DOC. 14 EINSTEIN AND

BESSO

MANUSCRIPT 469

[p. 52]

(Besso)

[241][p.

52]

is

the

verso

of

[p. 51].

[242]On

[p.

52],

deleted

in its

entirety,

three different

attempts

are

made

to

recover

the relation

k

=

(8n/c2)K

(see

[p.

1],

[eq. 3])

between the

gravitational constant

K in

Newton's

theory

and

its

counterpart

k

in

the "Entwurf"

theory through

the consideration of

(slow

motion

in)

the

weak

field of the

sun

in both theories. Besso

may

have done these calculations in connection

with

[eqs.

361-362]

on [p.

53],

where the relation between

K and

the

gravitational constant

k

in

the Nordström

theory

is

derived.

Only

the third of the

attempts

on [p. 52]

succeeds.

In

the

first

attempt (see

[eqs.

346-347]),

the Newtonian

potential

for

the gravitational field

of the

sun is

set

equal

to

minus

(1)Y44.

[Eqs.

352-353]

give

the Newtonian

potentials

0i

and

(pa

for the interior

and exterior

field

of the

sun

conceived of

as a

sphere

of

uniform

density

p,

radius

R,

and

total

mass

M.

A factor pK

is

omitted

on

the

right-hand

side of

[eq. 352].

In

checking

that

[eq.

352]

is

a

solution of the Poisson

equation,

the

relation

A0

=

d2(j)/dr2

+ (2/r)d(j)/dr

is

used

(see

note

12).

An

expression

for

(1)Y44

can

be

read off from

[eq. 354],

the solution of the "Entwurf"

field

equation

[eq. 346]

for this

case (see [eqs. 2, 4, 6] on [p.

1]).

The result of

comparing

(pa

and

(1)Y44

is

k

=

4jtc2K

([eq.

347]).

In

the second

attempt (see

[eqs.

348-349]),

the Newtonian

force

on a

test particle

of

mass m

in the

gravitational field

of

the

sun

is set

equal

to

the force

kx

=

–1/2m(dg44/dx)/

g44 given

by

the "Entwurf"

theory

(g44 can

be

read off

from

[eqs.

5-6]

on [p. 1]).

This

yields

k

=

(8n/c)K. In

the third

attempt (see

[eqs.

350-351]),

the

equation

of motion for

a

test

particle

in

the

field

of the

sun

in the "Entwurf"

theory

is

compared to

its

Newtonian

counterpart

(the same

calculation

can

be

found

on

[p. 13],

[eqs.

94-95]).

This

finally

gives

the

correct

result.