JAMIN OX METALLIC REFLEXION. 9^ 



be expressed by the ratio of the vibration in the plane of inci- 

 dence to the vibration perpendicular, and we shall have 



, I'"cos« /I\'" 



cota?=Y--. — =(^) cot a. 

 J"'sin« \J/ 



Thus, in order to obtain, after (m) reflexions, the tangent of re- 

 stored polarization at a given angle, we should have to calculate 



for this incidence the ratio y, raise this ratio to the mth power, 



and multiply it by the tangent of the azimuth of the incident ray. 

 Let us revert to a remark already made : the incidence of re- 

 stored polarization depends only on the difference of phase ; its 

 azimuth, only on the ratio of the intensities. Too much im- 

 portance cannot be attached to this phaenomenon of restored po- 

 larization, which is the result of two modifications in the light ; 

 a change of phase and a modification of amplitude, in which 

 there are two things to be measured, an incidence and an azi- 

 muth, which are separate functions of the ditference of phase and 

 of the ratio of the intensities of the principal rays ; so that the 

 observation of the incidences has served us to determine the 

 phases, and that of the azimuths might, if we had not other 

 means, have led to the discovery of the ratio of the intensities. 

 This phaenomenon therefore sulfices for the determination of all 

 the elements of metallic reflexion. 



The experiments of Sir David Brewster verify the consequences 

 of the theory for the particular case where the incidence is that 

 of maximum polarization ; on this subject I shall refer the reader 

 to the memoir of M. de Senarmont. I have thought it right to 

 make new experiments on a metal hitherto not tried, namely 

 copper, to determine at the same time the incidences and the 

 azimuths of restored polarization for all the numbers of reflexion 

 possible, and to calculate theoretically the results. Although one 

 may be sure beforehand, of finding experiment and calculation 

 agree, this last verification was not without its use. 



VOL. v. I'ART XVII. 



