the principal oscillations, we write for r, where r0, denotes a vector which is independent of the time, and n denotes the frequency of the principal oscillation: substituting in the equation, we have
.
![{\displaystyle (k^{2}-mn^{2})\mathbf {r} _{0}=en{\sqrt {-1}}[\mathbf {r_{0}.K} ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2de899fa8098ed3b092c20cfbc97d51be236048d)
2 G
