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.