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.
§11. Typical Representations of the Fundamental Equations.
In the statement of the fundamental equations, our leading idea had been that they should retain a covariance of form, when subjected to a group of Lorentz-transformations. Now we have to deal with ponderomotive reactions and energy in the electro-magnetic field. Here from the very first there can be no doubt that the settlement of this question is in some way connected with the simplest forms which can be given to the fundamental equations, satisfying the conditions of covariance. In order to arrive at such forms, I shall first of all put the fundamental equations in a typical form which brings out clearly their covariance in case of a Lorentz-transformation. Here I am using a method of calculation, which enables us to deal in a simple manner with the space-time vectors of the 1st, and 2nd kind, and of which the rules, as far as required are given below.
A system of magnitudes ah k formed into the matrix
| a₁₁.......a1 q |
| |