758 
the quantities ya‘) on the left hand side being subject to the con- 
ditions 
Wig SO, eo Abbe == ae, ek A Ae ed 
so that they represent 6 mutually independent numerical values. 
These are the components of the electric foree E and the magnetic 
force H. We have indeed k 
Wy, — E>. ’ Wis —— E, ’ Ws = E., ) (27) 
Wes He ’ Ws, =F Hy ’ Wie = H:, y : 
and it is thus seen that the first three of the formulae (25) express 
the connection between the magnetic field and the electric current. 
The fourth shows how the electric field is connected with the charge. 
On passing to another system of coordinates we have for iq the 
transformation formula 
Mn Pp > (b) Kha Why 
which can easily be deduced, while for w,, we shall assume the 
formula 
UW ab pl (dd) Ter ndi Wed» nn ee EN 
In virtue of this assumption the equations (25) are covariant for 
any change of coordinates. 
§ 8. Beside yy, we shall introduce certain other quantities yas 
which we define by 
Was = =: (cd) Gen Gab Wed 2s Ge es (29) 
ange 
or with regard to (26) 
1 
Wab = o = (cd) (gen Jdb—Jda Geb) Weds - - . + (30) 
in which last equation the bar over cd means that in the sum each 
combination of two numbers occurs only once. 
As a consequence of this definition we have 
Wan = 0, Weg Saabs ys ©) ia) eee (31) 
and we find by inversion *) 
War = V —y = (cd) Yac Yod Wed 2 dost) te 0 
1) The quantities y,, are connected with the components vg, of the tensor 
introduced by Einstein by the equations af, = V Ly (Dake 
2) By the definition of the quantities y (§ 3) we have 
2 (6) Geb Gaba oe ie gee 1e RENE 
and for 6=|= 
~ 
> (a) Gab Yar = 9, Ot (B)igta Vene a eee 
Substituting for ged an expression similar to (29) with other letters as indices, 
