110

DOC.

22

ADDENDUM TO DOC.

21

Based

upon

this

system

one

can-by

retroactive choice of

coordinates-return

to

those laws which I established

in

my

recent

paper,

and without

any

actual

change

in these

laws,

because it is clear that

we

can

introduce

a new

coordinate

system

such

that relative to

it

V-g

=

1

holds

everywhere.

Sim

then vanishes and

one

returns

to

the

system

of

field

equations

Ruv

=

-KTuv

(16)

of the

recent

paper.

The formulas of absolute differential calculus

degenerate exactly

in the

manner

shown in said

paper.

And

our

choice

of coordinates still allows

only

transformations of determinant

1.

The

only

difference in content between the field

equations

derived

from

general

covariance and those

of

the recent

paper

is that the value

of

L-g

could not be

prescribed

in the latter. This value

was

rather determined

by

the

equation

{1}

a

_____

=

-KET:.

Xa

Xp

U

(21a)

This

equation

shows that

here

yf-g can

only

be

constant

if

the scalar of the

energy

tensor

vanishes.

Under

our

present

derivation

yf-g

=

1

due

to

our arbitrary

choice of

coordinates.

The

vanishing

of the scalar of the

energy

tensor

of

"matter" follows

now

from

our

field

equations

instead

of

from

equation (21a).

The

generally

covariant

field

equations

(16b),

which

form

our

starting point,

do

not

lead

to

a

contradiction

only

when the

hypothesis,

which

we

explained

in

the

introduction,

applies.

Then, however,

we are

also entitled

to

add to

our previous

field

equation

the

limiting

condition:

v/-g

=

1.

(21b)

Additional

note

by

translator

{1}

The

"dxa"

inside of the

parentheses

has been corrected to

"dxß."