JAMIN ON METALLIC REFLEXION. 77 



ence of phase is nothing at an incidence of 0^ ; that it increases 

 progressively up to the grazing {rasante) incidence or 90^, for 

 which it becomes equal to a semi-undulation, and that at the 



angle of maximum polarization it takes the value ( j ) • 



This lavr of the variation of phase results from experiments 

 made on metallic oxides by a process inapplicable to metals ; 

 but as these oxides and metals act on light in the same way, 

 according to the expei'iments of Sir David Brewster, it is incon- 

 testable that the difference of phase produced by the reflexion of 

 metals will vary in the same direction between the limits of the in- 

 cidences: we shall assume, therefore, that for metals, the difference 

 of phase between the reflected rays polarized in the principal 

 azimuths, is nothing for a normal incidence, and that it increases 

 progressively at the same time as the inclination of the ray to 

 the surface : this generalisation of a fact verified in a particular 

 case is moreover conformable to the result obtained by M. de 

 Senarmont. 



Starting from this law, I shall by a new method find the value 

 of the difference of phase for particular incidences : this method 

 possesses the advantage of employing nothing intermediate in 

 order to modify the phase, and will for this reason be free from 

 the objections to which the processes hitherto used are liable. 

 The following is my mode of proceeding. 



When we direct a beam polarized in any plane upon a metallic 

 mirror, we may always consider it as formed by two rays of the 

 same phase, polarized in azimuths of 0^ and 90°, azimuths which 

 are not altered by the reflexion. If they be again reflected any 

 number of times from mirrors of the same substance parallel to 

 the former, the angle and the plane of incidence remaining the 

 same, they will undergo each time the same action on the part 

 of the metal ; and after 2, 3, 4 .... m reflexions they will have 

 differences of phases equal to 2, 3,4 .... m times that produced 

 in them by a single reflexion. If then we can find the first, it 

 will be sufficient to divide them by the number of reflexions to 

 obtain the second : this determination will be very easy in certain 

 particular cases. 



We know, in fact, by the experiments of Sir David Brewster, 

 that after having been reflected several times by a metal, the ray 

 has acquired a polarization,generally elliptical,but which becomes 

 rectilinear for certain particular values of the angle of incidence : 



