1871.] 



Successive Polarization of Light, 



387 



to the plane of reflection of the silver plate, they are 45° from the plane of 

 reflection of the polarizing mirror. 



The polarized ray is then resolved into two components polarized at right 

 angles to each other ; one component is polarized in the plane of reflec- 

 tion of the silver plate, the other perpendicular thereto ; and one is re- 

 tarded upon the other by a quarter of an undulation. 



When the analyzer is at 0° or 90° no colours are seen, because there is 

 no interference; but when it is placed at 45° or 135°, interference 

 takes place, and the same colour is seen as if light circularly polarized 

 had been passed through the film. The bisected and inverted film (fig. 4) 

 shows simultaneously the two complementary colours. 



But when the film is placed with one of its principal sections 22|° from 

 the plane of reflection of the polarizing mirror, on turning round the ana- 

 lyzer the appearances of successive polarization are reproduced exactly as 

 when the planes of reflection of the silver plate and of the polarizing mirror 

 coincide. In this case the components of the light oppositely polarized in 

 the two sections are unequal, being as cos 22|° to sin 22|°; these com- 

 ponents respectively fall 22|° from the plane of reflection of the silver 

 plate and from the perpendicular plane, and are each resolved in the same 

 proportion in these two planes. The weak component of the first, and the 

 strong component of the second, are resolved into the normal plane, while 

 the strong component of the first and the weak component of the second 

 are resolved into the perpendicular plane. 



VIII. 



As bearing intimately on the subject of this paper, I will here quote 

 a passage from a memoir presented by Fresnel to the French Academy of 

 Sciences in 1817, and published, in abstract, in the * Annales de Chimie,' 

 t. xxviii. 1825 : — 



" If a thin crystallized plate be placed between two parallelepipeds of 

 glass crossed at right angles, in each of which the light previously po- 

 larized undergoes two total reflections at the incidence of 54|°, first 

 before its entrance into the plate (which we suppose perpendicular to the 

 rays), and subsequently after its emergence, and if, besides, the plate be 

 turned so that its axis makes an angle of 45° with the two planes of double 

 reflection, this system will present the optical properties of plates of rock- 

 crystal perpendicular to the axis, and of liquids which colour polarized 

 light. When the principal section of the rhomboid with which the emer- 

 gent light is analyzed is turned round, the two images will gradually 

 change colour, instead of experiencing only simple variations in the vivid- 

 ness of their tints, as occurs in the ordinary case of thin crystallized 

 plates ; besides, the nature of these colours depends only on the respective 

 inclination of the primitive plane of polarization and the principal section 

 of the rhomboid — that is to say, of the two extreme planes of polarization ; 

 thus, when this angle remains constant, the system of the crystallized 



