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RESEARCH NOTES ON
RELATIVITY 199
gravitation
tensor
when
working
with
Grossmann,
but
had
abandoned
it
when
he
came
to believe,
incorrectly,
that
it
did
not
yield
the correct
Newtonian
limit.
On
[p.
45]
Einstein
briefly
considers another
way
of
generating
a new
quantity,
tensorial under
a more
restricted
group
of
transformations,
that also
has the
form of
eq. (1),
without
the
need for coordinate conditions. But
all
these efforts
are
in vain.
By [pp.
51-52]
Einstein
has
abandoned
the
search for
a
generally
covariant
gravitation
tensor.[29] In
a
neat hand,
Einstein
now
writes
out
a
synopsis
of
the
derivation of
the
gravitational
field
equations
of Einstein and Grossmann
1913
(Doc. 13).
The
remaining pages
of
Part
III
are
given
over
almost
completely
to the
task of
finding a
generally
covariant
formulation of
electrodynamics,
such
as
appears
in
Einstein and Grossmann
1913
(Doc. 13),
pp.
17-20.
[29]For
the
conjecture
that Einstein abandoned
the
gravitation
tensor
of
[p.
44]
because
its
associated coordinate condition
is
incompatible
with
the
metric of
a
Minkowski
space-time
viewed
in
uniformly rotating
coordinates,
see
Norton
1984,
sec.
4.

10.
Research Notes
on a
Generalized
Theory
of
Relativity
ds2
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YjG\\xdx\dx
X
2
X
3
X
4
x1 »11 «21 «31 «41
x2
»12
x3
«13
x4
«14
[ca.
August
1912]
Jt, Xo
Xi
X,
[1]
[2]
1
[p.
1]
X
Pi.
ß
12
ß
13
ß
14
II
G^dxxdx]l =
II
G'podx'pdx'a
^X[L p5ap\a5\i
P
*
G'
ol^OC
"rdxrdxr
PG
pT|
GL,
T1 C,
X
'
=
Y
a
jc
r
Lm4
rs s
analog
GV
=
II5p.ßp^
P
O
d
dxs
II
-M
a
""dx'
r
Spezialfall
für die
Gj[3]
G11
G12
G13
G14
1
0 0 0
0
1
0
0
0 0
1
0
0 0 0
c2
[eq. 1]
cAc
- ^grad2c
[4]
2
c
de
dx
de 2
d2c
2(^0
+
2c--
dx
dx
A
(c2)
=
2grad2c
+ 2cAc
grad
(c2)
=
2cgradc
=
Y
Ay
=
grad
2c
+
cAc
grady
=
cgradc
c2
grad
y
2y~
=
grad
2c
3
grad2r
[eq.2]
iY
4
y