XIX. On the electromagnetic theory of the reflection and refraction of light

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Abstract
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 and its components P, Q, R, and the electric displacement D 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 = -1/2∭S D . dxdydz = 1/2∭(P f + Q y + R h ) dxdydz

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