CAUCHY ON THE THEORY OF LIGHT. 275 
division of several luminous rays, which should set out simul- 
taneously from the same point. Finally, we might construct 
the surface of three sheets, which, at the end of the time ¢, 
would pass through the extremities of these rays, and which we 
call the wave-surface. As to the intensity of the light, it will 
be measured in each ray by the square of the velocity of the 
molecules. This being laid down, if the elasticity of the zthe- 
real fluid remain the same in every direction around any axis 
parallel to the axis of z, we shall have 
Gap Ely Ta Mi aR Pe Gis, cil tia tuilelie) 
and consequently the nine coefficients dependent on the distri- 
bution of the molecules in space will be reduced to five, viz. 
H,1, N,Q, R. Further, two sheets, of the surface above-men- 
tioned, may be reduced to the system of two ellipsoids of revo- 
lution circumscribed one on the other; and for this last reduc- 
tion to take place, it will suffice that the condition 
(3R — Q) (N—Q)=4Q?. . . . (2) 
be fulfilled. In fine, one of the two ellipsoids will become a 
sphere, which will have for diameter the axis of revolution of 
the other ellipsoid, if we suppose 
Bia Bs oy. tote line 4 wor ade 
and then the course of the two polarized rays will be precisely 
that which the theorem of Huyghens indicates, relative to cry- 
stals which present a single optical axis. Now, the accuracy of 
this theorem having been put out of doubt by the numerous ex- 
periments of the most skilful physicists, it results from our ana- 
lysis, that in crystals having one optical axis, the coefficients 
H, I, N, Q, R, verify the conditions (2.) and (3.)._ Besides, the 
elasticity of the zthereal fluid not being, by hypothesis, the same 
in all directions, but only around the axis of Z, it is not natural 
to admit that we should have G = H = I, unless we suppose the 
three coefficients G, H, I, generally evanescent. It is then very 
probable that in its natural state these three coefficients disap- 
pear in zther, and with them the pressures sustained by any 
plane. This hypothesis being admitted, the ellipsoid and the 
sphere above mentioned will be represented by the equations 
ety? 2 at yt + 22 9% 
a The a 
so that V Q will be the semi-diameter of the sphere, and V R 
the semi-diameter of the equator in the ellipsoid. It is impor- 
tant to observe, that in crystals possessing but one optical 
= t*; 
