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should have an influence upon the observations of a co-moving observer. Yet H. A. Lorentz^[1] succeeded – by suitable hypotheses concerning the modifications that the electrical and mechanical properties should experience in their motion through the aether – in adapting his theory to the postulate of relativity. That this is possible, can be explained from the properties of the field equations for the aether, which go over into themselves by certain transformations of coordinates and of the path of light: the so-called^[2] Lorentz transformations.

It is not my intention, to discuss in this paper the whole complex of questions, which are connected to the postulate of relativity; I have taken position to some of these questions at another place^[3]. Here, this postulate is of interest to us, only in so far as it is connected with the electrodynamics of ponderable matter. A paper of H. Minkowski^[4] which appeared recently, has placed just this question at the top; here, such a form is given to the fundamental equations of moving bodies, so that they pass into Maxwell's field equations for moving bodies by the Lorentz transformation.

Minkowski's fundamental equations, as well as the ones of E. Cohn and of H. A. Lorentz, explain all existing experimental results; they and Cohn's fundamental equation – with which they are in agreement (neglecting magnitudes of second order in the ratio of the velocity of matter and that of light) – have the symmetry of electric and magnetic quantities in common. However, Lorentz's fundamental equations in their initial form, in which this symmetry is not present, already deviate in terms of first order from the ones of the two other theories; though this deviation (which was noticed by E. Cohn^[5]) only concerns the para- and diamagnetic isolators, and because of their insignificance they escape any experimental test.

However, it is not hard to modify the relations of electric and magnetic vectors assumed by Lorentz, so that the symmetry is maintained; the paragraphs (8) and (10) of the present investigations are concerned with the form of Lorentz's theory modified in this way. It will be shown, that it is fully in agreement with Minkowski's theory in terms of its actual content. The formal difference lies in the interpretation, which is given to the vectors designated by ${\mathfrak {E}}$ and ${\mathfrak {H}}$;

1. H. A. Lorentz, Electromagnetische verschijnselen in een stelsel dot sich met willekeurige snelheid, kleiner dan die van het licht, beweegt [Koningklijde Akademie van Wetenschappen te Amsterdam, Deel XII (1904), 2, pp. 986-1009].
2. H. Poincaré, Sur la dynamique de l’électron [Rendiconti del Circolo Matematico di Palermo, t. XXI (1° semestre 1906), pp. 129-176].
3. M. Abraham, Theorie der Elektrizität, Bd. II, Auflage 2 (Leipzig 1908), pp. 356-397.
4. H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern [Nachrichten der Kgl. Gesellschaft der Wissenschaften zu Göttingen, 1908, pp. 53-111].}}
5. E. Cohn, Zur Elektrodynamik bewegter Systeme. I. [Sitzungsberichte der Kgl. Preussischen Akademie der Wissenschaften (Berlin), Jahrgang 1904, pp. 1294-1303], p. 1301.