CAUCHY ON THE THEORY OF LIGHT. 269 
be effected in an elastic body, it is necessary that the coefficients, 
or at least certain functions of the coefficients included in the 
partial differential equations which represent the motion of the 
elastic body, should remain positive. In the opposite case, the 
plane waves will no longer be able to propagate themselves, and 
we should be apprised of it by the calculus, which would give for 
the velocities of propagation imaginary values. 
In the theory of light, under the name of ether, is designated 
the imponderable fluid, which is considered as the elastic medium 
in which the luminous waves are propagated. The point of 
meeting | point de rencontre] of a great number of plane waves, 
the planes of which are slightly inclined to each other, is that in 
which we suppose that light may be perceived by the eye. The 
series of positions which this point of meeting takes in space 
whilst the waves are displaced, constitutes what we call a lumi- 
nous ray; and the velocity of the light, measured in the direc- 
tion of this ray, should be carefully distinguished ; 1st, from the 
velocity of propagation of the plane waves ; 2nd, from the proper 
velocity of the zthereal molecules. Lastly, we call polarized rays 
those which correspond to plane waves, in which the vibrations 
of the molecules remain constantly parallel to a given right line, 
whatever may be the directions of the initial vibrations. 
For greater generality, we shall say that in a luminous ray 
the light is polarized parallel to a right line or a given plane, 
when the vibrations of the luminous molecules shall be parallel 
to this right line or to this plane, without being parallel in every 
case to the directions of the initial vibrations; and we will call 
the plane of polarization the plane which will include the direc- 
tion of the luminous ray, and that of the proper velocities of 
zthereal molecules. These definitions, as we shall see hereafter, 
agree with the received denominations. 
This granted, it results from the principles above established, 
that in setting out from a given point in space, a ray of light, 
in which the proper velocities of the molecules have any given 
directions whatever, will generally be subdivided into three rays 
of light, polarized parallel to the three axes of a certain ellipsoid. 
But each of these polarized rays can be no further divided by 
the action of the elastic fluid, in which the light is propagated. 
Moreover, the mode of polarization will depend upon the consti- 
tution of this fluid, that is to say, upon the distribution of its 
molecules in space, or in a transparent body, and upon the plane 
