Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/145

 oscillatory motion is executed at right angles to the plane of polarization."

This result afforded Fresnel a foothold in dealing with the problem which occupied the rest of his life: henceforth his aim was to base the theory of light on the dynamical properties of the luminiferous medium.

The first topic which he attacked from this point of view was the propagation of light in crystalline bodies. Since Brewster's discovery that many crystals do not conform to the type to which Huygens' construction is applicable, the wave theory had to some extent lost credit in this region. Fresnel, now, by what was perhaps the most brilliant of all his efforts, not only reconquered the lost territory, but added a new domain to science.

He had, as he tells us himself, never believed the doctrine that in crystals there are two different luminiferous media, one to transmit the ordinary, and the other the extraordinary waves. The alternative to which he inclined was that the two velocities of propagation were really the two roots of a quadratic equation, derivable in some way from the theory of a single aether. Could this equation be obtained, he was confident of finding the explanation, not only of double refraction, but also of the polarization by which it is always accompanied.

The first step was to take the case of uniaxal crystals, which had been discussed by Huygens, and to see whether Huygens' sphere and spheroid could be replaced by, or made to depend on, a single surface.

Now a wave propagated in any direction through a uniaxal