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Chapter X.
The Followers of Maxwell.
The most notable imperfection in the electromagnetic theory of light, as presented in Maxwell's original memoirs, was the absence of any explanation of reflexion and refraction. Before the publication of Maxwell's Treatise, however, a method of supplying the omission was indicated by Helmholtz.[1] The principles on which the explanation depends are that tho normal component of the electric displacement D, the tangential components of the electric force E, and the magnetic vector B or H, are to be continuous across the interface at which the reflexion takes place; the optical difference between the contiguous bodies being represented by a difference in their dielectric constants, and the electric vector being assumed to be at right angles to the plane of polarization.[2] The analysis required is a mere transcription of MacCullagh's theory of reflexion,[3] if the derivate of MacCullagh's displacement e with respect to the time be interpreted as the magnetic force; μ curl e as the electric force, and curl e as the electric displacement. The mathematical details of the solution were not given by Helmholtz himself, but were supplied a few years later in the inaugural dissertation of H. A. Lorentz.[4]
In the years immediately following the publication of Maxwell's Treatise, a certain amount of evidence in favour of
- ↑ Journal für Math. lxxii (1870), p. 68, note.
- ↑ Helmholtz (loc. cit.) pointed out that if the optical difference between the media were assumed to be due to a difference in their magnetic permeabilities, it would be necessary to suppose the magnetic vector at right angles to the plane of polarization in order to obtain Fresnel's sine and tangent formulae of reflexion.
- ↑ Cf. pp. 148, 149, 154-156.
- ↑ Zeitschrift für Muth. 1. Phys. xxii (1877), pp. 1, 205: Over de theorie der terugkaatsing en breking van het licht, Årnhem, 1875. Lorentz's work was based on Helmholtz's equations, but remains substantiully unchangod when Maxwell's formulae are substituted.
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