370 FOURTH REPORT — 1834. 



Reducing his formuhe to numbers, in the case of St. Gobaiu 

 glass, Fresncl found that tlie difference of phase of the two por- 

 tions of the reflected light amounted exactly to one eighth of an 

 undulation, when the angle of incidence was 54° 37'. Polishing, 

 therefore, a parallelopiped of this glass, whose faces of incidence 

 and emergence were inclined to the other sides at these angles, 

 it followed that a ray incident perpendicularly on one of these 

 faces, and once reflected at each of the sides, would emerge per- 

 pendicularly at the opposite face, — the difference of phase in the 

 two portions of the twice-reflected ray amounting to a quarter of 

 an undulation. If, then, the incident ray be polarized in a plane 

 inclined at an angle of 45° to the plane of reflexion, the emergent 

 light will be circidarly-jjolarized. This was found to be the 

 case on trial ; and the parallelopiped thus constructed, and which 

 is known under the name of FresneVs rhomb, is of essential ser- 

 vice in experiments on circular and elliptic polarization. The 

 results of this remarkable theory have been confirmed byFresnel 

 by other well-chosen experiments ; so that although the reason- 

 ing on which it is based is far from rigorous, thei*e can remain 

 little doubt of its general truth. Fresnel was himself fully aware 

 of the incompleteness of his solution, 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 hypothesis ; 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 conditions which must be fulfilled at the separating sur- 

 face of the two media ; and it assumes that the density of the 

 ether is the same in both. The expi-essions obtained for the 

 amplitudes of the vibrations in the reflected wave agree with 

 those of Fresnel. The corresponding 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 re- 

 fraction, which occurs as a factor in both cases ; and, thus, 

 though the formulse 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 molecviles in the refracted wave are 

 greater than in the incident ; so that the law of the vis viva is 



* Bulletin Unicersel, torn. xiv. p. 6. 



