the electric and luminiferous medium. 
723 
Part I.—Physical Optics. 
Preliminary and Historiccd. 
8. The development of the analytical theory of the aether which will be set forth 
in this paper originated in an examination of Professor G. F. FitzGerald’s Memoir, 
“ On the Electro-magnetic Theory of the Peflection and Refraction of Light,” * 
of which the earlier part is put forward by the author as being a translation of 
MacCullagh’s analysis of the problem of reflexion into the language of the electro¬ 
magnetic theory. Later on in the Memoir the author discusses the rotation of the 
plane of polarization of the light, which is produced by reflexion from the surface 
of a magnetized medium, assumed in the analysis to be transparent ; but the 
application of MacCullagh’s method to this case leads him to more surface- 
conditions than can be satisfied by the available variables, and the rigorous 
solution of the problem is not attained. After satisfying myself that this contradic¬ 
tion is really due to the omission from consideration of the ^wasi-hydrostatic pressure 
which must exist in the medium and assist in satisfying the stress-conditions 
at an interface, though on account of the incompressible character of the medium 
this pressure takes no part in the play of energy on which the kinetic phenomena 
depend, it was natural to turn to MacCullagh’s optical writings,! in order to 
ascertain whether a similar idea had already presented itself. An examination, 
particularly of “An Essay towards a Dynamical Theory of Crystalline Reflexion and 
Eefraction,” ^ led in another direction, and showed that to MacCullagh must be 
assigned the credit of one of the very first notable applications to physical problems 
of that dynamical method which in the hands of Maxwell, Lord Kelvin, 
VON Helmholtz, and others, has since been so productive, namely, the complete 
realization of Lagrange’s theory that all the phenomena of any purely dynamical 
system free from viscous forces are deducible from the single analytical function of its 
configuration and motion which expresses the value of its energy. The problem 
proposed to himself by MacCullagh was to determine the form of this function for 
a continuous medium,§ such as would lead to all the various laws of the propagation 
and reflexion of light that had been ascertained by Fresnel, supplemented by the 
exact and crucial observations on the polarization produced by reflexion at the 
surfaces of crystals and of metallic media, which had been made by Brewster and 
* G. F. FitzGerald, ‘Phil. Trans.,’ 1880. 
t ‘The Collected Works of James MacCdllagh,’ eel. Jellett and HAacHTON, 1880. 
-X MacCullagh, loc. cit., p. 145 ; ‘ Trans. Roy. Irish Acad.,’ XXI., Dec. 9, 1839. 
§ The problem had already been fully analyzed by Green, shortly before, and unknown to 
MacCullagh, precisely on these principles, but without success owing to his restriction to elasticity 
of the type of an ordinary solid body; cf, Green’s “ Memoir on Ordinary Refraction,” ‘ Trans. Camb. 
Phil. Soc.,’ Dec. II, 1837, introduction, and his “Memoir on Crystalline Propagation,” ‘Trans. Camb. 
Phil. Soc.,’ May 20, 1839. 
