Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/236

of Halle.^[1] Neumann assumed that every element of an electric current exerts force on the particles of the aether; and in particular that this is true of the molecular currents which constitute magnetization, although in this case the force vanishes except when the aethereal particle is already in motion. If e donote the displacement of the aethereal particle m, the force in question may be represented by the term

$km[\mathbf {e.K} ]$

where K denotes the imposed magnetic field, and k denotes a magneto-optic constant characteristic the body. When this term is introduced into the equations of motion of the aether, they take the form which had been suggested by Airy; whence Neumann's hypothesis is seen to lead to the incorrect conclusion that the rotation is independent of the wave-length.

The rotation of plane-polarized light depends, as Fresnel had shown,^[2] on a difference between the velocities of propagation of the right-handed and left-handed circularly polarized waves into which plane-polarized light may be resolved. In the case of magnetic rotation, this difference was shown by Verdet to be proportional to the component of the magnetic force in the direction of propagation of the light; and Cornu^[3] showed further that the mean of the velocities of the right-handed and left-handed waves is equal to the velocity of light in the medium when there is no magnetic field. From these data, by Fresnel's geometrical method, the wave-surface in the medium may be obtained; it is found to consist of two spheres (one relating to the right-handed and one to the left-handed light), each identical with the spherical wave-surface of the unmagnetized medium, displaced from each other along the lines of magnetic force.^[4]

The discovery of the connexion between magnetism and

1. Explicare tentatur, quomodo fiat, ut lucis planum polarisationis per vires el. vel mag. declinetur. Halis Saxonum, 1858. The results were republished in a tract Die magnetische Drehung der Polarisationaebere des Lichtes. Hallo, 1863.
2. Cf. p. 174.
3. Comples Rendus, xcii (1881), p. 1368.
4. Cornui, Comptes Rendus, xeix (1884), p. 1045.