§10. Fundamental Equations of E. Cohn.
E. Cohn assumes the following fundamental equations.
(31) Curl (M + [u E]) = dE/dt + u div. E + J
- Curl [E - (u. M)] = dM/dt + u div. M.
(32) J = σ E, = ε E - [u M], M = μ (m + [u E.])
where E M are the electric and magnetic field intensities (forces), E, M are the electric and magnetic polarisation (induction). The equations also permit the existence of true magnetism; if we do not take into account this consideration, div. M. is to be put = 0.
An objection to this system of equations, is that according to these, for ε = 1, μ = 1, the vectors force and induction do not coincide. If in the equations, we conceive E and M and not E - (U. M), and M + [U E] as electric and magnetic forces, and with a glance to this we substitute for E, M, E, M, div. E, the symbols e, M, E + [U M], m - [u e], ρ, then the differential equations transform to our equations, and the conditions (32) transform into
J = σ(E + [u M])
e + [u, (m - [u e])] = ε(E + [u M])
M - [u, (E + u M)] = μ(m - [u e])
then in fact the equations of Cohn become the same as those required by the relativity principle, if errors of the order u² are neglected in comparison to 1.
It may be mentioned here that the equations of Hertz become the same as those of Cohn, if the auxiliary conditions are
(33) E = εE, M = μM, J = σE.