863 
0 
d Nut = = OT {Ora Nw — Ort d Nw} 
is the contravariant vector-divergency of this tensor, multiplied by 
Vg, and thus of the same nature as Nw itself. 
In like manner the second variation 
Om 
d' Nw = = (b) AE {Ora JNwt — Or’ SNw%} 
x 
is a contravariant vector multiplied by p/q again. 
It follows that our results are in complete accordance with relativity 
theory in the most general sense, and we are justified in applying any 
theorem of that theory. 
Having thus recognized the true character of our tensor, we shall 
henceforth write Yg 7 instead of 7’? 
Va Te) = eGre Nw? — eOr Nwt + $ & Ore d Nw — Or d Nw%}. 
This will cause no confusion. 
We must further keep in mind that 2* is no four-dimensional vector, 
but w* da/ds is. We shall not introduce a new notation for this 
velocity vector. 
The General Covariant Equations for the Field. 
14. The covariant tensor of the field can be written as the rotation 
of the potential vector ga: 
= (GER WS ile); (14.1) 
From these we get the contravariant components: 
Fab = & (ed) gee 94 fear 
and the fundamental equations of the theory of electrons are 
ò : 
rr (EM Os (14.2) 
where o is the density of the electric charges, and ev" is a contra- 
Jab 
a 
variant vector multiplied by Vg. 
From the relations (14.1) arises another equation. Multiply by 
the contravariant fourth rank tensor 4d¢¢/)/g, and contract twice. 
Here deed ig 1 whenever the figures abcd constitute an even permu- 
tation of 1234, and in other cases vanishes. Then we get the conjugate 
tensor/,@” *): 
"al > (ed) 1 fabled f. 
a — * a0c6 
fet = Eed) — dated fg 
') In order to get the covariant conjugate tensor components /*ay from the 
contravariant fed, multiply in the same way by the covariant tensor 
Ig Vg Dabed - Oabed = jabed), 
Proceedings Royal Acad. Amsterdam. Vol XXII. 
