And so we have come back to the original hypothesis of Dalton; but we have extended and modified that hypothesis--we have distinguished two orders of small particles, the molecule (of a compound or of an element) and the atom (of an element). The combination of two or more elements is now regarded as being preceded by the decomposition of the molecules of these elements into atoms. We have defined molecule and we have defined atom, but before we can determine the relative weights of elementary atoms we must have a means of determining the relative weights of compound molecules. The old difficulty still stares us in the face--how can we find the number of elementary atoms in the molecule of a given compound? The same naturalist who enriched chemical science by the discovery of the molecule as distinct from the atom, placed in the hands of chemists the instrument for determining the relative weights of molecules, and thus also the relative weights of atoms. The great generalization, usually known as _Avogadro's law_, runs thus: "_Equal volumes of gases measured at the same temperature and under the same pressure contain equal numbers of molecules._" Gay-Lussac had concluded that "equal volumes of gases contain equal numbers of atoms;" but this conclusion was rejected, and rightly rejected by Dalton, who however at the same time refused to admit that there is a simple relation between the combining volumes of elements. The generalization of Avogadro has however stood the test of experiment, and is now accepted as one of the fundamental "laws" of chemical science. Like the atomic theory itself, Avogadro's law is an outcome of physical work and of physical reasoning. Of late years the great naturalists, Clausius, Helmholtz, Joule, Rankine, Clerk Maxwell and Thomson have developed the physical theory of molecules, and have shown that Avogadro's law may be deduced as a necessary consequence from a few simple physical assumptions. This law has thus been raised, from being a purely empirical generalization, to the rank of a deduction from a wide, yet simple physical theory. Now, if "equal volumes of gases contain equal numbers of molecules," it follows that the ratio of the densities of any two gases must also be the ratio of the weights of the molecules which constitute these gases. Thus, a given volume of water vapour weighs nine times more than an equal volume of hydrogen; therefore the molecule of gaseous water is nine times heavier than the molecule of hydrogen. One has therefore only to adopt a standard of reference for molecular weights, and Avogadro's law gives the means of determining the number of times any gaseous molecule is heavier than that of the standard molecule.