252 DOC.
10
RESEARCH NOTES
[111]Einstein
convinces himself that
g44
is
the
only nonconstant
metrical coefficient
in
a
static
field,
an
assumption clearly
stated
in
Einstein and
Grossmann
1913 (Doc.
13),
p.
7. He
asserts
that the
space-time components
g14, g24,
etc.,
vanish. From the fact that the accelera-
tion of fall of
all
bodies
is
the
same
it follows that the
force
[eq.
161]
on a mass
and
its
energy
[eq. 162]
must
be
proportional.
Unless
all
space-space components
of the metric
are
constant,
however,
the ratio between force
and
energy
will
vary
according to
the
velocity
of the
mass.
Einstein's
statement
that
"g11,
g22
etc.
vanish"
actually
refers
to
the derivatives of these
quantities.
This
simplified
form
of
the
static metric
is incompatible
with the harmonic coordi-
nate condition,
which
no
longer appears in
the notebook.
[112][Eq.
164]
corresponds
to
the
x-x
component
of the
gravitational field
stress tensor
of
Einstein 1912d
(Doc. 4),
p.
456.
Equation
(5)
on p.
456 of this
paper
is
reexpressed
as
[eq.
140]
in
terms
of the coefficients of the
corresponding
metric
[eq.
163]
by means
of the
substitutions
c
=
J-G,
g44
=
c2,
y44
=
1/c2.
[p. 43]
dY X'
^iv
dx'
=
0
(IV
=
1
a
XIlvi3x.
{^lioc^vßYaß}
®
=
5^a1k7i
'a
+
XVvi
dPliaPvß
dX:
^
5Pvß
^P\x a
verschwindet,
wenn
dp
*
|1(X
=
ZYa;-^-
+
IyaßV
5/7vß
Funkt. Det.
=
1.
dx:
=E6(raiPma)-
P
H,,
a
'K,
+
^aß^(iaPv$ ^x
** dx:
0
^
^vß
^ai~dx~
+y*-VPvunvi-fo~
dxf^i(xiP^a
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