DOC.
492
MARCH
1918 513
are
devoid of content.
What
they
contain
is
a
part of
the
content
of
the
field
equations[2]
K+
*& =
o.
This
naturally
also
applies
to
equations equivalent
in substance to
(1)
y-
9C%
+
g)
"
^
dr
(2)
The
value of
(2)
against
(1)
lies
in
the
fact
that it
provides
three
integral
relations.
If
a
physical system exists,
at
the
spatial
boundaries
of
which
the
Tvo’s
and
tvo’s
always vanish,
then
(2)
yields
d/dx4{/Z4o+:w=o.
The
temporal
constancy
of these four
integrals
is
a
nontrivial
consequence
of
the
field equations
and
can
be looked
upon
as
entirely
similar and
equivalent
to
the
momentum
and
energy
conservation law in
the
classical mechanics of continua.
What
distinguishes
the
tvo’s
from
other
quantities,
which
likewise
are capable
of
giving
relations
of
the
form of
(2),
is
the
circumstance
that
the
tvo’s
depend only
on
the
{uv/o}'s
but not
on
their
derivatives. The
{uv/o}’s
are
the
quantities
analogous
to
the
field
components
in
electrodynamics.[3]
With this letter
I
am
sending you
an
article.[4])
in
which,
with
the
aid
of
equation
(2), a
mechanical
system’s energy
loss
through
the
emission of
gravitational
waves
is
calculated.
The
idea
of
making,
through
a
special
choice of
coordinates,
the
quantities
Z1/2guvTuv
equal
to
zero,
in order to be able to
uphold
the
energy law[5]
zTvo/dxu=0
for matter
alone,[6]
I
also
had
considered sometime
ago.
This route
is
not
feasible,
though, just
because
according
to
the
theory, energy
losses
from
gravitational
waves exist,
which cannot
be
taken
into
account
in this
way.[7]
On
your comparison
of
my
cosmological
consideration to Schwarzschild’s
case
of the
sphere,
I
remark
that
these two
cases
differ
fundamentally
from each
other
in that, for
Schwarzschild,
g44
is
variable and
equilibrium
is
only possible
with
spa-
tially
variable
pressure,
whereas for
me,
matter with
negligible
interior
pressure
is