CAUCHY ON THE THEORY OF LIGHT. 271 
will end by being always sensibly perpendicular to the surfaces 
of the waves which the motion produces in propagating itself ; 
and from that time the polarization, such as it has been previous- 
ly defined, will become impossible, and will disappear completely. 
Thus, also, the surface of the waves will always be an ellipsoid, 
and will present only a single sheet, so that, in order to explain 
the double refraction, we should be obliged to suppose two 
zthereal fluids simultaneously inclosed in the same medium. 
But it must be remarked, that the author, as he himself says, 
had deduced these different consequences from the integration of 
the known partial differential equations, which represent the 
motions of elastic fluids, and of that which is thence deduced, 
when we suppose the three coefficients of the partial deriva- 
tives of the principal variable unequal. Now, these equations 
do not appear applicable to the propagation of luminous waves 
in an ethereal fluid; and the remarkable agreement of the 
theory which I propose with experiment, seems to me suffi- 
cient to confirm the assertion which I have already published in 
a former Memoir on the motion of light,—to wit, that the dif- 
ferential equations of this motion are comprised in those con- 
tained in the 3lst and 32nd Numbers of the Evercices de 
Mathématiques. 
In the second part of this memoir, which | intend to read at 
the next meeting, I shall apply the principles which I have just 
established to the determination of the laws according to which 
light is propagated in crystals having but one, or two, optical 
axes; and I shall show how rules proper to make known the 
velocities of propagation of the elementary waves may be deduced 
from my formule and the planes of polarization of the luminous 
rays. When we stop at a first degree of approximation, these 
rules agree in a manner worthy of remark with those which 
several physicists have deduced from experiment, or from the 
hypothesis of undulations, and in particular with those which 
Fresnel has given in his excellent memoir on double refraction. 
Only he was mistaken in admitting that the vibrations of the 
_ athereal molecules in a luminous ray were sensibly perpendicular 
to the plane generally called the plane of polarization. In re- 
ality, the plane of polarization contains the direction of the ray 
and that of the vibrations of the zther. A young geometrician, 
M. Blanchet, had, independently, and indeed before me, deduced 
this consequence, and the laws of polarization for the crystals 
