DOCS.
77,
78
APRIL
1915
91
as
not
sound.
In accordance
with
my
proof,
let
6guv
=
61guv
+
62guv
bguv
should be
a
“quasi
constant” whose value
(7uv) re-
mains
unchanged by
the
act of
forming
the
limit
of
the reduction
of
E.[4]
This is
by
no means
to
say
that then
the
values
for the
61guv
and
b2guv
terms
can
increase
more,
the
smaller
E
becomes.
proof implicitly
assumes,
however,
that the
quantities
you
have
designated
for
huv
remain finite
at
vanishing xv.
For
were
this
not
the
and
ƒQux3vdr
would
not
vanish
at
the
limit.
One
can
say
somewhat
illogically:
The smaller
that
E
is,
the
more
you
have
to
struggle
with the
b1guv’s
and
b2guv's
in order
to
squeeze
the
arbitrarily
given
bguv's
out
of
the
small differences in
the
guv’s
within
the
region. Only
when
the
guv’s are
completely
constant does this become
impossible
for
the
reason
discussed earlier.
Awaiting
your
always
with
great
interest,
I
am
with cordial
greet-
ings, yours,
Einstein.
78. To Tullio Levi-Civita
Berlin, 21
April
[1915]
Dear
Colleague,
I
presented
to
you
the
example
H
=
const.[1] not
to refute
your
new
argument
(re.
the
independence
of
the
Auv’s)[2]
but
to
refute
the
original objection.[3]
I
wanted
to
show
(with
this
example),
that
if
ƒ
T^^gbg^dr
is
an
invariant with
freely
selectable
bguv's
vanishing
at
the
boundary,
that then
Tuv is
a
tensor
(actually
ƒTuv/-gbguvdr, which
is
the
same, though).
From
your
postcard
I
see
that
you
attach
great weight
to
your
new
argument
which culminates in
the
statement
that the
Auv’s
vanish, by
which
you
once again
find
the theorem
inapplicable.
But
I
hope
that the letter
I sent off
yesterday[4]
will
convince
you
that
an
impermissible
limit exists there.
With
cordial
greetings, yours,
Einstein.
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