CAUCHY ON THE THEORY OF LIGHT. 279 
When the three quantities P, Q, R, are unequal, the ellipsoid, 
represented by the equation (10.), may have circular sections 
formed by two diametral planes, both of which include the 
mean axis; therefore, the two polarized rays are superposed when 
the plane waves become parallel to one of these planes. Then, 
the common direction of the two rays is what is called an optical 
axis; for crystals then, in which the elasticity of the ether is not 
the same in every direction around an axis, there exist two 
optical axes, in the direction of which the rays show no further 
trace of polarization. 
All these consequences of our analysis are conformable with 
experience, and even, in the lectures given at the Royal College 
of France, M. Ampére had already remarked that the construc- 
tion of the ellipsoid, represented by the equation (10.), furnishes 
the means of determining the velocities of propagation of the 
plane waves, and of the planes of polarization of the luminous 
rays. Only these planes, which were supposed perpendicular to 
the directions of the proper velocities of the ethereal molecules, 
on the contrary contain these same directions. 
We will add, that for the equation (10.), the following might 
be substituted :— 
Bae 4 Qg? RZ? dete aly whoo RE) 
Tn fact, the two sections made by one and the same plane, in the 
_ two ellipsoids which the equations (10.) and (12.) represent, 
_haye their axes parallel, and those of the second section are re- 
‘spectively equal to the quotients which are obtained by dividing 
unity by the axes of the first. 
P.S. In order that the principles above set forth should be 
better comprehended, I shall unfold, in a second Memoir, the 
different formulz which I have only mentioned here. I will also 
make two important remarks with regard to the same principles ; 
first, when we speak of the mutual attraction or repulsion of 
the molecules of an zthereal fluid, we should only understand 
that, in the theory of light, everything goes on as if the mole- 
cules of ather effectively attracted or repelled each other. Thus, 
the investigation of the laws which the very diversified phano- 
mena of the propagation, reflection, refraction, etc., of light pre- 
sent, is reduced to the discovery of a more eal law, which 
includes all the others. It is thus that, in aie system of the 
universe, we reduce the determination of the laws, according: to 
