Page:Grundgleichungen (Minkowski).djvu/35

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(58) ,


, etc.


The vector fulfills the relation

(59) ,

which we can write as

and is also normal to w. In case , we have , and

(60) ,

I shall call , which is a space-time vector 1st kind the Rest-Ray.

As for the relation E), which introduces the conductivity , we have

This expression gives us the rest-density of electricity (see §8 and §4). Then


represents a space-time vector of the 1st kind, which since , is normal to w, and which I may call the rest-current. Let us now conceive of the first three component of this vector as the x-, y-, z co-ordinates of the space-vector, then the component in the direction of is

and the component in a perpendicular direction is .

This space-vector is connected with the space-vector , which we denoted in § 8 as the conduction-current.

Now by comparing with , the relation (E) can be brought into the form

(E) .