Reflexion and Refraction . 135 



tions, which I have not had time to make. With the view, 

 however, of showing clearly, from theory, that the range of 

 the deviation is unlimited, I have considered the simple case 

 in which N = J3, or in which the refractive index of the fluid 

 is exactly equal to the ordinary index of the crystal. This case, 

 moreover, is remarkable on its own account ; and it might be 

 worth while to try whether it could not be verified by direct 

 experiment. If a fluid could -be procured whose refractive 

 index, for some definite ray of the spectrum, should be equal 

 to the ordinary index of the crystal for the same ray, and if 

 common light, incident at any angle and in any azimuth, were 

 reflected at the confines of the fluid and the crystal, then, 

 supposing the theory to be exact, the definite ray aforesaid 

 would, as we have seen, be completely polarized by reflexion, 

 and the plane of polarization would always be perpendicular 

 to a plane drawn through the direction of the reflected ray 

 and the axis of the crystal. This experiment would be an 

 elegant test of the theory in its application to these extreme 

 and trying cases ; and if it were successful, no doubt could 

 be entertained* as to the rigorous accuracy of the geome- 

 trical laws of reflexion. 



* I was at this time in doubt whether the phenomena observed with oil of 

 cassia could be reconciled to theory ; and when the note in page 93 was written, 

 I was almost certain that they could not. But I have since, I think, found out 

 the cause of this perplexity. Some of Brewster's experiments were made with 

 natural surfaces of Iceland spar ; others with surfaces artificially polished. I 

 believe (though I have made very few calculations relative to the point) that the 

 former class of experiments will be perfectly explained by the theory ; the latter 

 I am certain cannot be so explained, nor ought we to expect that they should. 

 For the process of artificial polishing must necessarily occasion small inequalities, 

 by exposing little elementary rhombs with their faces inclined to the general 

 surface ; and the action of these faces may produce the unsymmetrical effects 

 which Brewster notices as so extraordinary (Sixth Report of the British Asso- 

 ciation, Transactions of the Sections, p. 16). If this will not account for such 

 effects, I do not know what will. From an old observation of Brewster (Phil. 

 Trans., 1819), it would appear that imperfect polish does actually produce a want 

 of symmetry in the phenomena; for when common light was reflected between 

 oil of cassia and a badly polished surface perpendicular to the axis, he found that 

 the reflected ray was polarized neither in the plane of incidence, nor perpendicular 



