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 such nature that no part of it is identical with any part of A alone or of B alone, nor of A+B, where the sign + denotes simple juxtaposition. It is identical, to be sure, with a perfect mixture of certain parts of A and B, but this is simply saying that it is identical with what it is now, that is, with itself, not with something that went before.
Probably no one now believes that water or any other kind of matter is a continuum, but the bearing of what has been said may be seen when we remember that this is precisely the present stage of our belief regarding energy.
No one, so far as I know, has ventured to suggest what may be termed a molecular theory of energy, a somewhat remarkable fact when we consider the control now exercised over all thought in physics by molecular theories of matter. While we now believe, for instance, that a material body, say a crystal, can by no possibility increase continuously in mass, but must do so step by step, the minimum mass of matter that can be added being the molecule, we believe on the contrary that the energy possessed by the same body can and may increase with absolutely perfect continuity, being hampered by no such restriction.
It is not the purpose of this paper to discuss whether we have grounds for belief that there is such a thing as a minimum quantity, or atom, of energy, that does not separate into smaller parts, no matter what changes it undergoes. Suffice it to say that there appears to be no _a priori_ absurdity in such an idea. At first sight both matter and energy appear non-molecular in structure. But we have been forced to look upon the gradual growth of a crystal as a step-by-step process, and we may some day, by equally cogent considerations, be forced to regard the gradual increase of energy of an accelerating body as also a step-by-step process, although the discontinuity is as invisible to the eye in the latter case as in the former.