Page:Grundgleichungen (Minkowski).djvu/34

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(54)

The vector is perpendicular to w; we can call it the Magnetic rest-force.

Relations analogous to these hold among the quantities and Relation (D) can be replaced by the formula

{D}

We can use the relations (C) and (D) to calculate F and f from and , we have

and applying the relation (45) and (46), we have

(55) ,
(56) ,

i.e.

, etc.

, etc.

Let us now consider the space-time vector of the second kind , with the components

,

,

Then the corresponding space-time vector of the first kind

vanishes identically owing to equations 49) and 53).

Let us now take the vector of the 1st kind

(57)

with the components

, etc.

Then by applying rule (45), we have