ble to the naked eye, like a
grain of lycopodium-dust, must be a million times bigger still.) Such a
grouping is likely to have properties differing not only in degree but
in kind from the properties of simple substances.

For it must not be thought that aggregation only produces quantitative
change and leaves quality unaltered. Fresh qualities altogether are
liable to be introduced or to make their appearance at certain
stages--certain critical stages--in the building up of a complex mass
(_cf._ p. 71).

The habitability of a house, for instance, depends on its possessing a
cavity of a certain size; there is a critical size of brick-aggregate
which enables it to serve as a dwelling. Nothing much smaller than this
would do at all. The aggregate retains this property, thus conferred
upon it by size, however big it may be made after that; until it
becomes a palace or a cathedral, when it may perhaps reach an upper
limit of size at which it would be crushed by its own weight, or at
which the span of roof is too great to be supported. But the
difference, as regards habitability, between a palace and a hovel is
far less than that between a hovel and one of the air-holes in a brick
or loaf, or any other cavity too small to act as a human habitation.
The difference as regards habitability is then an infinite difference.

To take a less trivial instance; a planet which is large enough to
retain an atmosphere by its gravitative attraction differs utterly, in
potentiality and importance, from the numerous lumps of matter
scattered throughout space, which, though they may be as large as a
haystack or a mountain or as the British Isles, or even Europe, are yet
too small to hold any trace of air to their surface, and therefore
cannot in any intelligible sense of the word be regarded as habitable.
One of the lumps of matter in space can become a habitable planet only
when it has attained a certain size, which conceivably it might do by
falling together with others into a complex aggregate under the
influence of gravitative attraction. The asteroids have not succeeded
in doing this, but the planets have; and, accordingly, one of them, at
any rate, has become a habitable world.

But observe that the great size and the consequent retention of an
atmosphere did not generate the inhabitants; it satisfied one of the
conditions necessary for their existence. How they arose is another
matter. All that we have seen so far is that an aggre