REFLECTED ON THE SURFACE OF A CRYSTAL. ()5 



enter farther on this subject, would be to swell the bulk of the present memoir 

 to little purpose. 



By making the equations slightly more general, and omitting the terms which 

 correspond to the transmitted rays, retaining only those which correspond to 

 the lost vibration, denoted by T, in the memoir, we obtain the formulae for 

 metallic reflexion. There is no difficulty whatever in deducing from such for- 

 mulae the following results: 1. That if light be reflected at the surface of 

 a metal, both the vibrations in the plane and perpendicular to the plane of re- 

 flexion, will suffer retardation. 2. That the retardation of the vibration, perpen- 

 dicular to the plane of reflexion, will be independent of the angle of incidence. 

 3. That vibrations in the plane of reflexion, will suffer retardation depending on 

 the angle of incidence. 4. That the intensity of the reflected vibrations perpendi- 

 cular to the plane of reflexion is equal to that of the incident ones. 5. That the 

 intensity of the vibrations in the plane of reflexion depends on the angle of inci- 

 dence. The interpretation of these results would be, 1. That polarized incident 

 light would suffer a change of polarization from plane to elliptical, from elliptical 

 to more or less elliptical. 2. That the tendency of a very great number of re- 

 flexions would be to change light polarized in any plane to light polarized in the 

 plane of incidence. 3. That the effect on common light would be twofold ; first, 

 to produce in it an excess of vibrations perpendicular to the plane of reflexion : 

 and, secondly, to change the phases of the two parts in, and perpendicular to, the 

 plane of reflexion relative to one another. The former change is analogous to 

 that which transparent media produce on light, the latter it is difficult to interpret. 

 All that would appear to result from it is the following : " That if a continual 

 succession of such retardations were to take pla,ce, the parts of the ray would be 

 totally disjoined from each other, and the result would be a ray consisting of two 

 perfectly polarized pencils, one in, and the other perpendicular to, the plane of 

 reflexion, travelling together ; the intensity of the former being much greater 

 than that of the latter. I regret that my limits do not permit me to produce any 

 equations. 



VOL. XV. PART I. 



