186
DOC. 30 FOUNDATION OF GENERAL RELATIVITY
first
place
or

ikheMS
*
t:

£)]•
With
the
choice of
coordinates
which
we
have
made,
the
term
deriving
from
the last
term in
round brackets
disappears
by reason
of
(29).
The other
two
may
be
combined,
and
together,
by (31),
they
give
i
so
that
in consideration
of
(54), we
have
the
identity
'bXa'bX
. .
(55)
From
(55)
and
(52a),
it
follows
that
55±32_a
. .
.
(56)
0Xy
Thus
it
results
from
our
field
equations
of
gravitation
that the
laws of conservation of
momentum and
energy are
satisfied.
This
may
be
seen
most
easily
from
the
consider
ation
which
leads to
equation (49a); except
that
here,
instead
of
the
energy
components
ta
of
the
gravitational field,
we
have
to introduce the
totality
of
the
energy components
of
matter
and
gravitational
field.
§
18.
The Laws
of
Momentum and Energy for Matter,
as
a
Consequence
of the Field
Equations
Multiplying
(53) by
aguv/axo, we
obtain,
by
the method
adopted
in
§
15,
in
view of
the
vanishing
of
g"
a*.
the
equation
K
+

0,
Ix
[26]