DOC. 14

EINSTEIN

AND BESSO MANUSCRIPT

375

[p. 8]

(Besso)

[34]See the

editorial

note,

"The Einstein-Besso

Manuscript

on

the

Motion of

the

Perihelion of

Mercury,"

sec.

II.1b, for

a

brief outline of

the

calculations

on [pp.

8-15].

The

page

and

equation

numbers

given on [p.

8]

all

refer

to

Einstein and Grossmann

1913

(Doc. 13).

[35][Eq.

48]

is the

x-component

of

the

Euler-Lagrange equations

for

a

point

mass m

in

an

arbitrary

metric

field.

Jx

is

defined

as

dH/dx

and

&x as

dH/dx, where H

=

-m

ds/dt

is the

Lagrangian. Inserting eqs.

7

and

8

from Einstein and Grossmann

1913 (Doc.

13),

p.

7,

into

[eq.

48],

one

obtains

[eq. 49].

For

a

point

mass

moving slowly in

a

static

metric

field,

[eq.

49]

reduces

to

[eq. 54].

[36][Eq. 50]

is the

equation

for

the

Hamiltonian of

a mass

point

m

in

an

arbitrary

metric

field.

This

equation

is

copied

from

eq.

9

in

Einstein and Grossmann

1913

(Doc.

13), p.

7.

For

a

unit

point

mass

in

a

static metric

field,

[eq. 50]

reduces

to

[eq. 51].

The minus

sign

in

[eq. 51]

should

be

a

plus

sign.

This mistake

is

corrected

in

[eq. 55].

[37][Eq. 52]

for ds/dt

is copied

from

eq.

5

in

Einstein and Grossmann

1913

(Doc. 13), p.

7.

Inserting

[eq. 42]

for

the

metric

field

of

the

sun

into

[eq. 52]

and

neglecting terms

smaller

than

of order

A2/r2,

one

arrives

at

[eq.

53].

[38]As

a

consequence

of

[eq.

54]

one

has

[eq.

56],

which in the

manuscript

is

called

the

area

law ("Flächensatz";

for

a

discussion of

[eq.

56],

see

the

editorial

note,

"The Einstein-Besso

Manuscript

on

the

Motion of

the

Perihelion of

Mercury,"

sec.

II.1b).

In

[eq. 57]

the

so-called

"area

velocity"

f

("Flächengeschwindigkeit")

is

introduced. The

constant

B

multiplied

by c0

is

called

the

"area

law

constant"

("Flächensatzkonstante").