DOC. 17 GRAVITY AND MATTER 85
A.
EINSTEIN
195
we
obtain from
(4a) by
inner
multiplication
by
Ja,
on
account
of
the
antisymmetry
of
duv,
the relation
DG
dxv
_
q
Dav
ds
(8)
Thus the
scalar
of
curvature
is
constant
on
every
world-line
of
the
motion
of
electricity. Equation (4a)
can
be
interpreted
in
a
graphic
manner
by
the
statement:
The scalar
of
curva-
ture
plays
the
part
of
a
negative pressure which,
outside of
the
electric
corpuscles,
has
a
constant value
G0.
In the
in-
terior
of
every corpuscle
there subsists
a
negative
pressure
(positive
G
-
G0)
the
fall of which
maintains the
electro-
dynamic
force in
equilibrium.
The minimum
of
pressure, or,
respectively,
the
maximum
of
the
scalar
of
curvature, does
not
change
with time
in
the interior
of
the
corpuscle.
We
now
write the
field
equations (1a)
in the form
(G~~
-
~g~G)
+
~q~VGO
-
+
-
G0)) (9)
On
the other
hand,
we
transform the
equations
supplied
with
the
cosmological
term
as
already
given
G""
-
\g»v
=
-
«(T^
-
igßVT).
Subtracting
the scalar
equation multiplied
by
1/2,
we
next
obtain
(G^i*
1.7V
)
+
g
¡XVA- -
«T
¡iv
Now
in
regions
where
only
electrical and
gravitational
fields
[17]
are
present,
the
right-hand
side of
this
equation
vanishes.
For
such
regions
we
obtain,
by forming
the
scalar,
-
G
+
4\
=
0.
In
such
regions,
therefore,
the scalar
of
curvature is
constant,
[18]
so
that
A
may
be
replaced by
1/4G0.
Thus
we
may
write the
earlier field
equation (1)
in the
form
[19]
Gm"
-
igv"G +
\g¡xVG0
=
-
*T
fiv
(10)
Comparing
(9)
with
(10),
we see
that there
is
no
difference
between the
new
field
equations
and the earlier
ones,
except
that instead
of
Tuv
as
tensor
of
“ gravitating mass ”
there
now
[16]