### § 13. The Product of the Field-vectors *f*F.

Finally let us enquire about the laws which lead to the determination of the vector *w* as a function of *x, y, z, t*. In these investigations, the expressions which *are obtained by the multiplication of two alternating matrices*

*are of much importance*. Let us write.

(70) |

Then (71)

(71) |

Let *L* now denote the symmetrical combination of the indices 1, 2, 3, 4, given by

(72) |

Then we shall have

(73) |

In order to express in a *real form*, we write

(74) |

Now