DOC. 14

EINSTEIN AND

BESSO MANUSCRIPT

391

[p.

15]

(Besso)

[72]On

[pp.

15-17],

a

summary

of

the

argument

on [pp.

1-14] is given.

This

summary

is

divided into

two parts.

In

the

first

part

the

general strategy

followed

on [pp.

1-7]

for

finding

the

metric

field

of the

sun

is

explained.

This

part

can

be found

on

[pp.

16-17].

The second

part,

on [p.

15], recapitulates

the calculations

on

[pp.

8-14]

for the

perihelion

motion

in

this

field.

Besso's discussion of

his

own

contributions

to

the calculations

([pp.

8-9]

and

[p.

14])

is

much

more

detailed than his discussion of Einstein's contributions.

[73][Eqs.

103-110]

are

in

essence

the main

steps

of the calculation

on

[p. 9].

There

are some

minor differences.

First,

the coefficient of

the A2/r2-term in

g44,

the

one

component

of

the

metric

field

in

[eq.

42]

on

[p.

6]

that

is

responsible

for the

perihelion

motion, is

left undetermined

(see

the

header of

[p.

15]

under

"2"

and

[eq. 106]).

Secondly,

the

A2/r2-term

in

[eq.

108]

is

taken

into

account

whereas

it

was

neglected

in

the corresponding

equation on [p. 9]

([eq.

66]).

This

does

not

make

any

difference,

however,

in

the

end

result. Other than

that,

almost

all

equations

on

[p.

15]

are equivalent

to

equations on [p. 9]:

[eqs.

103-104] to

[eqs.

58-59],

[eqs.

107-108] to

[eqs.

65-66],

and

[eqs.

109-110]

to

[eqs.

67-68].

On

the

left-hand side

of

[eq. 110],

the integral

sign

is

omitted.

[74]The rest

of

[p.

15]

summarizes the calculations

on [p.

14].

With

the

help

of

[eq.

84] on

[p.

11],

[eq.

110]

for the

angle

between

perihelion

and

aphelion

is

expressed

in terms

of the

roots

of the

polynomial

under the

square root sign

in

[eq.

110]

(see

the

first

step

in

[eq.

114]). Using

[eqs.

111-113]-equivalent to

[p.

14],

[eqs.

98-100] (see notes 68 and

69)-for

these

roots,

one

arrives

at

the

final

expression given

in

[eq. 114].

For

n

=

3/8,

the value of

n

for the metric

field

of

the

sun

in

[eq. 42] on

[p.

6]

(see

[eq. 106]

and

note 73), this

expression

is

seen to

be

equivalent

to

the

expressions

for the

angle

between

perihelion

and aphelion

given

in

[eq.

101]

on [p.

14]

(F

is

defined

in

[eq. 61]

on

[p. 9] as Bc20/E).