178 DOC.
182
JANUARY
1916
the
conservation
equations
Y-21
+
ypr
=
0
are
already
a
consequence
of the
field
equations.
Proof
roughly
as on
the
postcard
you
did
not
understand.[5]
I
repeat[6]
ZSR/DX-Zruov=-k(Tm-1/2gimT)...
E^
+
Erir.-a..
(1)
(2)
1
+
2^^T'mdxadg*
The
contention is
that
from
(1)
it
follows
that
the four
spatial
functions
Ao
vanish.
Proof: If
you multiply
(1)
by
gim
and
perform
a
summation
over
i
and
m,
you
obtain
through computation
Ed2gaB/dxadxB-k(T+t)=0...
(3)
If
you
also
multiply
(1)
by
gmu,
sum
over
m,
and have
the result
undergo
the
operation
Ed/dxy,
then
you
obtain
with
the
aid
of
the
equation
drawn from
(1)
and
(2)[7]
E^X
+
tt)-A
the
equation[8]
_d_
dx"
V-
d2Cß
,rr
,
^
E
-
T
+
*)
aß
dxndxr-
+
2kAu
=
0...
(4)
From
(3)
and
(4),
Au
=
0
results. Thus the conservation law of matter
is
a
consequence
of
(1).
You will
find
the
necessary
hints for
performing
the math
in
both
of
the
brief
papers.[9]
(There
must
naturally
be
a
less
bumpy
method
for
this
proof,
but
I
do not know
it.)[10]
In
this
dependence
of
both
fund.
equa, systs.
also lies
your “inevitability”
guarantee requirement
for
the additional
term[11]
-1/2gimT.
The
tensor
character
of
the
right-hand
side
requires
generally[12]
-K(Tim
+
XT),
(A
=
number)