one obtains

Due to the identity which is easily to be verified

the relation is obtained

(5) |

ยง 3. **The energy equation and the momentum equations.**

We understand under coordinates and the time, measured in a reference system in which the observer has a fixed location. The ponderomotive force measured by him, which is acting (due to the electromagnetic process) on the unit volume of moving matter, shall have the components:

(6) |

The vector which arises here, is denoted by us as "*electromagnetic momentum density*" or shortly as "*momentum density*". The system of "*fictitious electromagnetic stresses*" consists of six quantities, namely the normal stresses , and the pairwise shear-stresses which are mutually equal:

(6a) |

To the "*momentum equations*" (6), the *energy equation* is added:

(7) |

Here, means the Joule-head, the electromagnetic energy density, the energy current.

While the momentum equations determine the momentum exerted by the electromagnetic field, the energy equation determines which energy-quantity per unit space and time is converted into a non-electromagnetic form (work and heat).

If one introduces into (6) and (7) the temporal derivative defined by (3) and (3a),