228 On the Law of Double Refraction. 



fore ; while the difference of the squares of the two velocities of 

 propagation will continue proportional to the product of the 

 sines of the angles which the wave normal makes with the optic 

 axes ; but the sum of the squares of these velocities will be in- 

 creased or diminished by a quantity proportional to the square 

 of a perpendicular let fall from the centre on the tangent plane 

 of a certain very small ellipsoid, this tangent plane being sup- 

 posed parallel to the wave. Such is the general result for biaxal 

 crystals ; but its bearing will be best perceived by taking the 

 case of a uniaxal crystal, wherein the law of Fresnel reduces 

 itself to that of Huyghens. 



In this case the wave-surface will, instead of the sphere and 

 spheroid of Huyghens, consist of two ellipsoids touching each 

 other at the extremities of a common diameter, which coincides 

 with the axis of the crystal; one ellipsoid differing slightly 

 from a sphere, the other slightly from a spheroid. Neither of 

 the rays will be refracted according to the ordinary law, nor 

 will the wave-surface be symmetrical round the axis. As the 

 law of refraction is unsymmetrical, that of reflexion will be so 

 likewise, and thus we may perhaps obtain an explanation of 

 the extraordinary phenomena observed by Sir David Brewster 

 in reflexion at the common surface of oil of cassia and Iceland 

 spar. 



It will no doubt appear strange to call in question the ac- 

 curacy of the Huyghejiian law, which is generally considered 

 to be established beyond dispute by the experiments of Wol- 

 laston and Malus. But the fact is, that no exact experiments 

 have ever been made on the refraction of the ordinary ray. 

 Neither of those philosophers seems to have entertained any 

 suspicion that the ordinary law might be inapplicable to it; 

 they both took for granted that it followed the law of Snellius. 

 But their results seem to be quite consistent with the suppo- 

 sition that the ordinary index, for rays passing in different 

 directions through Iceland spar, may vary in the third place 

 of decimals, perhaps even in the second. The experiments of 

 Eudberg throw no light upon the question, for it happens, 



