The vector fulfills the relation
which we can write as
and is also normal to w. In case , we have , and
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