although the situations of the parts of that portion might be and probably
were widely different in the two classes. To assert this is of course a
very different thing from asserting that the identity of the two portions
or any parts thereof could have been practically shown by following them
during all their changes of location or state. That cannot be done even in
the case of some simple changes that are effected in a fraction of a
second. For instance, if water from the pail A be mixed with water from
the pail B there is no possible way of telling which pail any given
portion of the mixture came from or in what proportions, yet it is certain
that such portion is identical with a portion of equal mass that recently
occupied part of one or both pails.

How far our certainty as to this is influenced by our ideas regarding the
ultimate constitution of the water is worthy of investigation. All who
accept the molecular theory, for instance, will regard our inability to
trace the elements of a mixture as due to purely physical limitations. A
set of Maxwell's "demons" if bidden to watch the molecules of the water in
pail A, one demon being assigned to each molecule, would be able to tell
us at any time the precise proportions of any given part of the mixture.
But if we should not accept the molecular theory and believe for instance,
that water is a continuum, absolutely homogeneous, no matter how small
portions of it be selected, then our demons would be as powerless as we
ourselves now are to trace the constituents in the mixture.

We are now in a position to ask the question: Is the matter in a mixture
of two continua identical with that of its constituents? The identity
certainly seems of a different kind or degree from that which obtains in
the first case, for there is no part, however small, that was derived from
one pail alone. The mixture is something more than a mere juxtaposition of
elements each of which has retained its identity; it is now of suck nature