1893.] the Electric and Luminiferous Medium. 441 



dynamical coherence and formal logical validity. Yet, the more the 

 phenomena of light were afterwards experimentally examined, the 

 stronger was the confirmation of the whole scheme of formulae at 

 which he had arrived. 



The explanation of the laws of physical optics advanced by Fresnel, 

 and verified by comparison with the phenomena, which was possible 

 in several very exact ways, chiefly by himself and Brewster, was, 

 about the year 1835, engaging the attention of several of the chief 

 mathematicians of that time Augustin Cauchy in France, Franz 

 Neumann in Germany, George Green in England, and James 

 MacCullagh in Ireland. The prevalent mode of attacking the 

 problem was through the analogy with the propagation of elastic 

 waves in solid bodies ; and the comparison of Fresnel's laws of pro- 

 pagation in crystalline media with the results of the mathematical 

 theory of the elasticity of crystalline bodies gave abundance of 

 crucial tests for the verification, modification, or disproof of the 

 principles assumed in these investigations. The treatment of Cauchy 

 is earliest in date, but somewhat empirical and unsatisfactory in its 

 logical aspects in the light of subsequent more precise knowledge of 

 the conditions of the problem of the elasticity of solids. The treat- 

 ment of Neumann is also a sound and original piece of investigation, 

 if we except the limited view of the elasticity of solids, that of Navier 

 and Poisson, on which he based it. The treatment by Green had the 

 great distinction of incidentally laying, with all the generality and 

 simplicity which we expect in an ultimate theory, the foundations on 

 which every theory of elastic action in ordinary material bodies must 

 in future be constructed ; it proceeded, in fact, on the basis of one of 

 those great generalisations, of which the aggregate constitutes the 

 all-embracing modern doctrine of energy. These three authors all 

 treated the question of reflexion and refraction of waves. Cauchy 

 could not make much of Fresnel's formulae in any logical manner. 

 Neumann had the merit of seeing clearly that the thing was impos- 

 sible on his elastic solid theory ; so he dropped it altogether, assumed 

 a sufficient number of principles which might be taken, with fair 

 probability, in accordance with general reasoning, to be satisfied in 

 the reflexion and refraction of light rays, viz., complete continuity of 

 the media and continuity of energy in crossing the boundary at 

 which the reflexion and refraction take place, and had the satisfac- 

 tion of evolving a solution which agreed with Fresnel's laws, and 

 easily extended them to the much more complicated circumstances of 

 crystalline media. But to obtain this solution he assumed, from 

 what he found necessary to make his very imperfect theory of pro- 

 pagation in crystals agree with Fresnel's laws, that the density of the 

 luminiferous medium is the same in all bodies, and that the displace- 

 ment of plane-polarised light is in the plane of polarisation. It may 



