DOCS.
70,
71
APRIL
1915 85
Affectionate kisses
to
you
and
Tete,
and
regards
also to
Mama, yours,
Papa,
who often
thinks
of
you.
71. To Tullio Levi-Civita
[Berlin,]
8 April
1915
Highly
esteemed
and
dear
Colleague,
I
see
from
your
postcard
of the 2nd
of
April
that
you
are
clinging
to
your
limit
objection.[1]
I
shall
try
to
disprove it, more
in order
gradually
to
come
to know
the
main
point
of
your
reservations.
I
select
the
óguv's
in the
following
way, as
shown in
the
figure
in
cross
section.
Within
an
inner
zone o,
which
makes
up
almost
the
entire
re-
gion,
let
ôguv
be
equal
to
the
constant
7uv.
A boundary
zone
brings
about the
gradual
transition
to
zero.
E-o/E
is
a genuine
break,
which
I
can
make
arbitrarily
small
without
injuring
the
continuity
conditions.
In the
proof,
I
then
proceed
to E
=
0
such
that
I
complete
the transition
at
constant
7uv
and constant
E-o/E.
The
smaller
I
choose
the
quantity
S-o/E,
the
more
accurately
the
equation
=
J
J^ôg^dr
=
^7^2
is
satisfied,
the
closer in
accuracy
is
the
validity
of
the
following
observation.
If
I
divide
the
equation[2]
E_e^
=
E
¡IV
1
3t1 3t1
1
\\xv
ar
dxlldxv
by
the
region
ƒdr
=
E and if
I
select
the
Sguv’s
according
to
the
above deter-
mination,
thus
with
the
aid of
the
indicated
expression
for
the
Auv’s
results
with
greater
accuracy,
the
smaller
the
selected
E-o/E
is:
V-'
ßl/
_
^CT
dx'adx'T
^
\Frg
^
V-Fdx^dxu.