DOCS.

77,

78

APRIL

1915

91

as

not

sound.

In accordance

with

my

proof,

let

6guv

=

61guv

+

62guv

with the addition that

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.

Your method of

proof implicitly

assumes,

however,

that the

quantities

you

have

designated

for

huv

remain finite

at

vanishing xv.

For

were

this

not

the

case, your quantities ƒKux3vdr

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

already

discussed earlier.

Awaiting

your

answer as

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.