981 
additional connexions. Estrin has shown that this indefiniteness 
in the extensions void of matter can never give rise to an indefiniteness 
in the observations that can be made with material instruments. 
The identity further confirms that in the absence of an external 
force the laws of conservation of energy and momentum hold for 
the matter. Indeed, from the field equation (6), which is given in 
(20) in another form, together with (21) it is evident that 
a 0 ge A Okin, ane an 
0 = Elm) WI (Ta HEE — HV ght (17 + i"). (22) 
We may even conclude that no other force can be exerted on the 
matter and the electro-magnetic field by any agency if this does 
not change the gravitation field at the same time. 
18. The second term on the left-hand- ae of (21) can be trans- 
formed. We may write for it 
i dg 
zz Dd = ie (Gi — $ gu G). 
According to (4d) this comes to the same as 
per EEN Ch a eB 07 | 
ee Ss dg de dg ap dare ml dg!’ 
The same may also be expressed as follows 
| gH ke; 0 (4o2*)+ 
0 
dg! Ja Oa dg"? 
oe YV—gH 
Ted Tia dl 
If now we put 
Og oY —qgH ddr 
Vg 2e = 2 (lbd) gi E = 4 gli ae as oan i 
a 9. 
a Oa ae 
ad dg’ a wa dg! a J . 
“cd ed 
then we have according to the hes equation and (21), (20): 
Edge EN y+ 205 SW) CD 
So we find in W—gze a Een le ‘“quasi-divergeney”” (no 
invariant) of which is the opposite of the quasi-divergency of the 
dynamical tensor of matter and electro-magnetic field. Lorentz *) 
and Dr Donper ®) have deduced another similar complex 
1) 1. e. XXV, p. 473. 
2) Tu. pe Donner, Les equations différentielles du champ gravifique d’E1nstTEeIN 
créé par un champ electromagnétique de Maxweir-Lorentz. Verslagen, Kon. Ac. . 
Wet. Amsterdam, XXV, p. 150. 
