The magnetic cleavage of the spectral lines is dependent on the size of the charge of the electron, or, more accurately, on the ratio between the mass and the charge of the electron.
Nature gives us all, including Prof. Lorentz, surprises. It was very quickly found that there are many exceptions to the rule of splitting of the lines only into triplets.
The rotation of the polarization plane is extraordinarily small in all gases, thus also in sodium vapour.
According to well-known electrodynamic laws, an electron moving in a magnetic field is acted upon by a force which runs perpendicular to the direction of motion of the electron and to the direction of the magnetic field, and whose magnitude is easily determined.
Now all oscillatory movements of such an electron can be conceived of as being split up into force, and two circular oscillations perpendicular to this direction rotating in opposite directions.
I should point out, however, that at first some difficulty was experienced in observing the phenomena predicted by the theory, owing to the extreme smallness of the variations in the period of oscillation.