DOC.

47

307

identical clock located

at

the coordinate

origin.

Suppose

an

observer located

somewhere

in

space

perceives

the

indications

of

the

two

clocks in

a

certain

way,

e.g.,

optically.

As

the time

Ar

that

elapses

between

the instants

at

which

a

clock indication

occurs

and at which

this indication is

perceived

by

the

observer is

independent

of

r,

for

an

observer

situated

somewhere

in

space

the clock in

point P

runs

(1

+

\)

times faster than the clock

at

the

c2

coordinate origin.

In this

sense we

may

say

that the

process

occurring

in the

clock, and,

more

generally,

any

physical

process,

proceeds

faster the

greater

the gravitational potential

at

the position of the

process

taking

place.

There

exist "clocks" that

are

present

at

locations

of

different

gravita-

tional

potentials and

whose

rates

can

be

controlled with

great precision;

these

are

the

producers

of spectral

lines. It

can

be

concluded

from

the

aforesaid1 that the

wave

length

of

light

coming

from

the

sun's surface,

which

originates from such

a

producer,

is

larger

by

about

one

part in

two

millionth

than that of light

produced

by

the

same

substance

on

earth. [100]

$20.

The

effect

of

gravitation

on

electromagnetic

phenomena

If

we

refer

an

electromagnetic

process at

some

point

of time

to

a non-

accelerated reference

system

S'

that is

instantaneously

at rest

relative

to

the reference

system E

accelerated

as

above,

then the

following

equations

will hold

according to

(5)

and (6):

1

c

and

p'ux +

W

1 dL1

dV

cJT

~

W

etc

dZ

etc.

In

accordance with the

above,

we

may

readily

equate

the S'-referred

quantities

p',

u',

X',

L', x',

etc.,

with the

corresponding

E-referred

1While

assuming

that

equation (30a)

holds for

an

inhomogeneous

gravitational

field

as

well.