Crystalline Reflexion and Refraction. 73 



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 polarised by 

 reflexion, and the plane of polarisation 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 enter- 

 tained* as to the rigorous accuracy of the geometrical laws of reflexion. 



• I was at this time in doubt whether the phenomena observed with oil of cassia could be recon- 

 ciled to theory, and when the note in page 36 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 arti/iciaUif polished. I believe 

 (though I have made very few calculations relative to the point) that the former class of experi- 

 ments 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 occa- 

 sion small inequalities, by exposing little elementary rhombs with their faces inclined to the general 

 surface ; and the action of these faces may produce the iinsymmetrical effects which Brewster notices 

 as so extraordinary (Sixth Report of the British Association, 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 suda.ce perpendicular to the axis, he found that the reflected ray was polarised neither 

 in the plane of incidence, nor perpendicular to it, but 75° out of it. The same surface, when the 

 light was reflected in air, gave the polarising angle more than two degrees below its proper value. 



To show that, in other respects, the general character of the phenomena is in accordance with 

 theory, we may observe that, when Nr=B, and X:=0 or 90°, if common light be incident at 45° in 

 the plane of the principal section of the crystal, the whole of the reflected light will be polarised 

 perpendicularly to that plane ; and therefore if n be nearly equal to b, while every thing else remains 

 the same, the reflected pencil will contain some unpolarised light, and will be only partially pola- 

 rised in a plane perpendicular to the plane of incidence; so that (as Brewster has found by 

 experiment) the crystal will then produce by reflexion the same effect which is produced by ordinary 

 refraction. This (as he also found) will not happen when x and the angle of incidence are each 

 equal to 45° ; because the light is then incident at the polarising angle. 



VOL. XVIII. t 



