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.