CAUCHY ON THE THEORY OF LIGHT. O78 
of a plane wave in an elastic medium. In fact, the sensation of 
light being supposed to be produced by the vibrations of the 
molecules of an ethereal fluid, to determine the direction and the 
laws according to which such vibrations, at first circumscribed 
in very narrow limits, around a certain point O, would propa- 
gate themselves through this fluid, it is sufficient to consider at 
the first instant a great number of plane waves, which are super- 
posed in the neighbourhood of the point O, and to admit that, 
the planes of these waves being slightly inclined one upon an- 
other, the vibrations of the molecules are small enough to remain 
insensible in each wave, taken separately, but become sensible 
by the superposition just mentioned. Now, calculation has 
shown us, that in an ethereal fluid, whose elasticity is not the 
same in every direction, each plane wave generally subdivides 
itself into three others of the same thickness, comprised in pa- 
rallel planes, but propagated with different velocities on each 
side of the plane which contained the initial wave. From this 
we concluded, that a system of plane waves, superposed at first 
in the vicinity of a given point O, subdivides into three systems 
of waves, which are successively superposed in different points 
of space, and we have given the name of a “ luminous ray” to 
the right line which contains, for one of the systems, all the 
points of superposition. We have also shown that three lumi- 
nous rays generally result from molecular vibrations, which at 
first spread but to a very small distance around the point O, 
We have, moreover, found that in each of these luminous rays 
the vibrations of the ethereal molecules remained constantly 
parallel to one of the three axes of a certain ellipsoid, and that 
consequently in the three rays the light was polarized in three 
directions perpendicular to each other, and parallel to the three 
axes of the ellipsoid, whatever in other respects might be the 
directions of the initial vibrations. We have seen the three 
rays reduced to two, or even to one only, when the initial vibra- 
tions were parallel to one of the principal planes of the ellipsoid, 
or to one of its axes, and hence it has been easy to comprehend 
why the polarized rays do not become subdivided to infinity. 
We have proved, that in the case where the elasticity of the 
ather is the same in every direction, the three rays become re- 
duced to two, to wit, a simple ray and a double ray, in the direc- 
tion of the same right line, and polarized, the first parallel, the 
second perpendicularly, to this right line. In fine, we have 
