356 FOURTH REPORT — 1834. 



rays will have a common direction, and two of them a common 

 velocity. They are thus reduced to two, a single and a double 

 ray, coincident in direction ; the vibrations of the former being 

 parallel to that direction, and those of the latter perpendicular 

 to it. If the initial vibrations in the system in question are 

 contained in a plane perpendicular to the direction of the rays, 

 the single ray will vanish, and the vibrations of the molecules 

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

 the initial displacements. This condition therefore reduces the 

 three rays to o}ie, which is tmpolarized ; and as this is known 

 by experience to be the case in media in which the light is pro- 

 pagated in all directions with the same velocity, it follows that 

 the propagation of transversal vibrations is a necessary conse- 

 quence 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 defec- 

 tive in its principle. There is one important and fundamental 

 difference, however, between the theories of M. Cauchy and 

 Fresnel ; a difference which seems to mark the limits to which 

 we have attained in this branch of mathematical physics. Ac- 

 cording to the latter authoi-, it has heen already stated, the vi- 

 brations 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 theoines must be decided, is their ap- 

 plication 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 ; j^et the result remained for more than one 

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

 mena, — the properties which light acquires in a greater or less 

 degree in almost every modification which it imdergoes, — 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- 



