at the Surface of Crystals. 57 



as glass. This simple case, it is well known, was solved by 

 Fresnel. The foregoing theory leads to a simple law, expressing 

 all the particulars of the case, but differing with regard to the 

 magnitude of the refracted vibration from the formulae of 

 Fresnel. The law may be stated by saying that the refracted 

 vibration is the resultant of the incident and reflected vibrations ; 

 the first vibration being the diagonal of a parallelogram, of 

 which the other two vibrations are the sides, just as in the com- 

 position of forces. The plane of the parallelogram is the plane 

 of polarization of the refracted ray. It is to be remembered, 

 that the vibrations in each ray are perpendicular to the ray itself, 

 and parallel to its plane of polarization. 



This simple case has been considered by M. Cauchy in a 

 short Paper inserted in the Bulletin Universel, torn. xiv. ; but it 

 does not seem to have been observed by anyone that his solu- 

 tion is erroneous. His formula for light polarized parallel to 

 the plane of reflexion is that which belongs to light polarized 

 perpendicular to the plane of reflexion, and vice versa. 



