294 Prof. MacCullagh on the Dispersion of the Optic Axes, 



nient. These directions coincide with the axes of the ellipsoid 

 by which he constructs his wave-surface ; and the position 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. Suc- 

 ceeding theorists, in their numerous attempts to deduce 

 Fresnel's beautiful laws from dynamical principles, have al- 

 ways been obliged to assume that the medium is symmetrically 

 arranged with respect to three rectangular planes ; and as, in 

 this hypothesis, the axes of elasticity, or of optical symmetry, 

 necessarily coincide with those of symmetrical arrangement, 

 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 experi- 

 ments of Sir J. Herschel (Phil. Trans. 1820) which are ap- 

 pealed 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 ascertained, that even when the 

 optic axes all lie in the same plane, there are cases, as in sul- 

 phate 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 suppo- 

 sition that the lines called the axes of elasticity have always 

 the same directions whatever be the colour of the light; they 

 are inconsistent with all received notions, and contradict every 

 theory that has been hitherto proposed. No person, as far 

 as I am aware, has even attempted to explain them. 



But in the theory which I have constructed to represent 

 the laws of the action of crystallized bodies upon light, and 

 which has already brought so much within its grasp, the 

 phenomena in question do not offer any difficulty whatever; 

 on the contrary, they are of a kind that would naturally be 

 looked for, antecedently to experiment. For in this theory, 

 I make no hypothesis as to the constitution of the sether, or 

 the arrangement of its molecules ; nor any hypothesis, like 



