DOC. 24 PERIHELION MOTION OF

MERCURY

243

Lecture delivered

to

the Prussian

Academy

of Sciences

in Berlin,

18

November

1915.

Pub-

lished

in

Königlich Preußische

Akademie der

Wissenschaften

(Berlin).

Sitzungsberichte

(1915):

831-839. Published

25

November

1915.

[1]See

Einstein

1915f

(Doc.

21).

[2]See

Einstein

1915g (Doc.

22).

[3]See

Einstein 1915i

(Doc. 25).

[4]For

historical

background

on

the

problem

of the

perihelion

motion of

Mercury,

see

Rose-

veare

1982. See Earman and Janssen

1993

for

a

historical discussion of this

paper

and

a

detailed reconstruction of Einstein's calculations. More than

two years

before the

publication

of this

paper

Einstein, in

collaboration with Michele

Besso,

had calculated the

perihelion

advance

predicted by

the "Entwurf"

theory,

the

early

version of

general relativity developed

in

Einstein and

Grossmann

1913. The earlier calculation shows

many

similarities with the

one

in

this

paper.

See

Vol.

4,

Doc.

14,

for Einstein and Besso's

calculations,

and

Vol.

4,

the edito-

rial

note,

"The Einstein-Besso

Manuscript

on

the Motion of the Perihelion of

Mercury,"

pp.

344-359,

for

a

discussion.

[5]Freundlich

1915a.

[6]A

minus

sign

is

missing

on

the

right-hand

side of the

first

equation.

[7]"v"

should be "r."

[8]See

Norton

1984

for

a

discussion of the

importance

for the

development

of

general

rela-

tivity

of Einstein's earlier

presupposition

that weak static

fields

should be

spatially

flat.

[9]See

Einstein 1916e

(Doc.

30),

pp.

821-822,

for

a

calculation. The earlier result

was

already

derived from the

equivalence principle

in

Einstein

1911h

(Vol.

3,

Doc.

23),

§4,

and

partially

rederived

in

the framework of the Einstein-Grossmann

theory

in

Einstein 1914o

(Doc. 9),

p.

1084.

The result

given

here

is in

fact

independent

of the later retracted condition

ETuu

=

0

(see

Einstein 1915i

[Doc.

25]).

[10]See

Einstein 1914o

(Doc.

9), p. 1084,

for

an

earlier result for the

redshift, and

Freundlich

1915b for the observations that

at

first seemed

to

confirm the

prediction

but later

proved to

be

inconclusive

(see

Earman and

Glymour

1980b and Hentschel

1994

for historical

discussions).

[11]"T"

should be "T."

[12]"r2" in

the first

term

on

the

right-hand

side should

be

"r3."

[13]A

minus

sign

is

missing

on

the

right-hand

side.

[14]"xr"

should

be

"xr."X

r

[15]A

factor 1/r

is missing

on

the

right-hand

side.

[16]"a"

in

the factor

in

front of the

integral

should

be

"a/2,"

both here and

in

the

next equa-

tion.

[17]The

values for the observed shift found

in

the

contemporary

literature

vary

from

41 to

45

seconds of

arc

per century (see

Earman and Janssen

1993,

pp.

131-132,

for

a

discussion).

In

a

letter

to

Arnold

Sommerfeld,

Einstein mentioned the

great

satisfaction the

agreement

be-

tween

the observed and calculated values

gave

him,

confessing

that

in

the

past

he

had

some-

times been

privately

amused

by

the

"pedantic accuracy

of

astronomy" ("pedantische

Ge-

nauigkeit

der

Astronomie"),

which had been

so

useful

in

this

case

(see

Einstein

to

Arnold

Sommerfeld,

9

December

1915).

[18]See

Newcomb

1895.