We shall have to consider in more detail the reasoning whereby Berzelius arrived at this conception of every compound atom as a _dual_ structure (see pp. 209-212). At present I wish to notice this conception as lying at the root of most of the work which he did in extending and applying the Daltonian theory. I wish to insist on the fact that the atomic theory could not advance without methods being found for determining the number of elementary atoms in a compound atom, without clear conceptions being gained of every compound atom as a structure, and without at least attempts being made to learn the laws in accordance with which that structure was built. Before the atomic weight of oxygen could be determined it was necessary that the number of oxygen and of hydrogen atoms in the atom of water should be known; otherwise all that could be stated was, the atomic weight of oxygen is a simple multiple of 8. Berzelius did much to advance chemical science by the introduction and application of a few simple rules whereby he determined the number of elementary atoms in various compound atoms. But as the science advanced, and as more facts came to be known, the Berzelian rules were found to be too narrow and too arbitrary; chemists sought for some surer and more generally applicable method than that which Berzelius had introduced, and the imperious demand for this method at last forced them to recognize the importance of the great generalization of the Italian naturalist Avogadro, which they had possessed since the year 1811, but the meaning of which they had so long failed to understand. Berzelius made one great step in the direction of recognizing Avogadro's distinction between atom and molecule when he accepted Gay-Lussac's generalization that "equal volumes of gases contain equal numbers of atoms:" but he refused to apply this to other than elementary gases. The weights of the volumes of elementary gases which combined were, for Berzelius, also the weights of the atoms of these elements. Thus, let the weight of one volume of hydrogen be called 1, then two volumes of hydrogen, weighing 2, combine with one volume of oxygen, weighing 16, to form two volumes of water vapour; therefore, said Berzelius, the atom of water consists of two atoms of hydrogen and one atom of oxygen, and the atom of the latter element is sixteen times heavier than the atom of the former. Three volumes of hydrogen, weighing 3, combine with one volume of nitrogen, weighing 14, to form two volumes of ammonia; therefore, said Berzelius, the atom of ammonia consists of three atoms of hydrogen combined with one atom of nitrogen, and the nitrogen atom is fourteen times heavier than the atom of hydrogen. While Berzelius was applying these rules to the determination of the atomic weights of the elements, and was conducting the most important series of analyses known in the annals of the science, two great physico-chemical discoveries were announced.