400 FOURTH REPORT — 1834. 



fere and produce fringes under the same circumstances as two 

 rays of common light; — that, when the planes of polarization 

 are inclined, the interference is diminished and the fringes de- 

 crease in intensity ; — and that, finally, when the angle between 

 these planes is a right angle, the rays no longer interfere at all. 

 Hence the two rays which emerge from a crystalline plate, being 

 oppositely polarized, cannot interfere ; and, to produce the phe- 

 nomena of colour in perfection, their planes of polarization must 

 be brought to coincidence by the analyser. 



The non-interference of rays oppositely polarized is a neces- 

 sary result of the mechanical theory of transversal vibrations. 

 Fresnel has shown, on the principles of that theory, that the 

 intensity of the light resulting from the union of two such rays 

 is constant, and equal to the sum of the intensities of the com- 

 ponents, whatever be the phases of vibration in which they meet. 

 But though the intensity of the light does not vary with the 

 phase of the component vibrations, the character of the result- 

 ing vibration will. It appears from theory that two rectilinear 

 and rectangular vibrations compound a single vibration, which 

 will be also rectilinear when the phases of the component vi- 

 brations differ by an exact number of semiundulations ; that, in 

 all other cases, the resulting vibration will be elliptic ; and that 

 the ellipse will become a circle, when the component vibrations 

 have equal amplitudes, and the difference of their phases is an 

 odd multiple of a quarter of a wave. These results of theory 

 have been completely confirmed by experiment. When a polar- 

 ized beam diverging from a luminous origin is transmitted 

 through two rhomboids of Iceland spar of equal thickness, hav- 

 ing their principal sections inclined 45° on either side of the 

 plane of primitive polarization, the emergent light will diverge 

 as if from two near points, and the two portions will be oppo- 

 sitely polarized. It was found by Fresnel and Arago that the 

 light resulting from the union of these pencils was plane, cir- 

 cularly, or ellipticallj/ polarized, according to the difference of 

 the paths traversed when they met. 



Here, then, we have an account of the facts which seem to 

 have suggested the theory of moveable polarization ; and we 

 learn moreover that they are but particular cases of the general 

 result. The light arising from the union of the ordinary and 

 extraordinary pencils which emerge from the crystalline plate, 

 will be polarized in the primitive plane, or in a plane inclined 

 to it at an angle equal to double the angle which it makes 

 with the principal section, according as the interval of re- 

 tardation of the two pencils is an even or an odd nndtiple of 

 half a wave. In all other cases, the thickness of the crystal 



