of time to the application of the Lorentz-transformation. The paper of Einstein which has been cited in the Introduction, has succeeded to some extent in presenting the nature of the transformation from the physical standpoint.

## PART II. ELECTRO-MAGNETIC PHENOMENA.

### § 7. Fundamental Equations for bodies at rest.

After these preparatory works, which have been first developed on account of the small amount of mathematics involved in the limitting case , let us turn to the electro-magnetic phenomena in matter. We look for those relations which make it possible for us — when proper fundamental data are given — to obtain the following quantities at every place and time, and therefore at every spacetime point as functions of *x, y, z, t*: — the vector of the electric force , the magnetic induction , the electrical induction , the magnetic force , the electrical space-density , the electric current (whose relation hereafter to the conduction current is known by the manner in which conductivity occurs in the process), and lastly the vector , the velocity of matter.

The relations in question can be divided into two classes.

*Firstly* — those equations, which, — when , the velocity of matter is given as a function of *x, y, z, t*, — lead us to a knowledge of other magnitude as functions of *x, y, z, t* — I shall call this first class of equations the *fundamental equations* —

*Secondly*, the expressions for the *ponderomotive force*, which, by the application of the Laws of Mechanics, gives us further information about the vector as functions of *x, y, z, t*.

For the case of *bodies at rest*, *i.e.* when , the theories of Maxwell (Heaviside, Hertz) and Lorentz lead to the same fundamental equations. They are ; —

(1) The *Differential Equations*: — which contain no constant referring to matter: —

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