The hypothesis that in crystals the inertia depends on direction seemed therefore to be discredited when the theory based on it was compared with the results of observation. But when, in 1888, W. Thomson (Lord Kelvin) revived Cauchy's. theory of the labile aether, the question naturally arose as to whether that theory could be extended so as to account for the optical properties of crystals: and it was shown by R. T. Glazebrook[1] that the correct formulae of crystal-optics are obtained when the Cauchy-Thomson hypothesis of zero velocity for the longitudinal wave is combined with the Stokes-Rankine-Rayleigh hypothesis of aelotropic inertia.
For on reference to the formulae which have been already given, it is obvious that the equation of motion of an aether having these properties must be
,
where e denotes the displacement, n the rigidity, and (ρ1, ρ2, ρ3) the inertia: and this equation leads by the usual analysis to Fresnel's wave-surface. The displacement e of the aethereal particles is not, however, accurately in the wave-front, as in Fresnel's theory, but is at right angles to the direction of the ray, in the plane passing through the ray and the wave-normal.[2]
Having now traced the progress of the elastic-solid theory so far as it is concerned with the propagation of light in ordinary isotropic media and in crystals, we must consider the attempts which were made about this time to account for the optical properties of a more peculiar class of substances.
It was found by Arago in 1811[3] that the state of polarization of a beam of light is altered when the beam is passed through a plate of quartz along the optic axis. The
- ↑ Phil. Mag. xxvi (1888), p. 521; xxvii (1889), p. 110.
- ↑ This theory of crystal-optics may be assimilated to the electro-magnetic theory by interpreting the elastic displacement e as electric force, and the vector (ρ1ex, ρ2ey, ρ3ez) as electric displacement.
- ↑ Mém. de l'Institut, 1812, Parti, p. 116, sqq.
