DOC. 14

EINSTEIN

AND

BESSO MANUSCRIPT 437

[p. 38]

(Einstein)

[174]Page

number

in

Besso's hand

(see

note

166).

[175]On

[p.

38],

the

effect of

a

rectilinear acceleration rather than

a

rotation of

a

spherical

shell

on a

test particle

at its center is

studied. Similar calculations

in the context

of Einstein's

1912

theory

can

be

found

in

Einstein

1912e (Doc.

7).

The result of

the

calculation

on [p. 38]

is-in

accordance

with the

requirements

of

the

relativity

of inertia

(see

Einstein

1912e

[Doc.

7], p. 40;

Einstein 1913c

[Doc. 17],

p.

1261)-that

the

induced acceleration of

the

test particle

is proportional

to the acceleration of

the shell.

The calculation

proceeds

as

follows. Consider

the

equation

of motion dJx/dt

=

sx

(see

[p.

8],

[eqs.

48-49];

Einstein and Grossmann

1913

[Doc. 13], p. 7, eqs.

5-8;

Einstein 1913c

[Doc. 17],

p.

1260,

eq.

1b")

for

a

point

mass m

at

rest at

the

center

of

the shell.

Since

g44

=

0

and dxi/dt

=

0,

sx

=

0

([eq.

235]).

Hence, the

equation

of

motion reduces

to [eq.

236]. From

[eq.

236] it

follows that

x

=

dg14/dt,

the first

part

of

[eq. 238] ([eq. 237]

should

be

differentiated

with

respect to

t).

When

the

expression

for

g14(x)

given

in

note 169

is

used to

evaluate

the field

produced at

the center

of

the shell

when

the shell

undergoes

a

rectilinear

acceleration X,

one

finds

g14(x

=

0)

=

k/4tz(MX/R).

This

is

the

expression

that

is

inserted for

gl4

in

[eq. 238] (x is

changed into X in

[eq.

239]).

It

follows

that the acceleration

x

of

the test

particle

is

proportional to the

acceleration

X

of

the shell.