432
DOC.
43 COSMOLOGICAL
CONSIDERATIONS
curvature
of
space
is variable
in time and
place, according
to
the distribution
of
matter,
but
we
may roughly approximate
to
it
by
means
of
a
spherical
space.
At
any
rate,
this
view is
logically
consistent,
and from the
standpoint
of
the
general
theory
of
relativity
lies
nearest
at
hand;
whether,
from
the
standpoint
of
present
astronomical
knowledge,
it
is tenable,
will
not here
be discussed.
In order
to
arrive
at
this
con-
sistent
view,
we
admittedly
had
to
introduce
an
extension
of
the
field
equations
of
gravitation
which
is
not
justified by
our
actual
knowledge
of
gravitation.
It
is
to be
emphasized,
however,
that
a positive
curvature of
space
is
given
by our
results,
even
if
the
supplementary
term is
not
introduced.
That
term is
necessary only
for
the
purpose
of
making
possible a quasi-static
distribution of matter,
as
required by
the fact
of
the
small velocities of
the
stars.
[16]