These equations are of the form
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(I)
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where the vectors E, H, D, B denote the electric force, magnetic force, electric displacement, and magnetic induction respectively, s denotes the current and ρ the volume density of electricity. The equations differ from those used by Lorentz by the fact that the vector H - [Pw] occurring in Lorentz's equations is replaced here by the vector H.[1] It should be remarked that Frank[2] has obtained Minkowski's equations by a process of averaging in the case of non-magnetic bodies.
We shall suppose that the electric polarisation P and the magnetic polarisation Q are connected with D, E, B, and H by the formulae
The electrodynamical equations (I) can be replaced by the two integral equations
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(II)
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(III)
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These equations are unaltered in form by a transformation from (x, y, z, t) to (x', y', z', t') if
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(IV)
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(V)
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(VI)
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where θ and φ are constants.
- ↑ This simply means that a different definition is adopted for H, the object being to retain the symmetry of the equations.
- ↑ Ann. d. Phys., Bd. 27, p. 1059 (1908).