482 Prof. Challis on the Theory of Double Refraction 



sequently if a ray be propagated in any principal plane of a uni- 

 axal or biaxal crystal, and its transverse vibrations be perpendi- 

 cular to the plane, the velocity of propagation will be the same 

 in all directions in the plane, and the ray will obey the ordinary 

 law of refraction. 



(2) If the principal plane of a uniaxal crystal be called the 

 plane of polarization of the ordinary ray, the transverse motions 

 are perpendicular to the plane of polarization. This result is in 

 accordance with that obtained, relatively to a ray completely 

 polarized by reflexion, at the end of the article " On the Direc- 

 tion of the Vibrations of a Polarized Ray," in the Philosophical 

 Magazine for February 1859. 



I beg to conclude this communication with a few words on 

 the history of the problem of double refraction. Although 

 Fresnel succeeded in obtaining the equation of the wave-surface, 

 he was himself aware that his theory rested on a defective dyna- 

 mical basis. After stating in his memoir " On Double Refrac- 

 tion" (Memoires de VInstitut, vol. vii. p. 53), that the mecha- 

 nical theory rests on the two hypotheses, that the luminous 

 vibrations are transverse, and that the elasticity of a doubly 

 refracting medium is different in different directions, he adds, 

 "As to the hypothesis on the nature of the luminous vibrations, 

 it appears at first sight much more difficult to admit [than the 

 other], because we do not easily see how transverse vibrations 

 can be indefinitely propagated in a fluid. Nevertheless if the 

 facts which already furnish so many probabilities in favour of the 

 system of undulations and so many objections against that of 

 emission, oblige us to recognize this character in the luminous 

 vibrations, there is more certainty in our referring here to expe- 

 rience than to the notions unhappily too incomplete which the 

 calculations of geometers have hitherto given us respecting the 

 vibrations of elastic fluids." The attempts subsequently made 

 to supply what was defective in the mechanical theory of double 

 refraction, were not directed towards improving the mathematical 

 theory of the motion of fluids, but were based on a hypothetical 

 isotropic medium of discrete atoms or centres of force, respecting 

 which we are left in doubt as to the exact relations of its consti- 

 tuents to the sether and to the doubly refracting substance. 

 These attempts are reviewed at considerable length by Professor 

 Stokes in his " Report on Double Refraction," contained in the 

 Report of the British Association for 1862 (p. 253). After 

 stating the results of the different theories, he adds, "I may 

 perhaps be permitted to express my own belief that the true dyna- 

 mical theory of double refraction has yet to be found." Then after 

 adverting to the fact, established by experiment, that a ray polar- 

 ized in a principal plane obeys the ordinary law of refraction, he 

 remarks, " this simple law, which ought, one would expect, to 



