Now by putting , the differential equation (29) is transformed into the same form as eq. (1) here when . Therefore it so happens that by a compensation of two contradictions to the relativity principle, the differential equations of Lorentz for moving non-magnetised bodies at last agree with the relativity postulate.
If we make use of (30) for non-magnetic bodies, and put accordingly , then in consequence of (C) in §8,
i.e. for the direction of
and for a perpendicular direction ,
i.e. it coincides with Lorentz's assumption, if we neglect in comparison to 1.
Also to the same order of approximation, Lorentz's form for corresponds to the conditions imposed by the relativity principle [comp. (E) § 8] — that the components of , are equal to the components of multiplied by or respectively.
§ 10. Fundamental Equations of E. Cohn.
E. Cohn assumes the following fundamental equations
where E, M are the electric and magnetic field intensities (forces), are the electric and magnetic polarisation (induction).
- Gött. Nachr. 1901, w. 74 (also in Ann. d. Phys. 7 (4), 1902, p. 29).