with the spheroid; just as Maupertuis' investigation led to a law of refraction for the ordinary ray identical with that found by Huygens' construction with the sphere.
The law of refraction for the extraordinary ray may also be deduced from Fermat's principle of least time, provided that the velocity is taken inversely proportional to that assumed in the principle of least action; and the velocity appropriate to Fermat's principle agrees with that found by Huygens, being, in fact, proportional to the radius of the spheroid. These results are obvious extensions of those already obtained for ordinary refraction.
Laplace's theory was promptly attacked by Young,[1] who pointed out the improbability of such a system of forces as would be required to impress the requisite change of velocity on the light-corpuscles. If the aim of controversial matter is to convince the contemporary world, Young's paper must be counted unsuccessful; but it permanently enriched science by proposing a dynamical foundation for double refraction on the principles of the wave-theory. "A solution," he says, "might be deduced upon the Huygenian principles, from the simplest possible supposition, that of a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by & substance somewhat less elastic Such a structure of the elementary atoms of the crystal may be understood by comparing them to a block of wood or of mica Mr. Chladni found that the mere obliquity of the fibres of a rod of Scotch fir reduced the velocity with which it transmitted sound in the proportion of 4 to 5. It is therefore obvious that a block of such wood must transmit every impulse in spheroidal—that is, oval—undulations, and it may also be demonstrated, as we shall show at the conclusion of this article, that the spheroid will be truly elliptical when the body consists either of plane and parallel strata, or of equidistant fibres, supposing both to be extremely thin, and to be connected by a less highly elastic
- ↑ Quarterly Review, Nov., 1809; Young's Works, i, p. 220.
