102 REPORT ON PHYSICAL OPTICS. 



tion, considered in an analytical point of view. In his memoir he 

 has adverted to the method to be adopted in order to obtain an 

 exact solution of the problem, unlimited by any arbitrary hypo- 

 thesis ; and he proposed himself to resume the question. But his 

 brilliant career of discovery was cut short by an untimely death. 



The problem of the reflexion and refraction of polarized light 

 has also engaged the attention of M. Cauchy.* The solution given 

 by this mathematician is derived from a consideration of the con- 

 ditions which must be fulfilled at the separating surface of the two 

 media ; and it assumes that the density of the ether is the same in 

 both. The expressions obtained for the amplitudes of the vibra- 

 tions in the reflected wave agree with those of Fresnel. The cor- 

 responding quantities for the refracted wave differ from those 

 deduced from Fresnel's theory, by the simple inversion of the 

 ratio of the sines of incidence and refraction, which occurs as a 

 factor in both cases ; and, thus, although the formulae are different, 

 their consequences agree in many instances, as, for example, in 

 the determination of the plane of polarization of the refracted 

 pencil. It is important to observe, however, that according to the 

 formulae of M. Cauchy, the velocities of the ethereal molecules in 

 the refracted wave are greater than in the incident ; so that the 

 law of the vis viva is violated. This is not the case in Fresnel's. 

 results, which are in fact derived from that law. 



The phenomena of metallic reflexion remain yet to be noticed in 

 connexion with this division of the science of light. 



The effects produced upon light by reflexion at the surfaces 

 of metals did not escape the scrutiny of Malus. From his first ex- 

 periments upon the subject, Malus concluded that metals had no 

 effect in polarizing the light. He soon, however, modified this 

 opinion, and found that the phenomenon of polarization was par- 

 tially produced, the effect increasing to a maximum as the inci- 

 dence approached a certain angle. But the most instructive mode 

 of studying these phenomena is to let fall upon the metallic re- 

 flector a ray polarized in a plane inclined at an angle of 45 to the 

 plane of reflexion, and to analyze the reflected pencil by a double- 

 refracting prism. Proceeding in this manner, Malus found that 

 when the incidence was very small, or very great, the reflected ray 

 was still* polarized ; while at moderate incidences it was depolarized,. 



* Bullttin Universe!, torn. xiv. p. 6. 



