DOC.

4

THEORY

OF

STATIC GRAVITATIONAL

FIELD

163

Published

in

Annalen der

Physik

38

(1912):

443-458. Received

23

March

1912, published

23

May

1912.

[1]See

Einstein 1912c

(Doc. 3).

[2]See Einstein

1907j (Vol. 2,

Doc.

47),

§20.

[3]See

Einstein 1912c

(Doc.

3).

[4]See

Born

1909, §5;

see

also

Einstein 1912c

(Doc.

3),

p.

356.

[5]In

all

earlier versions of Maxwell's

equations (in

vector notation) in

Einstein's

published

writings,

"curl"

is

used instead of "rot."

In

his

manuscript

on

the

special theory

of

relativity

(Doc.

1),

he

changes

notation from "curl"

to

"rot"

on [p.

61].

See

also

[pp.

38-39]

of Einstein's

"Scratch Notebook"

(Vol. 3, Appendix A),

where Maxwell's

equations are

written with

"curl"

as

well

as

"rot."

[6]See

Einstein 1912c

(Doc. 3),

p.

359.

[7]"dt" should

be

"dt."

[8]The

second

term

on

the

right

should have

no

factor

1/c.

[9]The

second

equal

sign

should

be

a

minus

sign.

[10]These

equations appear

in

a

similar

context

on [pp.

38-39]

of Einstein's "Scratch

Notebook"

(Vol.

3,

Appendix A).

[11]Einstein

met

Ehrenfest for the

first

time when the latter visited him

in

Prague

from

23

to

29

February

1912 (see

Einstein

to Paul Ehrenfest, 12

February

1912

[Vol. 5,

Doc.

357],

and

Einstein

to Paul Ehrenfest,

10

March

1912

[Vol. 5,

Doc.

369]).

For

an

account

of

this meeting,

see

Klein,

M.

1970,

pp.

175-179.

[12]See

Einstein 1912c

(Doc. 3),

p.

367.

[13]"v"

should

be

"r."

[14]This

expression

for

the

energy density

as

well

as

the

expressions

below for

the

energy

flux

and for the

x

and

y

components

of the

stresses

are

also written

on [p. 39]

of Einstein's

"Scratch

Notebook"

(Vol. 3,

Appendix

A).

[15]See,

e.g.,

Lorentz

1895,

§12.

[16]See

Einstein 1912c

(Doc. 3), pp.

363-364.

[17]See

Einstein 1911h

(Vol.

3,

Doc.

23).

[18]The

problem

of

(special)

relativistic

thermodynamics

was

first

treated

in

Planck 1907

and

is

also discussed

in

Einstein

1907j

(Vol.

2,

Doc. 47),

§15.

Einstein did

not

publish anything

further

on

this

subject.

[19]See

Einstein 1912c

(Doc.

3),

p.

367,

for the conclusion

that,

according

to

Einstein's

theory

of static

gravitation,

the

energy

of

a

system

should

be

proportional

to

c.

[20]Since Einstein had

already

used

equation

number 4

on

p.

449,

the

numbering

of the

equations

becomes inconsistent

at this

point.

[21]See

Einstein 1912c

(Doc.

3),

p.

360,

for the derivation of

the field

equation

(3a).

In fn.

1

on

the

same

page

Einstein

announces a

detailed discussion of

the problems

connected with

this

equation.

On

[p. 38]

of

the

"Scratch Notebook"

(Vol. 3,

Appendix

A)

the

equation

appears

together

with the remark "untenable"

("unhaltbar").

[22]The

reference

is to

equation

(4) on p.

449.

All

further references

to

equations

(3)

and

(4)

concern

the

equations

on

p.

452

(see also

note 20).

[23]See

Einstein 1912c

(Doc. 3),

p.

364.

[24]The

factor "dc" should be omitted.

[25]See

Einstein 1912c

(Doc. 3),

p.

364.

[26]The

conclusion that

the equivalence principle

can

only be valid in infinitely small fields

puzzled

Einstein for

some time;

he mentioned

it,

for

instance,

in

a

letter

to

Paul Ehrenfest

(Einstein

to

Paul

Ehrenfest,

before

20

June

1912

[Vol.

5,

Doc.

409]).

For

a

historical discussion

of

this

problem,

see

Stachel 1980 and Norton

1985.

[27]This

and the

following equation appear

on [p. 39]

of Einstein's "Scratch Notebook"

(Vol.

3, Appendix A),

under

the

heading

"static

gravitational

field"

("Statisches Schwerefeld").

[28]The

equations

in the

second

line

of

(5) are

written

on

[p.

39]

of Einstein's "Scratch

Notebook"

(Vol.

3,

Appendix A).