80 REPORT ON PHYSICAL OPTICS. 



rays, the single ray will vanish, and the vibrations of the mole- 

 cules of the double ray will be constantly parallel to the direction 

 of the initial displacements. This condition therefore reduces the 

 three rays to one, which is unpolarized; and as this is known by 

 experience to be the case in media in which the light is propagated 

 in all directions with the same velocity, it follows that the propa- 

 gation of transversal vibrations is a necessary consequence of the 

 general theory. 



Thus the theory of Young and Fresnel has received the 

 strongest possible confirmation ; and when we consider the nu- 

 merous and important conclusions which have been reproduced and 

 confirmed by M. Cauchy in the development of his analysis, it is 

 scarcely possible to believe that there is anything defective in its 

 principle. There is one important and fundamental difference, 

 however, between the theories of M. Cauchy and Fresnel a dif- 

 ference which seems to mark the limits to which we have attained 

 in this branch of mathematical physics. According to the latter 

 author, it has been already stated, the vibrations are perpendicular 

 to the plane of polarization, as it is usually defined : according to 

 M. Cauchy they are parallel to that plane. I am inclined to think 

 that the field on which this question between the two theories 

 must be decided is their application to the laws of reflexion of 

 polarized light ; and, if so, there seems already reason for believing 

 that the hypothesis of Fresnel is the true one. 



II. Reflexion and Refraction of Polarized Light. 



Although the phenomenon discovered by Huygens was one- 

 of the highest interest in itself, and in its bearings of such im- 

 portance, in the mind of Newton, as to force him to admit the- 

 existence of properties in the rays of light which until then had 

 never been imagined ; yet the result remained for more than one- 

 hundred years a unique fact in science, and the kindred pheno- 

 menathe properties which light acquires in a greater or less 

 degree in almost every modification which it undergoes re- 

 mained unnoticed until the beginning of the present century. 

 In the year 1808, while Malus was engaged in his experimental 

 researches on the Huygenian law of double refraction, he dis- 

 covered the important fact, that when a ray of light is reflected 

 from the surface of glass or water at certain angles, the reflected 



