In many physical reasonings and mathematical calculations we are
accustomed to argue as if such substances as air, water, or metal,
which appear to our senses uniform and continuous, were strictly and
mathematically uniform and continuous.
We know that we can divide a pint of water into many millions of
portions, each of which is as fully endowed with all the properties of
water as the whole pint was; and it seems only natural to conclude
that we might go on subdividing the water for ever, just as we can
never come to a limit in subdividing the space in which it is
contained. We have heard how Faraday divided a grain of gold into an
inconceivable number of separate particles, and we may see Dr Tyndall
produce from a mere suspicion of nitrite of butyle an immense cloud,
the minute visible portion of which is still cloud, and therefore must
contain many molecules of nitrite of butyle.
But evidence from different and independent sources is now crowding in
upon us which compels us to admit that if we could push the process of
subdivision still further we should come to a limit, because each
portion would then contain only one molecule, an individual body, one
and indivisible, unalterable by any power in nature.
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