and the equations (III) and (IV), are

(B) |

### § 8. The Fundamental Equations for Moving Bodies.

We are now in a position to establish in a unique way the fundamental equations for bodies moving in any manner by means of these three axioms exclusively.

The *first* Axion shall be, —

When a detached region of matter is at rest at any moment, therefore the vector is zero, for a system *x, y, z, t* — the neighbourhood may be supposed to be in motion in any possible manner, then for the spacetime point *x, y, z, t* the same relations (A) (B) (V) which hold in the case when all matter is at rest, snail also hold between , the vectors and their differentials with respect to *x, y, z, t*.

The *second* axiom shall be : —

*Every velocity of matter is < 1, smaller than the velocity of propagation of light.*

The *third* axiom shall be : —

*The fundamental equations are of such a kind that when* x, y, z, it *are subjected to a Lorentz transformation and thereby and are transformed into space-time vectors of the second kind, as a space-time vector of the 1st kind, the equations are transformed into essentially identical forms involving the transformed magnitudes.*

Shortly I can signify the third axiom as ; —

* and are space-time vectors of the second kind, is a space-time vector of the first kind.*

This axiom I call the *Principle of Relativity*.