82 EEPOET ON PHYSICAL OPTICS. 



shown to be a necessary consequence of the laws of interference of 

 polarized light, if the theory of waves be admitted at all. It fol- 

 lows, in fact, from the laws of composition of vibrations, that the 

 intensity of the light resulting from the union of two rays oppo- 

 sitely polarized will be constant, and independent of the phase as 

 was proved to be the case in the experimental researches of MM. 

 Arago and Fresnel only when the vibrations normal to the wave 

 are evanescent. It appears from the same investigation that the 

 actual vibrations are either parallel or perpendicular to the plane 

 of polarization. As far as the phenomena of interference are 

 concerned, it is indifferent which of these results be assumed to be 

 the fact. But the theory of transversal vibrations itself, when 

 applied to the laws of double-refraction, leads to the conclusion 

 that the vibrations which constitute the ordinary ray in uniaxal 

 crystals are perpendicular to the principal plane ; and this being its 

 plane of polarization, Fresnel concluded that the vibrations of a 

 polarized ray are on the surface of the wave, and perpendicular to 

 the plane of polarization* 



The principle of transversal vibrations, thus deduced from the 

 phenomena of interference of polarized light, is easily extended to 

 the case of common or unpolarized light. For when a ray of such 

 light falls perpendicularly upon a double-refracting crystal, it is 

 divided into two polarized pencils, neither of which, it appears 

 from the preceding, can contain vibrations normal to the surface 

 of the wave. If, then, there were any such in the incident ray, 

 they would be destroyed by refraction, and there would ensue a loss 

 of vis viva, and consequently a diminution in the intensity of 

 the light ; in other words, the sum of the intensities of the two 

 refracted pencils would be less than that of the incident, which is 

 contrary to observation. In unpolarized light, therefore, as in 

 polarized, the vibrations are only on the surface of the waves ; and 

 we must conceive such light to consist of a rapid succession of sys- 

 tems of waves polarized in every possible plane passing through 

 the normal to the front of the wave. The phenomenon of po- 

 larization then, in this theory, consists simply in the resolution 

 of the vibrations into two sets, in two rectangular directions, and 

 the subsequent separation of the two Systems of waves thus pro- 

 duced. 



* " Memoira sur la Double Refraction.' 1 Mem. Inst., 



torn. vii. 



