504

DOC. 487

MARCH

1918

4)

For

field

equations

we

have

my

(16a), (16b)

and

your

(7),

(8)

corresponding

to

a)

the

ten:

Kuv

+

aQuv,

=

0,

or

Kvo

+

aQvo

=

0

b)

the

remaining: Qp

=

0.

5)

Between

your

left-hand

sides

the

identities

(17)

of

my

note

hold,

which

I

would

like

to

reproduce

here in

this

way:

ddKZ

+ aQX-a^gQVq,)

^

"

dwv

¿

LM,

" P

6)

Using

field

equations

(b)

I

shall cancel out

the

Qp's

on

the

left

and

right–

hand

sides,

but

only apply

field equations

(a)

on

the

right-hand

side.

I

then

have:

Td{KZ

+ aZ)

__Q

"

dwv

7)

These

equations

naturally

are

physically meaningless,

since

the

Kvo

+

aQvo's

are

of themselves

zero

in

consequence

of

(a);

the

zero

on

the

right-hand

side

does not

result

from

the

differentiation.

It

is just

for

this

reason

that

these

equations

(6) are

not

analogous

to

the

law

of

the conservation

of

energy

in classical

mechanics

ewgeg

=

0).

8)

Now,

however, you set, according

to

(18),

(19)

of

your paper,[9]

lrgwekrg

weg

e4wge

hyjh

ytkyr

rweh

and

you

note in

(17)

that-because

G

is

an

invariant

built

in

a

particular

way

against arbitrary

transformations of

x-

weg

t234t

4t2

wgegw

efe3rtf

9)

Your

equations

hence

distinguish

themselves from

(6)

only

in

that

you

have

inserted under the

differentiation

symbol

a

term

whose

divergence

vanishes

identically. Besides,

this

term

depends only

on

the

guv's

and in

no

way

on

the

qp's.