222 On the Dispersion of the Optic Axes, and 



placement. These directions coincide with the axes of the 

 ellipsoid by which he constructs his wave-surface ; and the po- 

 sition of the axes being thus fixed, it is only their lengths that 

 can be supposed to vary for the differently coloured rays. 

 Such is the view taken by Fresnel with regard to crystalline 

 dispersion, and it is obviously the only view that his theory 

 admits. Succeeding theorists, in their numerous attempts to 

 deduce Fresnel's beautiful laws from dynamical principles, have 

 always been obliged to assume that the medium is symmetri- 

 cally arranged with respect to three rectangular planes ; and 

 as, in this hypothesis, the axes of elasticity, or of optical sym- 

 metry, necessarily coincide with those of symmetrical arrange- 

 ment, their directions are fixed, as before, independently of 

 colour. 



From these principles it follows that the optic axes for dif- 

 ferent colours all lie in the same plane, namely, the plane of 

 the greatest and least axes of the ellipsoid, and that they are 

 equally inclined to each of the latter axes, so that the angle 

 made by any pair, to whatever colour they belong, is always 

 bisected by the same right line. This was accordingly, for a 

 long time, believed to be the case ; and the earlier experiments 

 of Sir J. Herschel,* which are appealed to by Fresnel, as well 

 as the observations of Sir David Brewster, seemed to establish 

 it as a general law. But it was afterwards discovered by Sir J". 

 Herschel that, in borax, the optic axes for different colours lie 

 in different planes inclined at very sensible angles to each 

 other ; and the same discovery was made about the same time 

 (1832) by M. Norrenberg. The latter observer further ascer- 

 tained, that even when the optic axes all lie in the same plane 

 there are cases, as in sulphate of lime, wherein their angles are 

 not bisected by the same right line. These facts, and others of 

 a like nature that have been since observed, show the falsehood 

 of the supposition that the lines called the axes of elasticity 

 have always the same directions whatever be the colour of the 



* Phil. Trans. 1820. 



