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 must cast a shadow with a bright spot in the centre. But this was found to be in accordance with fact. The theory was taken up by another great mathematician, Hamilton, who from his formulæ predicted conical refraction, verified experimentally by Lloyd. These predictions do not prove, however, that Fresnel's formulæ are correct, for these prophecies might have been made by other forms of the wave-theory. The theory was placed on a sounder dynamical basis by the writings of Cauchy, Biot, Green, C. Neumann, Kirchhoff, McCullagh, Stokes, Saint-Venant, Sarrau, Lorenz, and Sir William Thomson. In the wave-theory, as taught by Green and others, the luminiferous ether was an incompressible elastic solid, for the reason that fluids could not propagate transverse vibrations. But, according to Green, such an elastic solid would transmit a longitudinal disturbance with infinite velocity. Stokes remarked, however, that the ether might act like a fluid in case of finite disturbances, and like an elastic solid in case of the infinitesimal disturbances in light propagation.

Fresnel postulated the density of ether to be different in different media, but the elasticity the same, while C. Neumann and McCullagh assume the density uniform and the elasticity different in all substances. On the latter assumption the direction of vibration lies in the plane of polarisation, and not perpendicular to it, as in the theory of Fresnel.

While the above writers endeavoured to explain all optical properties of a medium on the supposition that they arise entirely from difference in rigidity or density of the ether in the medium, there is another school advancing theories in which the mutual action between the molecules of the body and the ether is considered the main cause of refraction and dispersion.[100] The chief workers in this field are J. Boussinesq, W. Sellmeyer, Helmholtz, E. Lommel, E. Ketteler, W. Voigt, and Sir William Thomson in his lectures delivered at the