DOC. 42 SPECIAL AND GENERAL

RELATIVITY 329

86

Relativity

other,

and

to

the

co-ordinate

system.

Should

we

be

justified

in

saying

that

for

this

reason

electrostatics is overthrown

by

the

field-equations

of

Maxwell

in

electrodynamics?

Not

in the

least. Electrostatics

is

contained in

electrodynamics

as a

lim-

iting case;

the

laws

of the latter lead

directly

to

those

of

the

former

for

the

case

in which the fields

are

invariable with

[45]

regard to

time. No fairer

destiny

could be allotted

to

any

physical theory,

than

that

it should

of

itself

point out

the

way

to

the

introduction of

a more

comprehensive theory,

in which

it lives

on as a

limiting

case.

In

the

example

of

the

transmission of

light

just

dealt

with,

we

have

seen

that

the

general theory

of

relativity

enables

us

to

derive

theoretically

the influence

of

a

gravitational

field

on

the

course

of natural

processes,

the

laws

of

which

are

already

known when

a

gravitational

field

is

absent. But the

most at-

tractive

problem, to

the solution

of

which the

general theory

of

relativity

supplies

the

key, concerns

the

investigation

of

the

laws

satisfied

by

the

gravitational

field itself.

Let

us

consider

this

for

a

moment.

We

are

acquainted

with

space-time

domains which

behave

(approximately)

in

a

"Galileian" fashion under suitable choice

of

reference-body, i.e.

domains in which

gravitational

fields

are

absent. If

we now

refer such

a

domain

to

a

reference-body

K'

possessing any

kind

of

motion,

then

relative

to

K' there exists

a

gravitational

field which

is

variable

with

respect

to

space

and

time.1

The

character

of

this

field will of

course

depend

on

the

motion chosen

for

K'.

According

to

the

general theory

of

rel-

1

This

follows

from

a

generalisation

of the discussion

in

Section

20.