from Bradley, to Fresnel. 125 



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.f 



Now a wave propagated in any direction through a uniaxal 



*His first memoir on Double Refraction was presented to the Academy on 

 Nov. 19th, 1821, but has not been published except in his collected works: 

 (Eitvres, ii, p. 261. It was followed by other papers in 1822; and the results were 

 finally collected in a memoir which was printed in 1827, Mem. de VAcad. vii, 

 p. 45, (Euvres, ii, p. 479. 



t In attempting to reconstruct Fresnel's course of thought at this period, the 

 present writer has derived much help from the Life prefixed to the (Euvres de 

 Fresnel. Both Fresnel and Young were singularly fortunate in their biographers : 

 Peacock's Life of Young, and this notice of Fresnel, which was the last work of 

 Verdet, are excellent reading. 



