Page:Grundgleichungen (Minkowski).djvu/33

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and further

(48) ,

Because F is an alternating matrix,

(49) ,

i.e. is perpendicular to the vector to w; we can also write

(50) ,

I shall call the space-time vector of the first kind as the Electric Rest Force.

Relations analogous to those holding between , hold amongst , and in particular -wf is normal to w. The relation (C) can be written as

{C}

The expression (wf) gives four components, but the fourth can be derived from the first three.

Let us now form the time-space vector 1st kind , whose components are

Of these, the first three are the x-, y-, z-components of the space-vector

(51) ,

and further

(52) ;

Among these there is the relation

(53) ,

which can also be written as