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CHAPTEE 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.* The 

 principles on which the explanation depends are that the 

 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 con- 

 tiguous 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.-)- The analysis 

 required is a mere transcription of MacCullagh's theory of 

 reflexion,| if the derivate of MacCullagh's displacement e with 

 respect to the time be interpreted as the magnetic force, 

 fi curl e as the electric force, and curl e as the electric displace- 

 ment. 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. 



In the years immediately following the publication of 

 Maxwell's Treatise, a certain amount of evidence in favour of 



* Journal fur Math. Ixxii (1870), p. 68, note. 



t 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. 



I Cf. pp. 148, 149, 154-156. 



Zeitschrift fiir Math. u. Phys. xxii (1877), pp. 1, 205 : Over de theorie der 

 terugkaatsing en breking van het licht, Arnhem, 1875. Lorentz's work was based 

 on Helmholtz's equations, but remains substantially unchanged when Maxwell's 

 formulae are substituted. 



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