DOC.

14

EINSTEIN

AND

BESSO MANUSCRIPT

395

[p. 17]

(Besso)

[82][P.

17]

is

the

recto

of

a

letter from C.-E.

Guye to

Einstein,

31

May

1913

(Vol. 5,

Doc.

443). Only

the calculations

on

the

adjoining page

of

the

letter

are

transcribed. The

importance

of

this

page

for the

dating

of

the

manuscript

is

discussed

in the

editorial

note,

"The Einstein-Besso

Manuscript on

the Motion of the Perihelion of

Mercury,"

sec.

III.

[83]The two

equations to

the far

right,

for the covariant

energy-momentum

tensor

Tpv

and for

the determinant of

a

static,

spherically symmetric

metric

(see the

identical

[eq. 19] on [p.

3]),

are

the

only two equations

on

this

page

in

Einstein's hand. The matrix underneath these

two

equations

is

obtained

by

inserting power

series

expansions

in

1/r for the functions

N,

T,

and

R

into

[eq. 17] on [p. 3],

in

which these functions

were

introduced.

[84]The sentence

under

"b)" is

the

only sentence

Besso devotes

to explaining

the

strategy

for

finding higher-order

contributions

to

the metric

field

of the

sun.

[85]The

purpose

of the calculation

in

Newtonian mechanics that

takes

up

the

rest

of

[p. 17]

appears

to be to show

that the

quantities

q2/c20

and

A/r

are

of

the

same

order of

magnitude.

First,

Newton's second

law is

used

to

derive

energy

conservation

([eq.

115])

and

the

area

law

for

a

planet orbiting

the

sun.

[Eq.

116]

follows from the

area

law

(see

note

116;

va,p

and

da,p

are

the

planet's velocity

and

its

distance from the

sun

both taken

at

aphelion

and

perihelion,

respectively). Setting

the

energy at aphelion equal to

the

energy at perihelion (see

[eq.

117]),

one

can,

with the

help

of

[eq.

116], express

the ratio of

v2

and

2MK/r-or,

equivalently,

q2/c20

and

A/r-at

perihelion

and

aphelion

in terms

of

dp/da.

The

expression given

in

[eq.

118]

is

incorrect, however;

the left-hand

side

should

be

1

+

1-dp/da.

From

[eq.

118],

in

both

its

corrected

and

its

uncorrected

form, it

follows

that,

since

dp

and

da are

of

the

same

order of

magnitude, v2

and 2MK/r

are

of

the

same

order of

magnitude

as

well.