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The Theory of Aether and Electrons in the

This equation may be satisfied either (1) if $r 0$ , is parallel to $K$ , in which case it reduces to

$\kappa ^{2}-mn^{2}=0$ ,

so that $n$ has the value $κm - 1 / 2$ , or (2) if $r 0$ is at right angles to $K$ , in which case by squaring both sides of the equation we obtain the result

$(k^{2}-mn^{2})^{2}=e^{2}n^{2}K^{2}$ ,

which gives for $n$ the approximate values $κm - 1 / 2 \pm eK /2 m$ .

When there is no external magnetic field, so that $K$ is zero, the three values of $n$ which have been obtained all reduce to $κm - 1 / 2$ , which represents the frequency of vibration of the emitted light before the magnetic field is applied. When the field is applied, this single frequency is replaced by the three frequencies. $κm - 1 / 2, κm - 1 / 2 + eK /2 m, κm - 1 / 2 - eK /2 m$ ; that is to say, the single line in the spectrum is replaced by three lines close together. The apparatus used by Zeeman in his earliest experiments was not of sufficient power to exhibit this triplication distinctly, and the effect was therefore described at first as a widening of the spectral lines.^[1]

We have seen above that the principal oscillation of the electron corresponding to the frequency $κm - 1 / 2$ is performed in a direction parallel to the magnetic force $K$ . It will therefore give rise to radiation resembling that of a Hertzian vibrator, and the electric vector of the radiation will be parallel to the lines of force of the external magnetic field. It follows that when the light received in the spectroscope is that which has been emitted in a direction at right angles to the magnetic field, this constituent (which is represented by the middle line of the triplet in the spectrum) will appear polarized in a plane at right angles to the field; but when the light received in the spectroscope is that which has been emitted in the direction of the magnetic force, this constituent will be absent.

We have also seen that the principal oscillations of the electron corresponding to the frequencies $κm - 1 / 2 \pm eK /2 m$ are

↑ Later observations, with more powerful apparatus, have shown that the primitive spectral line is frequently replaced by more than three components.

[1] Later observations, with more powerful apparatus, have shown that the primitive spectral line is frequently replaced by more than three components.

[1]