Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/472

inward to the axis of z (so as to shorten the period), the charge on the electron must be negative.

The value of e/m for this negative electron may be determined by measurement of the separation between the components of the triplet in a magnetic field of known strength; for, as we have seen, the difference of the frequencies of the outer components is eK/m. The values of e/m thus determined agree well with the estimations^[1] of e/m for the corpuscles of cathode rays.

The phenomenon discovered by Zeeman is closely related to the magnetic rotation of the plane of polarization of light.^[2] Both effects may be explained by supposing that the molecules of material bodies contain electric systems which possess natural periods of vibration, the simplest example of such a system being an electron which is attracted to a fixed centre with a force proportional to the distance. Zeeman's effect represents the influence of al external magnetic field on the free oscillations of these electric systems, while Faraday's effect represents the influence of the external magnetic field on the forced oscillations which the systems perform under the stimulus of incident light. The latter phenomenon may be analysed without difficulty on these principles, the equation of motion of one of the electrons being taken in the form

$m\mathbf {\ddot {r}} +\kappa ^{2}\mathbf {r} =e\mathbf {E} +e[\mathbf {{\dot {r}}.H} ]$

where m denotes the mass and e the charge of the electron, r its distance from the centre of force, κ²r the restitutive force, E and H the electric and magnetic forces. When the electron performs forced oscillations under the influence of light of frequency n, this equation becomes

$(\kappa ^{2}-mn^{2})\mathbf {r} =e\mathbf {E} +e[\mathbf {{\dot {r}}.H} ]$

The influence of the magnetic force on the motion of the electron is small compared with the influence of the electric force, i.e. the second term on the right is small compared with the first term; so in the second term we may replace r by its

1. Cf. p. 405.
2. Cf. pp. 213-216, 307-309, 367-370.