therefore, in the contractile aether, the conditions that the tangential components of e and of n curl e shall be continuous across an interface are satisfied by the distortional part of the disturbance taken alone. The condition that the component of e normal to the interface is to be continuous is not satisfied by the distortional part of the disturbance taken alone, but is satisfied when the distortional and compressional parts are taken together.
The energy carried away by the longitudinal waves is infinitesimal, as might be expected, since no work is required in order to generate an irrotational displacement. Hence, with this aether, the behaviour of the transverse waves at an interface may be specified without considering the irrotational part of the disturbance at all, by the conditions that the conservation of energy is to hold and that the tangential components of e and of n curl e are to be continuous. But if we identify these transverse waves with light, assuming that the displacement e is at right angles to the plane of polarization of the light, and assuming moreover that the rigidity n is the same in all media[1] (the differences between media depending on differences in the inertia ρ), we have exactly the assumptions of Fresnel's theory of light: whence it follows that transverse waves in the labile aether must obey in reflexion the sinc-law and tangent-law of Fresnel.
The great advantage of the labile aether is that it overcomes the difficulty about securing continuity of the normal component of displacement at an interface between two media: the light-waves taken alone do not satisfy this condition of continuity; but the total disturbance consisting of light-waves and irrotational disturbance taken together does satisfy it; and this is ensured without allowing the irrotational disturbance to carry off any of the energy.[2]
- ↑ This condition is in any case necessary for stability, as was shown by R. T. Glazebrook: ef. Thomson, Phil. Mag. xxvi, p. 500.
- ↑ The labile-aether theory of light may be compared with the electro-magnetic theory, by interpreting the displacement e as the electric force, and ρe as the electric displacement.
