72 DOC.
60 MARCH
1915
purpose you specially
choose
H
=
g11,
and
show
that
in
this
case,
the
value calculated
according
to
(72)
and
(73),
1/-gEdguvEuv,
is
not
an
invariant.
On
page 1069,
however,
it
is
pointed
out
that H
must
be
chosen
in
such
a
way
that
it
is
invariant for
linear substitutions. Without
this
precondition,
formula
(65),
which
is
fundamental
to what
follows,
obviously
is
not
valid.[4]
As
g11
is not
an
invariant for
linear
substitutions,
your counterexample
does not
constitute
a
refutation of
my
stated theorem.-
As far
as
the
first
part
of
your
letter
is concerned, I
do not
see
why
the
conclusion drawn from
(71)
ought
not
apply.
Variation calculations
are always
carried out in
the
way
in which
I
have done it.
I
know
that
JdTE(dguv)...
(71)
is
an
invariant
when
the
boundary
conditions for
the
dguv's are
observed, regard-
less of how
the
dguv's are
chosen.[5]
Now,
let
the
dguv's
differ from
zero
only
inside
an oo
small
area
o.
The
Euv’s
may
be
treated
as
constant in
the
integration.
If
you
set
dr
=
t
Ja
and
ƒdguvdr
=
dguvr,
whereby
the
dguv's
signify
spatial
mean
values
of
the
dguv
terms,
then
it
is
possible
to set
instead of
(71)
EdguvEuv.
The theorem
follows
from
this, taking
into consideration
that
owing
to
the
small-
ness
of
area
o,
the
dguv’s
transform
at
one
place
within
o,
like
the
dguv's,
i.e.,
also
like
the
guv's.-
I
urge you earnestly
to
inform
me
of
your opinion
of
the
proof upon
reconsid-
eration.
With
cordial
greetings, yours very truly,
A. Einstein.
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