186
DOC.
185
JANUARY
1916
Calculation
aid
[Hilfsrechnung]:
d9TV
__
ax.
=
(because
of
B')
=
~9T£9vi
ea
+
£
thus
dgJ f
ea
1
"C
í
ea
\
dxri
~9‘
l
-
.
r®
1
1
-
1
(r)
The third
of these
terms[12]
cancels out with
the
one
formed
from
the
second of
(2a).
Hence
you
obtain
initially
_d_ OT
ea TO
dxn
9'
a
+
g£
v
a
(6)
From
the
definition
of
taß
and
the
equations
(1)
&
(5)
you
obtain
t?
=
hi?
+
7
(
°T
1
ds’
ß
2
ß
2d
a
dxß
On
transforming
the
second term
according
to
(7)
and
combining
both
the thus
formed terms
tß~2^
OT
eß
K
a
(7)
Disregarding
the
factor
-1/k
and
the
index
designation,
the
right-hand
side
of
(7)
corresponds
to
the
second term in
(6),
so
that
you
can
write
or
dxa a
=
«
(
ex+k)
-
2^(r+
(8)
This
equation is interesting
because
it shows
that the
source
of
the
gravitation
lines
is
determined
solely by
the
sum
Tav
+
tav,
as
must
obviously
be
expected.[13]
(Second sheet)
4)
Proof
that
the
Au’s
vanish.
Now
comes
the
main issue.
a)
If
(8)
is
multiplied
by
dov,
then
your
obtain
the scalar
equation
UT
dxc
a
=
-k(T
+
t).
.
(9)