DOC.

561

JUNE

1918 583

are

established

up

to

relatively

infinitesimal

orders,

and these

quantities

form

a

four

vector.-

Now I

introduce

through

linear

transformation

a

second reference

system

K'.

Then

according

to

(2)

for

the

transformation[6]

J'

=

yi_

dxß

A

a

dxa

dx’e

ß

y

Üï^Axdxa

A

applies.

This

formula

applies

also

when

I choose

the

unprimed

system

in such

a

way

that

Ax1

=

Ax2

=

Ax3

=

0.[7]

In this

case,

it

takes

on

the

simpler

form[8]

ji

_

sy

dxß

(3)

Now, our proof

would be finished

if

this formula

were

proven

also for

the transition

from reference

system

K'

to

a

third

K".[9] This is

easily

done.

According

to

(3)

we

also have

pi

__

sy

dxß

On

the other

hand,

we

have

through

the

inversion

of

(3)

JB=Edx'TJ/dxB.

Hence,[10]

jii

_

^xß

v

_

dx'T

,

°-fTdxßdx"a

T_Z-9x"

T'

Thus

the

proof

is

complete.

With

all due

respect

and

greetings

from

yours truly,

A.

Einstein.

[5]Recipient’s

label: “world

strand.”

[6]Recipient’s

comment: “Instead of

this

it

ought

to be

possible

to

show

that

all

AaB's,

whose

a’s

differ from

4, are zero.

Yes!”

[7]Recipient’s

comment:

“E.

seems

to

compensate

the

first

error

with the

2nd.

(I

really

do not have

Ax1, Ax2, Ax3 freely

at

my disposal anymore;

they

are

given by

the

integration domain,

and

therefore

0

but

very

small relative to

Ax4.)”

[10]Recipient’s

comment:

“What about the

difference between

cogradient

and

con-

tragradient?”