242
DOC.
248 AUGUST
1916
I
thank
you
heartily
for
kindly
communicating
to
me
the
device
by
which
you
make
the
terms
Giklmgik,
lm
of
(-g)1/2C
disappear
by replacing
them with
dGiklm
7
9ik,
m
•
dxi
Unfortunately,
the
tvo’s
which this
method
provides
are
unacceptable; indeed,
the
10
eqs.
of
gravitation
deduced from
S
ƒ
(L*
+
M)dr
=
0
will not
be
invariant for all
the
chang[es]
in variables
x1,
x2,
x3, x4.
Therefore,
one
will obtain,
in
general:[3]
0abl
±
0abL*.
Thus
(chapter VII,
(352))[4]
it
is
necessary
that
dM
0aßl
=
-
dgaß
Hence,
0aßL*
±
-
dM
dg«?'
Thus,
so
that[5]
dL*
one
could deduce
the
“energy
momentum
conservation
law”:[6]
Eg
=VI1.344).
It
is
necessary
to have:
0aßL*
=
-
dM
dgat3
Any
spec[ific]
case
amounts to
leaving
aside
a
certain
number of terms.
The
result of
this
is
that the
only
known
rigorous
method
of
establishing
the
energy
momentum conservation law is
the
one
presented
in
my
note.