CONFIRMATION OF THE UNDULATORY THEORY. 121 



tlmt lie could account for the phenomena of qiurtz, already observed 

 by M. Arago; as we have noticed in Chap, ix., by supposing two circu- 

 larly-polarized rays to pass, with, different velocities, along the axis. 

 The curious succession of colors, following each other in right-handed 

 or left-handed circular order, of which we have already spoken, might 

 thus be hypothetically explained. 



But was this hypothesis of two circularly-polarized rays, travelling 

 along the axis of such crystals, to be received, merely because it 

 accounted for the phenomena ? Fresnel's ingenuity again enabled him 

 to avoid such a defect in theorizing. If there were two such rays, 

 they might be visibly separated 7 by the same artifice, of a pile of 

 prisms properly achromatized, which he had used for compressed glass. 

 The result was, that he did obtain a visible separation of the rays ; 

 and this result has since been confirmed by others, for instance, Pro- 

 fessor Airy. 8 The rays were found to be in all respects identical with 

 the circularly-polarized rays produced by the internal reflections in 

 Fresnel's rhomb. This kind of double refraction gave a hypothetical 

 explanation of the laws which M. Biot had obtained for the phenomena 

 of this class ; for example, 9 the rule, that the deviation of the plane of 

 polarization of the emergent ray is inversely as the square of the length 

 of an undulation for each kind of rays. And thus the phenomena 

 produced by light passing along the axis of quartz were reduced into 

 complete conformity with the theory. 



[2nd Ed.] [I believe, however, Fresnel did not deduce the pheno- 

 menon from the mathematical. formula, without the previous sugges- 

 tion of experiment. He observed appearances which implied a differ- 

 ence of retardation in the two differently-polarized rays at total reflec- 

 tion; as Sir D. Brewster observed in reflection of metals phenomena 

 having a like character. The general fact being observed, Fresnel 

 used the theory to discover the law of this retardation, and to deter- 

 mine a construction in which, one ray being a quarter of an undula- 

 tion retarded more than the other, circular polarization would be pro- 

 duced. And this anticipation was verified by the construction of his 

 rhomb. 



As a still more curious verification of this law, another of Frc-sucl's 

 experiments may be mentioned. He found the proper angles for a 

 circularly-polarizing glass rhomb on the supposition that there Tv 



7 Bull, el's Sc. 1S22, p. 193. B Coinlrid'je Trans, iv. p. 80. 



13 Bull. Jes Sc. 1822, p. I'.'?. 



