DOC.
10
RESEARCH NOTES
269
[137]The equations [eq.
210],
[eq. 211] are
Maxwell's
equations,
written
in
a
form similar
to
Einstein and Grossmann 1913
(Doc. 13),
part
1,
equations (23)
and
(24).
0aß
is
the
con
travariant Maxwell
field
tensor
and
Ta$
its covariant dual,
with the
two
tensors
related
by
[eq.
218].
After the insertion
of
a
factor of
1/2,
[eq. 218]
corresponds to equation
(41)
on p.
34
of Einstein and Grossmann 1913
(Doc. 13)
and
JGe
aß
to
the
completely antisymmet
ric
tensor
e
defined
by
equation
(38) on p.
32
of Einstein and Grossmann
1913 (Doc.
r1r2...rn
13).
[138]The
sum
of
transformationally
similar
forms of
[eq. 212]
and
[eq. 213]
is
the electro
magnetic
field
stressenergy tensor
tva
of
[p. 55]. [Eq. 214]
and
[eq.
215]
are
the covariant
divergences
of
[eq.
212]
and
[eq.
213],
which
yield
[eq. 216]
and
[eq.
217]
on
substitution
from
[eq.
212]
and
[eq.
213].
[eq.
219]
0
vömvvn/
9 ?X
uxn
A
UAm
d
[139]
d
1
3?uv
_
^dxdydz
1
(Kvrw
dxdyd?)

2
jT[ivdxdydz
dxt
=
dt,dr\dC,ds
[p.
58]
ds
dxv
di
di
V
1
dx^dxv
y
2J
dm
P
ds ds Jq dt
1
f
dt\jG
dx.
1 1
^g[iv
dx\i
dxv
dk
dt
^mv
ds
I
2
Jq
dxm
dt
dt it ds
d f
1
gu,vxv\
1 1
dt\
JG
[IV"V
w
dxm
X^Xy
2
JG W
d
f
1
dw
\
1
dw
dt
(jGdxmJ
Jcdxm
[eq.
220]
[139]Einstein integrates
[eq.
219], the
vanishing
of the
divergence
of the
stressenergy
ten
sor
T
over an infinitesimal
volume
dxdydz.
Under the substitution
r
v
Tjiv
=
P
(dxy/ds)
(dxv/ds),
which
represents
a
pressureless fluid,
and
for
constant
p
and
V,
[eq.
219]
reduces
to
the
vanishing
of
[eq.
220],
where
w
=
ds/dt.
On
this
page parts
written
beginning
from different ends of the notebook
meet (see
the
descriptive
note).
For the invert
ed
text
on
this
page,
see [p.
9].