DOUBLE REFRACTION. 125 



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 spheroid of the Huy- 

 genian law, provided that the remaining constants fulfil two 

 assigned equations 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 ; 

 and he finds that for two sheets of that surface they are 

 reduced to the circle and ellipse of FresneFs theory, provided that 

 the constants fulfil three assigned equations of condition. The 

 wave-surface itself differs a little from the surface of the fourth 

 order obtained by Fresnel ; but is reducible to it when the excen- 

 tricities of the ellipses just mentioned are small, as is the case in 

 all known crystals. 



Thus the results obtained 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 solution 

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

 plete physical solution. In other words, the phenomena of light 

 are not connected directly with any given physical hypothesis ; but 

 are shown to be comprehended in the results of the general theory, 

 in virtue of certain assumed relations among the constants which 

 that theory involves. If, indeed, we were able to assign the 

 precise physical meaning of these equations of condition, we should 

 have nothing more to desire in the general theory of light ; for 

 these equations must necessarily express the characteristic properties 

 of the vibrating medium. In this point of view their discussion 

 becomes a subject of the highest interest ; and it is probable that 

 the important conclusions of which we have yet to speak may in 

 this manner be confirmed and extended. 



These conclusions are contained in a memoir presented to the 

 French Academy by M. Lame, in the spring of the present year,* 



* " Memoire sur les Lois dc 1'Equilibre dc 1'Ether dans les Corps dinphanes." A full 

 account of this paper is given in the Annaki de Chimie for March. The memoir iUelf 

 is not yet published. 



