442 Mr. J. Larmor. A Dynamical Theory of [Dec. 7, 



be shown, as is now indeed to be expected, that this is a totally wrong 

 foundation to work upon, that Neumann's general principles for the 

 solution of the problem of reflexion are inconsistent with his elastic 

 theory. If he had adopted a converse procedure, and worked out the 

 problem of the reflexion of a ray on his general principles, and then 

 deduced, by comparison with Fresnel's formulae, the law of density of 

 the luminiferous medium and the direction of the vibration in plane- 

 polarised light, he would have been entitled to the credit of a joint 

 discoverer in the domain of the dynamics of reflexion. But, for the 

 reasons here indicated, the credit of that discovery must, I think, be 

 assigned to MacCullagh. 



The achievements by which the memory of MacCullagh is now to 

 a great extent preserved are his very elegant investigations in the 

 domain of pure Euclidian geometry. He may be claimed to be an 

 instance of the numerous cases from Archimedes down through 

 Descartes, Newton, and, we may add, Thomas Young, in which keen 

 geometrical insight has formed a key for unlocking the formal laws 

 of physical actions. He was first attracted to Fresnel's laws oi 

 optics by the very simple and elegant geometrical relations to which 

 they lead. At a later period he proposed to himself the problem to 

 hit off the extension of Fresnel's laws of reflexion which would apply 

 to crystalline media, in the light of the crucial conditions afforded by 

 the delicate experiments of Brewster and, at a later stage, Seebeck, 

 to which such a theory must conform. He had thus to cast about 

 for geometrical principles on which Fresnel's laws might be founded, 

 such as would admit of easy extension to the more general problem. 

 He early came upon the principle of continuity of the media, which 

 he put in the geometrical form that the resultant of the displace- 

 ments in the refracted waves is equal to the resultant of the dis- 

 placements in the incident and reflected waves. As regards the other 

 necessary condition, he was not at first successful. The density of 

 the medium he took to be the same in all bodies, because he could not 

 imagine it to be seolotropic, or different in different directions, in 

 crystalline media. He assumed the vibrations to be in the plane of 

 polarisation, from considerations of geometrical symmetry and neces- 

 sity, confirmed in the earlier stage by one of the theories of Cauchy. 

 The other condition above referred to he took to be equality of 

 certain pressures in the media, as imagined by Cauchy ; and by this 

 means he arrived at a satisfactory explanation of Brewster's obser- 

 vations on the polarising angle in reflexion from crystals. But 

 Seebeck pointed out that this solution would not account for the 

 values of the deviation of the plane of polarisation from the plane of 

 reflexion, by means of which he had himself tested it. Owing to 

 this criticism MacCullagh was finally led to abolish Cauchy 's notion 

 of pressure, and assume simply the continuity of energy in its place. 



