REPORT ON PHYSICAL OPTICS. 391 



does not slate the precise physical condition on which the 

 existence of the third ray depends. It would seem, however, 

 that it must arise from the circumstance that the vibration 

 normal to the wave is not absolutely insensible, or that the 

 actual vibrations are not accurately in the plane of the wave. 

 He states that the intensity of this ray- will be in all cases very 

 small, and tliat its observation thei-efore will be a matter of dif- 

 ficulty ; but he promises in a future communication to point out 

 the means of manifesting its existence. 



The formulas, on which the solution of the general problem 

 depends, may be reduced to contain nine constant coefficients 

 dependhig on the law of distribution of the molecules in space. 

 Three of them represent the pressures sustained in the natural 

 condition of the medium by any three planes parallel to those of 

 the three coordinates; and these, M. Cauchy afterwards con- 

 cludes, vanish of themselves. When the general theory is applied 

 to the case in which the elasticity is the same in all directions 

 round any line parallel to one of the axes of coordinates, 

 M. Cauchy finds that the nine coefficients are reduced to five ^ 

 and that two sheets of the wave-surface become the sphere and 

 sj)/ieroid of the Huygenian law, provided that the remaining 

 constants fulfill two assigned e(|uations of condition. In the 

 general case, in which the elasticity is unequal in all directions, 

 he investigates the sections of the wave-surface made by the 

 planes of the three coordinates j and he finds that, — for two 

 sheets of that surface, — they are reduced to the circle and ellipse 

 of Fresncl's theory, provided that the constants fulfill three 

 assigned equations of condition. The vv'ave- surface itself differs 

 a little from the surface of the fourth order obtained by Fresnel ;. 

 but is reducible to it when the excentricities of the ellipses just 

 mentioned are small, as is the case in all known crystals. 



Thus the results obtiiined by M. Cauchy embrace and confirm 

 those of Fresnel ; and the mathematical laws of the propagation 

 of light are shown to be particular cases of the more general laws 

 of the propagation of vibratory motion in any elastic medium 

 composed of attracting and repelling molecules. Considered, 

 however, simply with reference to the theory of light, the solu- 

 tion given by M. Cauchy cannot, I conceive, be considered as a 

 complete physical solution. In other words, the phenomena of 

 light are not connected directly with any given physical hypo- 

 thesis ', but arc shown to be comprehended in the results of the 

 general theory, in virtue of certain assimied relations among 

 the constants which that theory involves. If, indeed, we were 

 able to assign the precise physical meaning of these eciuations 

 of condition, we should have nothing more to desire in the 



