DOC.

14

EINSTEIN AND BESSO MANUSCRIPT

363

[p.

2]

(Einstein)

(2)

[6]On

[p. 2], [eq.

16]

for

g44

is

derived

with

the

help

of the

"Entwurf"

field

equations

in

the form

-Duv

=

K(tuv

+

Tuv)

(for

a

possible

motivation for

this calculation,

see

note 78).

The

44-component

of

this

equation

states that all

second-order

terms in -D44(g)

-k

t44

(see

[eq. 12])

cancel

one

another.

In

[eqs.

8-11],

the various second-order

terms in

this

expression

are

evaluated

(the

expression

is

similar

to

eq. (2)

in

the editorial

note,

"The

Einstein-Besso

Manuscript

on

the Motion of the Perihelion of

Mercury").

First, -D44(g) is

dealt

with.

The

(2)

second-order contribution

to this term

can

be written

as

the

sum

of three

terms:

Ag44,

and the

second-order contributions to

[eq. 9]

and

[eq.

10]

(with u

=

v

=

4).

The minus

sign in

front of

[eq. 10]

should

be

a plus

sign.

These

contributions

are

evaluated with the

help

of

the

first-order

metric

given

in

[eqs.

4-5]

on [p.

1]

and

at

the

top right

corner

of

[p.

2].

The

three

expressions

under

[eq. 9]

all should have

a

plus

instead of

a

minus

sign.

With

the results found for the

terms

in

[eq.

9]

and

[eq.

10],

-D44(g)

turns into

[eq. 8].

Because of

the

sign

error

in

[eq.

10],

the

last

term

of

[eq. 8]

should

have

a

minus instead of

a

plus

sign

(the

sign error

in

evaluating

[eq.

9]

is

corrected

in

[eq.

8]).

Next,

the second-order contributions

to

-Kt44

are

evaluated

(see

[eq.

11],

u

= v

=

4). Inserting

the results found for

-D44(g)

and

-Kt44

into

[eq. 12], one

arrives

at

[eq.

13].

Because of

the

sign

errors

in

[eq.

10]

and

[eq. 8],

the factor

5/4

in

[eq. 13]

should be

-3/4.

(2)

[7]In

[eq.

14]

the

assumption

is

made that

g44

is

of

the

form a/r2,

with

a a

constant.

Inserting

(2)

this form of

g44

into

[eq.

13],

one

arrives

at

[eq.

15],

from which

a

can easily

be

determined.

[8]Inserting the value found for

the constant

a

(see note

7)

into

[eq.

14], one

arrives

at

[eq.

16]

(2)

for

g44.

Because of the

error

in

[eq.

13]

(see

note

6),

the factor

-5/8

should

be

3/8,

in

agreement

with

[eq.

42]

for

guv on [p. 6].

[9]The

material

in

the lower

right

corner

is in

Besso's hand.