398 FOURTH nEPORT — 1834, 



gravity, the axes of polarization being carried alternately to one 

 side or other of the axis of the crystal, or of the perpen- 

 dicular line. These oscillations being isochronous, the thick- 

 ness traversed by the molecule in its motion of translation du- 

 ring each of them is constant, and is assumed to be equal to 

 double the depth to which it has penetrated before commencing 

 its vibrations. The oscillatory movement is supposed to stop, 

 when the molecules repass into air through the second face of 

 the crystal ; and the emergent ray has ?l fixed polarization, the 

 same as if the last oscillation of the molecules had been actually 

 completed at the instant of emergence. Thus a polarized ray 

 which has traversed a thin crystalline plate is ultimately polar- 

 ized either in the primitive plane, or in a plane inclined to it at 

 an angle equal to double the angle which it forms with the prin- 

 cipal section, according as the thickness of the crystal is an odd 

 or an even multiple of a certain length *. The formuhne deduced 

 from these postulates is found to represent all the more obvious 

 laws of the tints with much fidelity. 



This assumed difference between the effects produced by thick 

 and thin crystals has however been completely disproved b)'^ the 

 decisive experiments of Fresnel. When two mirrors, slightly in- 

 clined, are placed so as to receive the incident light at the polar- 

 izing angle, and two laminae of sulphate of lime of the same 

 thickness are interposed, — one in the path of each of the reflect- 

 ed pencils, and so that their principal sections are inclined at 

 angles of 45° on either side of the plane of primitive polarization, 

 —the phenomena of the interference bands prove in the clearest 

 manner that the light emergent from each consists of two pencils 

 polarized respectively in the pi'incipal section and in the per- 

 pendicular section of the crystals ; and that the results differ 

 from those produced by thick crystals only in this, that the two 

 pencils are superposed f. The light resulting from the iniion of 

 these oppositely polarized pencils has, in certain cases, the 

 properties ascribed to it in the theory of M. Biot; but these 

 properties are immediate and necessary consequences of the 

 laws of interference of polarized light, and of the theory of 

 transversal vibrations. 



• " Sur iin nouveau genre d'Oscillation," &'c., Mem. lust. 1S12. 



t See Report made to the Academy of Sciences, in 1821, on the memoir of 

 Fresnel relative to the colours of crystallized plates, Annahs de C/iimie, torn. xvii. 

 Indeed, a more obvious objection to M. Biot's theory may bo drawn from the 

 fact which he has himself observed ; — namely, that the jihenomena of colour 

 may be produced by crossivg two thick plates of nearly the same thickness, 

 although the thickness in each was suHicient to furnish two images sensibly 

 separated, and therefore having & fixed polarization. 



