368 DOC.

71

PRINCETON

LECTURES

THE GENERAL THEORY

it

follows from

these

equations

that

inertia

depends,

at

least in

part, upon

mutual actions between

masses.

Thereby

Mach’s idea

gains

in

probability,

as

it

is

an

unsatisfactory

assumption

to

make that

inertia

depends

in part

upon

mutual

actions,

and

in

part

upon

an

independent

property

of

space.

But

this

idea

of

Mach’s

corresponds only to

a

finite

universe,

bounded in

space,

and

not to

a

quasi-

Euclidean,

infinite

universe. From the

standpoint

of

epistemology

it

is

more

satisfying

to

have the mechanical

properties

of

space

completely

determined

by

matter,

and

this

is

the

case

only

in

a

closed universe.

3.

An

infinite universe

is possible

only

if the

mean

density

of

matter

in the universe

vanishes.

Although

such

an

assumption

is

logically possible,

it

is less probable

than the

assumption

that there

is

a

finite

mean

density

of

matter

in

[145]

the

universe.

Translator’s

Notes

{1}

The

“+” should be

"=."

{2}

The second

subscript

should be

UV

not

VU.

{3}

Zv

is

missing preceding

dx2v.

{4}

“at” should be

replaced by

“all.”

{5}

Correct formula

is

Ta44

=

_

1/2

ƒ

-2

df/dx

instead

of gaB

APPENDIXES

have

not

been selected for translation.