

1893.] the Electric and Luminiferous Medium. 443 



This principle of energy, which gives a quadratic equation between 

 the displacements at the interface, he succeeded to his satisfaction, as 

 regards the confirmation of his views, in replacing by linear relations. 

 And then he gave his two magnificent geometrical theorems that of 

 transversals and that of the polar plane, which contain each in a 

 sentence the complete specification of the laws of reflexion for the 

 most general case of a transparent medium, and which form 

 the culmination of the geometrical relations by which he was 

 guided throughout this whole process of synthetical discovery. His 

 laws of reflexion are the same as Neumann's ; of them, as formal 

 laws, these two authors must be regarded as the independent dis- 

 coverers Neumann by a happy assumption suggested by reasoning 

 at bottom illogical in the light of subsequent knowledge, MacCullagh 

 by a resolute attack on the observed facts with a view to reducing 

 them to simple formulae. 



But the greatest achievement of MacCullagh is that contained in 

 his memoir of 1839, two years after, entitled an " Essay towards a 

 Dynamical Theory of Crystalline Reflexion and Refraction." He is 

 in quest of a dynamical foundation for the whole scheme of optical 

 laws, which had been notably extended and confirmed by himself 

 already. He recognises, I think for the first time in a capital 

 physical problem, that what is required is the discovery of the 

 potential- energy function of Lagrange on which the action of the 

 medium depends, and that the explanation of the form of that 

 function is another question which can be treated separately. His 

 memoir is subsequent to, but apparently quite independent of, that of 

 Green, in which Green restricted the medium to a constitution like 

 an elastic solid, laid down the general laws of such constitution for 

 the first time, and made a magnificent failure of his attempt to 

 explain optical phenomena on that basis. If this thing was to be 

 done, the power, simplicity, and logical rigour of Green's analysis 

 might have been expected to do it ; and nothing further has come 

 of the matter until the recent new departure of Lord Kelvin in his 

 speculation as to a labile elastic-solid aether. To return to Mac- 

 Cullagh, he is easily able to hit off a simple form of the potential- 

 energy function, which on the basis of Lagrange's general dynamics, 

 or more compactly on the basis of the law of Least Action absolutely 

 sweeps the whole field of optical theory so far as all phenomena are 

 concerned in which absorption of the light does not play a prominent 

 part. He is confident, as any 'one who follows him in detail must be, 

 that he is on the right track. He tries hard to obtain a dynamical 

 basis for his energy-function, that is, to imagine some material 

 medium that shall serve as a model for it and illustrate its possibility 

 and its mode of action ; he records his failure in this respect, but at 

 the same time he protests against the limited view which would tie 



