136
DOC.
129
OCTOBER
1915
of
my
article[2] I
had
frivolously
introduced
the
condition
that H
was
invariant
against
linear
transformations.
If this condition
is
relinquished,
then the
following
result
is
obtained.
However
Q
is
selected,
if
the
coordinate
system
is
chosen
so
that
with
a
given
gravitational field
J
becomes
an
extremum[3] through
the
choice
of
coordinates,
or
that
C

B
V'

0
where
S')
awet
trawt
taw34 watwwyhtum
i6j
jy
2^
dgffi
+
2^*
then
dQ
d
Í
8Q\
QgilV
2J
gXa
^
gg^
J
is
always
a
tensor
related
to
such
coordinate
systems.[4]
The
postulate
of covari
ance or
relativity
thus
cannot
serve
to
determine function
Q.
This
determination
is
best based
upon
the
following physical postulate.[5]
The
field
equations
read in mixed form
as
qwrF
QERT2
3tytu56 r6u
=
K*Í
+
w
W4TTUJ
KYUK6uyi67
ymyi
fdf,
the
conservation
equations,[6]
£
d
dxx
K
+
tx,)
=
o.
.
where t* 32ter 4t
uy45u4ui
tjri
fyjr
The
gravitational
field’s
divergence
must
be determined
according
to
the
field
equations
from
the
sum
of
the
gravitational
masses
(energies) of
both
the matter
and the
gravitational
field.
This
applies
in
our
field equation only
when
the
second
term
on
the
righthand
side
is equated
with
the
gravitational field’s
energy
tensor
tAu
multiplied by
k.
Thus
we
arrive at
the
condition
sAu
=
0.
This
is
simultaneously
the
condition for
QdV
being
an
invariant in
relation
to
linear
substitutions.[7] The
latter
situation
would be
trivial
on
its
own.
But
it