886 
Then the components of the velocity of the matter are: 
a a, a 
“u—_ —* ; ee : en RE, le (6) 
dys Qa, Ass 
If we consider a definite particle of the matter, then it is always 
possible to introduce a special system of coordinates, in which this 
particle is at rest, while at that point the g,, ’s have their normal 
values. Quantities determined with respect to this system of coordi- 
nates will be indicated by the index 0. Now 
Bg a og Oe 
For a line element we have in general 
ds? ‘= — de,’ —dz,° — dn. da! =de dap day. ae 
[454 
and for its projection ds, on the space perpendicular to the world line 
2 2 2 
ds =d — ds, — de, = 2 Yar dag Tt," . Soe 
eid 
y.. being a covariant tensor. In the system of coordinates S° y°,, = 
Yaa = —1, while all other components are zero. Because 
of these properties we easily find a general expression for y,,, if a 
certain tensor is subtracted from g,,. In-order to find this tensor 
we first form the contravariant tensor a.,¢-, from the velocity 
vector «4, and then divide it by the scalar quantity = Gag Ans Ups. 
Z., [3 
—— 
0 
d 22 
Of the tensor 
A74 Arg de. dr- 
DN PEREN ds ds 
a.s 
| 
which we obtain in this way, only the component (,,) differs from 
zero; it is equal to 1 so that it can neutralize ge. In order to 
“44 
render’ the tensor covariant it must still twice be multiplied by 
the covariant fundamental tensor. We then find for y,,: 
=) 540-4 
sis = ian OS ga ge ee ee 
ae = Yuga a 
ANC 
sl 
For the scalar quantity in the denominator 
2 
Sed Wet eee (10) 
zp 
Now Hererorz’s considerations from $ 5 of his article may easily 
be generalized as much as is necessary for our case. HmreLorz 
supposed a kinetic potential fff | 3,18, dE 56 to exist. Let us do 
