362

DOC.

42

SPECIAL AND

GENERAL RELATIVITY

120

Relativity

tiness.

The

stellar universe

ought

to

be

a

finite island

in

the

infinite

ocean

of

space.1

This

conception is

in

itself

not very satisfactory.

It

is

still

less

satisfactory

because

it

leads

to

the result that the

light

emitted

by

the

stars

and

also

individual

stars

of the stellar

system

are perpetually passing

out

into infinite

space,

never

to

return,

and

without

ever again

coming

into interaction with

other

objects

of

nature.

Such

a

finite

material universe would

be destined

to

become

gradually

but

systematically impover-

ished.

In order

to escape

this

dilemma,

Seeliger suggested

a

mod-

ification

of Newton's

law,

in

which he

assumes

that

for

great

distances the

force

of attraction between

two

masses

dimin-

ishes

more rapidly

than would result

from

the inverse

square

law.

In this

way

it

is possible

for

the

mean

density

of

matter

to

be

constant

everywhere,

even

to

infinity,

without

infinitely

large

gravitational

fields

being

produced.

We

thus free

our-

selves

from

the distasteful

conception

that the material uni-

verse

ought

to

possess something

of the

nature

of

a

centre.

Of

course

we

purchase

our

emancipation

from

the fundamental

difficulties

mentioned,

at

the

cost

of

a

modification and

com-

plication

of Newton's

law

which

has

neither

empirical

nor

[72]

[73]

1

Proof-According

to

the

theory

of

Newton,

the number of "lines of force" which

come

from

infinity

and terminate in

a mass m

is proportional

to

the

mass m. If, on

the

average,

the

mass

density

p0

is

constant

throughout

the

universe,

then

a

sphere

of volume

V

will

enclose the

average

mass

p0V.

Thus the number of lines of force

passing through

the surface F of the

sphere

into

its

interior

is

proportional to

p0V.

For unit

area

of the surface of the

sphere

the number of lines of

force which

enters

the

sphere

is

thus

proportional to p0

V/f

or to

p0R.

Hence the

intensity

of the

field

at

the surface would

ultimately

become infinite with

increasing

radius

R

of the

sphere,

which

is impossible.