DOC.

492

MARCH

1918 513

are

devoid of content.

What

they

contain

is

a

part of

the

content

of

the

field

equations[2]

K+

*& =

o.

This

naturally

also

applies

to

equations equivalent

in substance to

(1)

y-

9C%

+

g)

"

^

dr

(2)

The

value of

(2)

against

(1)

lies

in

the

fact

that it

provides

three

integral

relations.

If

a

physical system exists,

at

the

spatial

boundaries

of

which

the

Tvo’s

and

tvo’s

always vanish,

then

(2)

yields

d/dx4{/Z4o+:w=o.

The

temporal

constancy

of these four

integrals

is

a

nontrivial

consequence

of

the

field equations

and

can

be looked

upon

as

entirely

similar and

equivalent

to

the

momentum

and

energy

conservation law in

the

classical mechanics of continua.

What

distinguishes

the

tvo’s

from

other

quantities,

which

likewise

are capable

of

giving

relations

of

the

form of

(2),

is

the

circumstance

that

the

tvo’s

depend only

on

the

{uv/o}'s

but not

on

their

derivatives. The

{uv/o}’s

are

the

quantities

analogous

to

the

field

components

in

electrodynamics.[3]

With this letter

I

am

sending you

an

article.[4])

in

which,

with

the

aid

of

equation

(2), a

mechanical

system’s energy

loss

through

the

emission of

gravitational

waves

is

calculated.

The

idea

of

making,

through

a

special

choice of

coordinates,

the

quantities

Z1/2guvTuv

equal

to

zero,

in order to be able to

uphold

the

energy law[5]

zTvo/dxu=0

for matter

alone,[6]

I

also

had

considered sometime

ago.

This route

is

not

feasible,

though, just

because

according

to

the

theory, energy

losses

from

gravitational

waves exist,

which cannot

be

taken

into

account

in this

way.[7]

On

your comparison

of

my

cosmological

consideration to Schwarzschild’s

case

of the

sphere,

I

remark

that

these two

cases

differ

fundamentally

from each

other

in that, for

Schwarzschild,

g44

is

variable and

equilibrium

is

only possible

with

spa-

tially

variable

pressure,

whereas for

me,

matter with

negligible

interior

pressure

is