78 On the Laws of Reflexion 



for this purpose, it will be convenient, when the first medium is 

 an ordinary one, to suppose that the incident 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 lateral pressure upon the separating surface is 

 the same in both media ; the lateral pressure being understood to 

 mean the pressure 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 ob- 

 tained 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 /. With the centre /and any radius, con- 

 ceive a sphere to be described, cutting in the point Z a vertical 

 line IZ drawn through the centre, z. 

 and let a radius ZP, parallel to the 

 axis of the crystal, meet the surface 

 of the sphere 'in P. Let the great 

 circle ZOEloe the plane of incidence, 

 containing both the direction 10 of 

 the ordinary refracted ray produced 

 backwards, and the direction IE of 

 a normal to the extraordinary wave ; 

 and draw the great circles PZ, PO, PE. The angle Zwill be the 

 azimuth of the plane of incidence. Let ZO = 0, ZE = 0', P0= */>, 

 PE = i/,', the angle ZOP = 0, and the angle ZEP = 0'. CaU the 

 angle of incidence i, and suppose b to be the reciprocal of the ordi- 

 nary refractive index and a the reciprocal of the extraordinary. 



Each of the refracted rays, in turn, may be made to disappear, 

 by polarizing the incident ray in a certain direction assigned by 

 theory. When the extraordinary ray disappears, the reflected 

 ray is polarized in a plane inclined to the plane of incidence at 



