76 DOCS.

63,

64

MARCH

1915

dE41/dt

vanishes in

the

static

case.

If

I

multiply

the

equation

by

x

and

integrate

over

the

entire

body,

then

I

(&r~

&r~

&r~\

~ax

ôy

i9zj

dx

dy

dz

=

0

changes

through partial

integration

to

ƒ

%\dx

dy

dz

=

0,

as

Laue has

already

recognized.[3]

Thus it

is

proven

that

for

the

planetary

prob-

lem[4]

a

g11

field

cannot

come

into

consideration.[5]

With best

regards, yours,

Einstein.

64. To

Tullio Levi-Civita

[Berlin,

20

March

1915]

Dear

Colleague,

I

have received

your

letter with

the

counterargument

to

disprove

the tensorial

character

of

1/-g

Euv,

which bases itself

on

the

case

where

among

the

adapted

coordinate

systems

such exist whose

guv's are

constant.[1]

You

say

under

(2)

“This

tensor

is,

to

the

contrary,

not

identical

to

zero

for

all

adapted

coordinate

systems;

this

is especially

obvious in Newton’s

case.”[2]

I

do

not

consider

this

correct, however.

It should be noted that, in

general,

it

is not

possible

to

alter

through

transformation

of

the

coordinates

any given

guv

field

into

one

in

which

the

guv's

are

constant. This

will

always

be

impossible

for

parts

of

a

Newtonian

field

containing masses,

for

ex.;

this

is

also

generally

true

of mass-free

regions, incidentally.

I

believe

that

the

proof

or

disproof

of

the statement

quoted

from

your

letter

is just

as

problematic as

the

proof

or

disproof

of

the

general

statement of

the

tensor

character

of

/Euv-g.

With cordial

greetings

and

hoping

for

a

prompt

reply, yours,

A.

Einstein.