[2] I do not say we can in any way avoid this far greater difficulty.
Our own material universe cannot even be conceived as limited in any way
save by void space of infinite extent; and it is as impossible for us to
conceive an infinite void as to conceive the infinite extension of
matter. Some modern mathematicians, indeed, assert that space is not
necessarily infinite, but they accompany the assertion (very justly)
with the admission that we cannot possibly conceive any boundary to
space; and as one of the things they ask mathematicians to admit is the
possibility that a straight line indefinitely produced both ways will at
length re-enter into itself, while another is the possibility that in
other parts of the universe two and two may make three or five, they are
not likely, I conceive, to persuade most mathematicians (profoundly
mathematical though they are themselves) that the mystery of infinity
has been as yet entirely expounded.
[3] Of course the reader will understand that when I here speak of the
earth's weight, I mean simply the pressure which would be exerted by the
quantity of matter contained in the earth, if each portion were only
subjected to an attractive force equal to that of gravity at the earth's
surface. The actual force with which the earth is drawn in any
direction, as a weight at the earth's surface is drawn downwards,
depends on the distance and mass of the attracting body as well as on
the mass of the earth; and strictly speaking, we ought not to say that
the earth weighs so many millions of tons, but that she contains so many
million times as much matter as a mass which at her surface weighs a
ton.
[Illustration]