DOC. 42 SPECIAL

AND GENERAL RELATIVITY 321

78

Relativity

transmits this motion

to

the

body

attached

to

it.

The

tension

of

the

rope

is

just large enough to

effect

the

acceleration of the

body.

That

which determines the

magnitude

of the tension

of

the

rope

is

the inertial

mass

of the

body."

Guided

by

this

example,

we

see

that

our

extension of

the

principle

of rela-

tivity implies

the

necessity

of

the

law

of

the

equality

of

inertial

and

gravitational

mass.

Thus

we

have obtained

a

physical

interpretation

of this

law.

From

our

consideration

of

the accelerated chest

we see

that

a

general theory

of

relativity must yield important

results

on

the

laws

of

gravitation.

In

point

of

fact,

the

systematic pursuit

of the

general

idea

of

relativity

has

supplied

the

laws

satisfied

by

the

gravitational

field.

Before

proceeding

farther, however,

I

must

warn

the

reader

against

a

misconception

suggested

by

these considerations. A

gravitational

field

exists for

the

man

in

the

chest,

despite

the fact that

there

was no

such

field for

the

co-ordinate

system

first

chosen. Now

we

might easily suppose

that the

existence

of

a

gravitational

field

is

always

only

an

apparent

one.

We

might

also

think

that,

regardless

of the kind

of

gravitational

field which

may

be

present, we

could

always

choose another

reference-body

such that

no

gravitational

field

exists with reference

to

it.

This

is by

no means

true

for all

gravitational

fields,

but

only

for those

of

quite special

form.

It

is,

for instance,

impossible to

choose

a

body

of

reference such

that,

as

judged

from

it,

the

gravitational

field of the earth

(in

its

entirety)

vanishes.

We

can now

appreciate why

that

argument

is

not

convinc-

ing,

which

we

brought

forward

against

the

general principle

of

relativity at

the

end of Section

18.

It

is

certainly true

that the