DOC.

14

EINSTEIN AND BESSO MANUSCRIPT

453

[p.

44]

(Einstein)

[205]The

heading

"Eulerscher Fall"

and

the

page

numbers

on [pp.

43-44]

are

in

Besso's

hand.

[206][Eq.

304]

is

obtained

as

follows:

begin

with

[eqs.

293-294]

on

[p. 43]

(see

note 199;

the

correction

to

[eq.

293]

in

[eq. 301]

is not

taken into

account

and the factor 1/c2

in

the

first term

of

[eq.

293]

is

omitted),

write

gi

=

y4i,

replace

1

by

u

(both

Greek

and

Latin indices

on

[p.

44]

run

from

1

through 3),

use

that

Agu

=

0

(as

follows from

[eq.

299] on

[p.

43]), and,

finally,

write

x4

=

t.

[207]With

the

help

of the

fully antisymmetric

tensor

eaXß,

ga

= y4a

=

x

x)a can

be

written

as ga

= -p£axßOxXß.

Substituting

Gaß

=

1/2\saxßOx

into

this

expression, one

arrives

at

[eq.

305].

When

[eq.

305]

is

substituted

into

[eq.

304],

the latter

equation

turns

into

[eq.

306].

Since

xß

is arbitrary,

[eq.

306] implies

[eq.

307].

Since

Gaß

is

antisymmetric (as

is

clear from

the

explicit

definition

given

above),

[eq.

307]

reduces

to

[eq.

308].

[208]From

the

antisymmetry

of

Gaß

and

from

[eq.

310], it

follows that

[eq.

308] can

also be

written

as [eq

309]. Notice, however,

that

[eq.

310]

is not

automatically

satisfied,

as one

verifies

by

substituting

Gaß

= 1/2saxßOx

(see note 207)

into the

equation.

[209][Eq.

311]

gives

the

x-component

of

curl

g,

where the

components

of

g

are

defined

in

[eq.

305]

(curl

g

also

occurs

in

[eq.

137]

on [p.

20]

and

in

[eqs.

227-228]

on

[p.

37]).

Since

Gaß

depends

only

on t

and

not

on

x,

curl

g

reduces

to

the

quantities

defined

as

yi

in

[eq.

312].

[210]Subtracting

[eq. 309]

from

[eq.

308], setting

u

=

3

and ß

=

2,

and

using

[eq.

312],

one

arrives

at

an

equation closely resembling

[eq.

313].

The minor

discrepancies seem to

be

due

to

trivial

errors.

[211]Comment

in

Besso's hand.