132 REPORT ON PHYSICAL OPTICS. 



the radii-vectores drawn from any point to the two poles, varies 

 inversely as the thickness of the plate for different plates of the 

 same substance, and increases from one curve to another in the 

 same plate in the ratio of the numbers of the natural series. 



To account for these varied phenomena in the hypothesis of 

 emission, M. Biot has imagined his ingenious and beautiful theory 

 of mo'veable polarization. When a polarized ray of any simple 

 colour enters a crystalline plate, the component molecules are 

 supposed, in this theory, to penetrate at first to a certain depth 

 without losing their primitive polarization ; and then to commence 

 a series of regular oscillations round their centres of gravity, the 

 axes of polarization being carried alternately to one side or other 

 of the axis of the crystal, or of the perpendicular line. These 

 oscillations being isochronous, the thickness transversed by the 

 molecule in its motion of translation during 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 

 a fixed polarization, the same as if the last oscillation of the mole- 

 cules had been actually completed at the instant of emergence. 

 Thus a polarized ray which has traversed a thin crystalline plate 

 is ultimately polarized 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 principal section, according as the thickness of the crystal 

 is an odd or an even multiple of a certain length.* The formulso 

 deduced from these postulates are 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 by 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 reflected 

 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 principal section, and in the perpendicular 



* " Sur un nouveau genre d'Oscillation," &c., J/,/:. 



