JAMIN ON METALLIC REFLEXION. 85 



III. Analysis of Light polarized elliptically . 



We have already remarked that Hght, in being reflected fi-om 

 metal, could only suffer alterations of its amplitudes and dis- 

 placements of the nodes of vibration. The formulae of M. 

 Cauchy, which represent vrith great accuracy the laws of these 

 modifications, comprise all the principles of metallic reflexion : 

 we are therefore allowed to leave to the calculus the task of fore- 

 seeing the phaenomena which remain to be studied, if they were 

 not interesting in themselves, and if it were not very important 

 to verify the theory even in its consequences. With this view, 

 we shall begin by causing to be reflected a single time from 

 metal a beam polarized in any plane whatever. 



It is known, from the experiments of Sir David Brewster, that 

 light ceases to be polarized when it has undergone the action of 

 metal ; and, according to this theory, this depolarization arises 

 from this, — that the vibrations of the ethereal molecules are per- 

 formed in an ellipse. We shall endeavour to verify this conse- 

 quence experimentally. 



In order to define completely an elliptical oscillatory move- 

 ment, the most simple plan is to determine the direction of the 

 axes and the ratio of their lengths : this we can always effect by 

 the calculus, but it can also be done by experiment. To show 

 this, we shall now prove, — 



Ist. That if an elliptical beam be made to fall on a doubly- 

 refracting prism, whose principal section is parallel to one of 

 the axes of the trajectory, it is decomposed into two rays, whose 

 phases differ by a quarter of an undulation, and of which one 

 has the greatest possible intensity, the other the least; 



2nd. That if the principal section of the prism is inclined at 

 45° to the direction of the axes of the ellipse, the intensities of 

 the two images are equal. 



Let (90° — a) be the azimuth of polarization of the incident 

 ray, we may replace this ray by two vibrations directed in the 

 principal azimuths, and whose amplitudes are sin a and cos a. 



By reflexion, these vibrations will be modified in their phase 

 and amplitude ; and taking account only of the difference of 

 their phases, we shall have the following equations for expressing 

 the co-ordinates of the vibrating molecules after reflexion : 



X = I cos a cos 2 TT fjf, vibration in the plane of incidence. 



