889 
is a scalar. .According to equation (68) of Herarorz the left-hand 
side of (21) divided by D represents the components of the tension- 
energy tensor for matter. If this formula of Hrrenorz holds in the 
general theory of relativity too, the components of the tension-energy 
tensor of matter are’): 
DE “Op one OP 
et, RE rente aS 
Nn (23) 
Cree 
in — Ujn 
G2 D n dain me D 
d 
At all events this formula is valid in the system of coordinates 
N° and from the general covariancy of both expressions for © can 
be concluded, that it holds for an arbitrary system of coordinates. 
In the following this will be proved directly by means of Haminron’s 
principle. 
Every function p of the g,,’s may also be regarded asa function 
of the contravariant g’’’s and in general. we have: 
a Jus us =e UP et eps ee A eA tee) 
geeks a Oye 
In analogy with the assumption (69) of HerGrorz we put 
= ? ke 
y= — D is e £ C > in e 5 (25) 
(8 = volume scalar). As ) depends on the a;;’s only and not on 
oJ 
the g”’’s, the second expression (23) for £; may then be written in 
the following way: 
ae OD OA 
RJ) = a - 
a re ee i = a eee 23a 
z Bon JI dai, 3 g Ogi ( ) 
Comparing this equation with (3) we see that they are identical if 
ie EP Ae che Be Ga cee og Sites (26) 
Thus we have found the connexion between Etnstetn’s theory of 
gravitation and Herer.orz’s mechanics. Now we have.still to deduet 
the first expression (23) for TL from Hamiton’s principle. This may 
be done in a way analogous to that used by prof. Lorentz for the 
case of incoherent masses. The integral 
[fs dz, de, de, de, 
must then be thus varied that the world-points w,,,,e,, a, of the 
matter are shifted by the increments dw,, de, Jv,, dv, of their coor- 
dinates, these increments being zero at the -boundary. As functions 
‘) The negative sign has to be added, in order that the tensions are taken 
with the same sign as in Einsretn’s calculation. 
Proceedings Royal Acad. Amsterdam, Vol. XIX. 
