a mean density of the ponderable matter in universal space differing
from zero. The smaller that mean density, the greater is the volume
of universal space.

I must not fail to mention that a theoretical argument can be adduced in
favour of the hypothesis of a finite universe. The general theory
of relativity teaches that the inertia of a given body is greater as
there are more ponderable masses in proximity to it; thus it seems
very natural to reduce the total effect of inertia of a body to
action and reaction between it and the other bodies in the universe,
as indeed, ever since Newton's time, gravity has been completely
reduced to action and reaction between bodies. From the equations
of the general theory of relativity it can be deduced that this
total reduction of inertia to reciprocal action between masses--as
required by E. Mach, for example--is possible only if the universe
is spatially finite.

On many physicists and astronomers this argument makes no impression.
Experience alone can finally decide which of the two possibilities
is realised in nature. How can experience furnish an answer? At first
it might seem possible to determine the mean density of matter by
observation of that part of the universe which is accessible to our
perception. This hope is illusory. The distribution of the visible
stars is extremely irregular, so that we on no account may venture
to set down the mean density of star-matter in the universe as
equal, let us say, to the mean density in the Milky Way. In any
case, however great the space examined may be, we could not feel
convinced that there were no more stars beyond that space. So it
seems impossible to estimate the mean density. But there is another
road, which seems to me more practicable, although it also presents