ject is very small, I can feel
it with my finger, but I cannot distinguish its parts by the sense of
touch. There seem to be limits beyond which I cannot go in either case.

Nevertheless, men often speak of thousandths of an inch, or of
millionths of an inch, or of distances even shorter. Have such
fractions of the magnitudes that we do know and can perceive any real
existence? The touch world of real things as it is revealed in our
experience does not appear to be divisible into such; it does not
appear to be divisible even so far, and much less does it appear to be
infinitely divisible.

But have we not seen that the touch world given in our experience must
be taken by the thoughtful man as itself the sign or appearance of a
reality more ultimate? The speck which appears to the naked eye to
have no parts is seen under the microscope to have parts; that is to
say, an experience apparently not extended has become the sign of
something that is seen to have part out of part. We have as yet
invented no instrument that will make directly perceptible to the
finger tip an atom of hydrogen or of oxygen, but the man of science
conceives of these little things as though they could be perceived.
They and the space in which they move--the system of actual and
possible relations between them--seem to be related to the world
revealed in touch very much as the space revealed in the field of the
microscope is related to the space of the speck looked at with the
naked eye.

Thus, when the thoughtful man speaks of _real space_, he cannot mean by
the word only the actual and possible relations of arrangement among
the things and the parts of things directly revealed to his sense of
touch. He may speak of real things too small to be thus perceived, and
of their motion as through spaces too small to be perceptible at all.
What limit shall he set to the possible subdivision of _real_ things?
Unless he can find an ultimate reality which cannot in its turn become
the appearance or sign of a further reality, it seems absurd to speak
of a limit at all.

We may, then, say that real space is infinitely divisible. By this
statement we should mean that certain experiences may be represented by
others, and that we may carry on our division in the case of the
latter, when a further subdivision of the former seems out of the
question. But it should not mean that any single experience furnished
us by any sense, or anything that we can repr