In the early days of the atomic theory, in the determinations by Wollaston, Berzelius, and others, attention was chiefly paid to the atomic weights in their aspect of combining numbers. They were primarily of use as factors in chemical calculations, and chemists naturally sought for their simplest expressions, with little regard to theoretical considerations. The laws of Avogadro, of Dulong and Petit, had, indeed, been announced, but the adjustment of the atomic weights to meet their requirements was long neglected. The importance of the adjustment was not realized, for it was obscured by the prevailing dualistic theory, but without it the deeper general relations of the atoms could not appear. Accordingly, a system of chemical formulæ grew up which was based upon a deceptive apparent simplicity of ratios, and by which the theory of valence could not be even suggested. The old formula for water, HO, expressed only its composition by weight, ignoring its composition by volume; it failed, therefore, to accord with Avogadro’s law or to give the slightest hint as to the relations which are now covered by the conception of chemical structure. A part of the existing knowledge was accurately symbolized, but the larger part was ignored, a state of affairs which could not last, although the change came about but slowly. The incentive to reform came from two sources. Physics, in the kinetic theory of gases, gave a new demonstration of the truth of Avogadro’s law, and led chemists to realize more clearly than before the distinction between atoms and molecules. Soon it was seen that the molecule was the smallest particle of matter which could exist as such, while the atom was the smallest particle which could take part in any chemical change. The metaphysical atom was really the modern molecule; the chemical atom was a new conception, due to the discoveries of chemistry alone. This distinction was found to hold good even for elementary bodies, and it became evident that free hydrogen or oxygen must contain two atoms to the molecule, while phosphorus and arsenic contained four. With mercury the atom and the molecule are identical, but in most cases the greater complexity exists, and the elements as we see them are compounds of like atoms with each other. That hydrogen can unite with hydrogen, oxygen with oxygen, carbon with carbon, is a conception to which the early chemists never attained, but which is a necessary consequence of Avogadro’s law in its application to observed phenomena.