106 REPORT ON PHYSICAL OPTICS. 



perpendicular to it ; and that with different surfaces the variation 

 depended on the inclination of the surface to the axis of the crystal. 

 The difference of the greatest and least angles in the case of Iceland 

 spar, and on one of the cleavage planes of the crystal, was found to 

 amount to more than 2. 



But the effects produced upon the plane of polarization are still 

 more remarkable. On weakening the reflecting force, by causing 

 the reflexion to take place at the surface of contact of the crystal 

 and some fluid such as oil of cassia which had nearly the same 

 refractive power, Sir David Brewster found that the ray was no 

 longer polarized in the plane of reflexion ; and that the deviation 

 of the plane of polarization from the plane of reflexion depended on 

 the angle which the incident ray formed with the axis of the crystal. 

 This relation Sir David Brewster found to be expressed by the 

 law, that the sine of half the deviation varied as the square-root 

 of the sine of inclination of the incident ray to the axis.* 



It is much to be desired that the attention of analysts should 

 be directed to the problem of reflexion at the surface of extraordi- 

 nary media. It is one of the very few important provinces of the 

 science of light, which has not yet yielded its tribute to the wave- 

 theory ; and we can hardly conceive a finer subject for the exercise- 

 of mathematical and physical skill.f 



* " On the action of Crystallized Surfaces upon Light." Phil. Trans. 1819. 



t Since the preceding was written, Mr. M'Cullagb. has arrived at an expression fcr 

 the angle of polarization at the surface of crystallized media, in the case in which the 

 plane of reflexion coincides with one of the principal sections of Fresnel's ellipsoid ;. 

 and he has found that the law, which he has extended by analogy to all cases, repre- 

 sents with much exactness the observations of Sir David Brewster. If a and b denote 

 the semiaxes of the elliptic section formed by the intersection of the plane of reflexion 

 with the ellipsoid of indices (or the ellipsoid whose axes coincide in direction with the- 

 axes of elasticity of the medium, and are equal to its three principal indices), and r the 

 radius of the same section coinciding with the face of the crystal, the angle of 

 polarization, *-, will be the same at whichsoever aide of the perpendicular the ray is 

 incident, its value being given by the formula, 



