which according to (37) and (40b) is to be brought into the form
In order to facilitate the comparison of our results with the approaches of Minkowski, we write
Then the momentum equations (6) and the energy equation (7) read
There, the relation exists according to (19a)
Now, relation (40) means
Together with (6a), these relations contain a remarkable symmetry property, which cannot be found in Minkowski's approach. Regarding the behavior under Lorentz transformations, the 10 quantities
transform as the squares and products of coordinates and of the light-path . Accordingly, this "space-time-tensor" satisfies the "principle of relativity" in the sense of Minkowski; Also the ponderomotive forces, which we are going to calculate in § 12, thus satisfies the relativity principle.
§ 10. The relation between the theories of Lorentz and Minkowski.
We have emphasized the illustrative meaning of vectors in Lorentz's theory, i.e., as being the contribution of the aether at the electric and magnetic excitation. In the theory of Minkowski, the vectors