374 FOURTH REPORT — 1834. 



tensive series of experiments on the subject of crystalline re- 

 flexion. One of the first results at which he arrived was, that 

 the angle of complete polarization on the same surface, varies 

 with the inclination of the plane of reflexion to the principal 

 section of the crystal ; being least when the plane of reflexion 

 coincides with the principal section, and greatest when it is 

 perpendicular to it ; — and that with different surfaces the varia- 

 tion 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 spai*, 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 re- 

 flexion 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 de- 

 viation varied as the square-root of the sine of the 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 extra- 

 ordinary 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. 



•f Since the preceding was written, Mr. M'Cullagh has arrived at an expres- 

 sion for 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, represents 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 polariza- 

 tion, s, will be the same at whichsoever side of the perpendicular the ray is in- 

 cident, its value being given by the formula, 



1-1 



Sin' -. = - 



^ u' W 



