[ 691 ] 
XIX. On the Electromagnetic Theory of the Reflection and Refraction of Light. 
By Geo. Fras. Fitzgerald, M.A ., Fellow of Trinity College, Dublin. 
Communicated by G. J. Stoney, M.A., F.R.S., Secretary of the Queens University 
of Ireland. 
Received October 26, 1878—Read January 9, 1879. 
In the second volume of his ‘Electricity and Magnetism’ Professor J. Clerk Maxwell 
has proposed a very remarkable electromagnetic theory of light, and has worked out 
the results as far as the transmission of light through uniform crystalline and magnetic 
media are concerned, leaving the questions of reflection and refraction untouched. 
These, however, may be very conveniently studied from his point of view. 
If we call W the electrostatic energy of the medium, it may be expressed in terms 
of the electromotive force and the electric displacement at each point as is done in 
Professor Maxwell’s ‘Electricity and Magnetism,’ vol. ii., part iv., ch. 9. I shall 
adopt his notation and call the electromotive force (5 and its components P, Q, R, and 
the electric displacement and its components f g, h. As several of the results of 
this paper admit of a very elegant expression in Quaternion notation I shall give the 
work and results in both Cartesian and Quaternion form, confining the German letters 
to the Quaternion notation. Between these quantities then we have the equation 
W= f (Pf+Qg+m)dxdydz 
Similarly the kinetic energy T may be expressed in terms of the magnetic induction, 
33, and the magnetic force, or their components a, b, c and a, /3, y by the equation 
T= — [ j j. S 33 £>. dxdydz = ~ 1 j j (««-}- 6/3+c y) dxdydz 
I shall at present assume this to be a complete expression for T and return to the case 
of magnetized media for separate treatment, as Professor Maxwell has proposed addi¬ 
tional terms in this case in order to account for their property of rotatory polarisation. 
I shall throughout assume the media to be isotropic as regards magnetic induction, for 
the contrary supposition would enormously complicate the question and be, besides, of 
doubtful physical applicability. For the present I shall not assume them to be electro¬ 
statically isotropic. Hence C is a linear vector and self-conjugate function of '£>, and 
