atoms in molecules is the ten-millionth part of 125 of an inch. Gaudin follows Thomson in the attempt to give some sensible notion of the truly amazing minuteness of a dimension like this. He calculates, upon this estimate, the number of chemical atoms contained in about the size of a pin's-head, and he finds that the number requires for its expression the figure 8 folio wed by twenty-one ciphers. So that, if we attempted to count the number of metallic atoms contained in a large pin's-head, separating each second ten millions of them, we should need to continue the operation for more than 250,000 years!
There are, then, atoms in matter, and atomism is a fact, whenever we rest in the affirmation of the existence of atoms. But these are not the real principles, the simple and irreducible elements of the world. After decomposing sensible matter into atoms, we must subject the latter to an analysis of the same kind. Let us, then, consider any two heterogeneous atoms whatever, an atom of iron and an atom of hydrogen, for instance, and examine in what respect they can really, essentially, differ from each other. What is it which at bottom truly distinguishes these two atoms, as atoms? It is not any peculiarity of form, solidity, fluidity, hardness, sonorousness, brightness, because these properties evidently depend on the mutual arrangement and disposition of atoms, that is, because they are not relative to the individuality of each atom, but to that of the whole which they form by being grouped together. Neither is it any caloric property, or optic, or electric, or magnetic one, because these properties result from the movements of the ether, within the more or less complex aggregate of the respective atoms of these two substances. Now, if these atoms, taken separately, differ from each other in virtue of none of the properties just enumerated, they can only be dissimilar as regards two attributes, dimension and weight; but difference in weight results from difference in dimension, and is not a qualitative difference, but simply a quantitative one. Consequently, any two heterogeneous atoms whatever, compared together, as atoms, have scarcely any of the differential attributes peculiar to the groups which they make up by aggregation, and represent no more than two distinct functions, two different values of one and the same initial matter, of one and the same primitive quality or energy. This simple demonstration establishes the unity of substance, not as a more or less plausible physical hypothesis, but as a metaphysical certainty, alike underivable and necessary. If we add now, reserving the demonstration for a later period, that dimension, corporeal extension itself, as Leibnitz said and as Magy has lately proved, is only a resultant of force, it will become evident that matter, in the last analysis, is reduced to force.
Tyndall, in his biography of Faraday, tells us that one of the favorite experiments of this physicist gives a true image of what he was: "He loved to show how water, in crystallizing, eliminates all foreign substances, however intimately mingled they may be with it.
