258 “ ~ REPORT—1862. 
mitted through a plate, the rays thus produced would be parallel to the inci- 
dent, or to the emergent rays of the kind usually considered; but if the plate 
were wedge-shaped the two would come out in different directions, and with 
sunlight the former could not fail to be perceived. The only way apparently 
of getting over this difficulty, is by making the perfectly gratuitous assumption 
that the medium, though perfectly transparent for the more nearly transversal 
vibrations, is intensely opaque for those more nearly normal. 
Lastly, Green’s argument respecting the necessity of supposing the velocity 
of propagation of normal vibrations very great has here full force as an 
objection against this theory. The constants P, Q, R are the squared reci- 
procals of the three principal indices of refraction, which are given by obser- 
vation, and L, M, N are determined in terms of P, Q, R by the equations (2), 
by the solution of a quadratic equation. In the case of a uniaxal erystal 
everything is symmetrical about one of the axes, suppose that of 2, which 
requires, as Cauchy has shown, that L=>M=3R, and P=Q; and of the 
equations (2) one is now satisfied identically, and the two others are identical 
with each other, and give 
4p? 
AS? gyorg 
For an isotropic medium we must have L=>M=N=3P=3Q=8SR, and the 
three equations (2) are satisfied identically. The velocity of propagation of 
normal must be to that of transversal vibrations as 73 to 1, and cannot 
therefore be assumed to be what may be convenient for explaining the law of 
intensity of reflected light. 
The theory which has just been discussed is essentially bound up with the 
supposition that in polarized light the yvibfations are parallel, not perpendicu- 
lar, to the plane of polarization. In prosecuting the study of light, Cauchy 
saw reason to change his views in this respect, and was induced to examine 
whether his theory could not be modified so as to be in accordance with the 
latter alternative. The result, constituting what may be called Cauchy’s 
second theory, is contained in a memoir read before the Academy, May 20, 
1839*. In this he refers to his memoir on dispersion, in which the funda- 
mental equations are obtained in a manner somewhat different from that given 
in his ‘ Exercices,’ but based on the same suppositions as to the constitution 
‘of the ether, In the new theory Cauchy retains the three constants G, H, I, 
expressing the pressures in equilibrium, which formerly he made vanish, the 
medium being supposed as before to be symmetrical with respect to three 
rectangular planes. The squares of the velocities of propagation, and the 
corresponding directions of vibration for the three waves which can be pro- 
pagated in the direction of each of the principal axes, are given by the fol- 
lowing Table. 
Waye-pormal., ii. isha acess x | y Zz 
igh x L+G R+H | Q41 
Direction..of. vibras. |, ee ee eee eee 
ath. iz, -4s Zea tate ate | M+H | PI 
| SF wand 
le bue Q+6 | P+H | N+I 
* “Sur la Polarisation rectiligne, et la double Réfraction,” Mém. de cy 8 tom. 
xviii. p. 153. 
