REPORT ox PHYSICAL OPTICS. 363 



The theory of waves, however, when combined with the prin- 

 ciple of transversal vibrations, has afforded the complete solu- 

 tion of the problem we have been considering. In this develop- 

 ment of his theory the character of Fresnel's genius is strongly 

 marked. Our imperfect knowledge of the precise physical con- 

 ditions of the question is supplied by bold, but highly probable 

 assumptions : the meaning of analysis is, as it were, intuitively 

 discerned, where its language has failed to guide ; and the con- 

 clusions thus sagaciously reached are finally confirmed by ex- 

 periments chosen in such a manner as to force Nature to bear 

 testimony to the truth or falsehood of the theory *. 



It is evident that the strata of ether in the two media, which 

 are adjacent to the bounding surface, must undergo equal dis- 

 placements parallel to that surface, in as much as one of them 

 cannot slide on the other. Consequently the amplitude of the 

 vibration, resolved in a direction parallel to the surface, must 

 be the same in the two media. Fresnel assumes that this 

 equality at the bounding surface is maintained at all distances ; 

 and this furnishes him with one relation among the amplitudes 

 of vibration of the incident, reflected, and refracted waves. A 

 second relation among the same quantities is afforded by the law 

 of the vis viva ; but to apply this it is necessary to know the 

 relative densities of the ether in the two media. Here Fresnel 

 assumes that the elasticity of the ether in these media is the 

 samef, but the density different ; and this being taken for 

 granted, it follows that the two densities are to one another 

 inversely as the squares of the velocities of propagation, and that 

 therefore their ratio is given when the refractive index is known. 

 The amplitudes of the reflected and refracted vibrations, and 

 therefore also the intensities of the light in the two pencils, are 

 obtained by simple elimination between the equations just 

 mentioned. 



The expressions for the intensity of the light in the reflected 

 ray are different, according as the incident light is polarized in 



* Fresnel's theory of reflexion is contained in a memoir read to the 

 Academy of Sciences in the year 1 823, entitled, " Memoire sur la Loi des Modi- 

 fications que la Reflexion imprime a la Lumiere polarisee." An incomplete ex- 

 tract of this memoir was published in the Annates de Chimie, 1825. The ori- 

 ginal pap^ was mislaid, and for a time supposed to be lost ; it has lately, how- 

 ever, been recovered among the papers of M. Fourier, and has been printed in 

 the ilth vol. of the Memoirs of the Institute. 



f Fresnel states that he had solved the problem of reflexion in the general 

 supposition that the two media differ in elasticity as well as density, — in the 

 case of rays polarized in the plane of reflexion ; and that the resulting fonnula 

 was the same as that to which he had already arrived on the more limited 

 hypothesis. A?i. Ckim., torn, xxiii. 



