110 The Luminiferous Medium, 



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 

 iact, 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,* 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 

 a substance somewhat less elastic. Such a structure of the 

 elementary atoms of the crystal may be understood by compar- 

 ing 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 Eeview, Nov., 1809 ; Young's Works, i, p. 220. 



