222 DOC. 10 RESEARCH NOTES
[43](p1
and
cp2
are
defined
on
[p. 16].
[44][Eq.
47] and
[eq.
48]
are
identities
produced
by
twice
differentiating
the
identity
yiKgiK
=
4, to
be
used
in
finding
an
alternative
expression
for
cp2.
[45]The term "gravitation
tensor"
suggests
that Einstein
is
seeking
a
tensor,
formed from
the metric
gik
and its derivatives,
for
gravitational
field
equations.
This
interpretation
is
prob-
lematic, however,
because
[eq.
49]
contains
only
first-order derivatives of the
metric,
which
makes
it
unsuitable for
gravitational
field
equations.
An
alternative
reading
is
that
[eq.
49]
is
a
candidate for the
stress-energy tensor
of the
gravitational field,
in
accordance with the older
usage
of the
term
"tensor" for second-rank
structures representing stress-energy-momentum.
The
divergence
[eq.
50]
would then
figure
in
the
energy-momentum
conservation
law.
[p.
18]
[connects
p. 17]
-p2
=
I
d
(
G
a+\
2
?/kTi
3Y"
x
«+,)G*+5
I
StetV
dg
po
V
dx.
1
^Yjk
^£po
a+^
d
3Y,k
^
=
(O+1)C°*5X«IKT Y
---I- G
X
I
8i«Y
dxv
dx
dx dx
v /
Selbstverst.,
weil
dG/dxv
Vektor zweiter
Art.
dx
Subst.
müssen
mehr
eingeschränkt
werden
"
/ /
J /
d
d [46]
^r^o^vpYa)(KidKKe^8e^
dx
Ke'Tfe'e')
[eq. 51]
Yl
171
Im
=
Zjhmdxl
Y, dxm
+
Transformation unendlich klein
1
K-e
i=5' k=e'