Jrom crystallized Surfaces. | 105 
of the crystal; x,y,z are the coordinates of a vibrating mo- 
lecule at the time ¢; &, 7, %. are the components of the dis- 
placement of the same molecule at the same time; a,b,c are 
the three principal indices of refraction out of the crystal into an 
ordinary medium in which the velocity of light is equal to V ; 
and g is the density of the ether, which density I suppose to be 
the same inall media. ‘The quantities A, F, E are the compo- 
nents, parallel to the axes of x, y, 2 respectively, of the pres- 
sure upon a plane perpendicular to the axis of x; F, B, D 
are the components of the pressure upon a plane perpendi- 
cular to the axis of y; and E, D, C, the components of the 
pressure upon a plane perpendicular to the axis of z. The 
values of D, E, F are the sameas those given by M. Cauchy; 
but the values of A, B, C are different from his, and much 
simpler. By introducing into the equations of M. Cauchy 
the condition that the vibrations shall be performed without 
any change of density, the resulting values of A, B, C might 
be shown to agree nearly with those given above. The six 
pressures, A, B, C, D, E, F, being known, it is easy to find 
the pressure upon a plane making any given angles with the 
axes of coordinates. 
These things being premised, it is time to mention the laws, 
or rather hypotheses, which’ I have imagined for discovering 
the relations that exist, as to direction and magnitude, among 
the vibrations in each ray, when reflexion and refraction take 
place at the separating surface of two media, whether crystal- 
lized or not. In stating the two very simple laws that have 
occurred to me for this purpose, it will be convenient, when 
the first medium is an ordinary one, to suppose that the inci- 
dent light is polarized. Then by the first law, the vibrations 
in one medium are equivalent to those in the other; that is to 
say, if the incident and reflected vibrations be compounded, 
like forces acting at a point, their resultant will be the same, 
both in length and direction, as the resultant of the refracted 
vibrations similarly compounded. By the second law, the la- 
terval pressure upon the separating surface is the same in both 
media; the lateral pressure being understood to mean the pres- 
sure in a direction perpendicular to the plane of incidence. 
As it would engage us too long to follow these laws into 
detail, I shall merely state some of the results which I have 
obtained from them, for the case of a uniaxal crystal into 
which the light passes out of an ordinary medium. 
Imagine the surface of the crystal to be horizontal, and call 
the point of incidence I. With the centre I and any radius, 
conceive asphere to be described, cutting in the point Z a 
vertical line I Z drawn through the centre, and let a radius 
Third Series. Vol. 8. No, 45. Feb. 1836. O 
