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.