The true significance of the hypotheses of Avogadro and Ampère was long obscured, first on account of their imperfect appreciation by the great leaders of chemical thought during the first half of the nineteenth century—Berzelius, Gay Lussac, Wollaston, and Gmelin—and, secondly, on account of the almost universal practice of deducing atomic weights from purely chemical considerations of equivalence. At the same time, it must be admitted that the recognition of the value of these hypotheses was still further retarded by the seeming anomalies which resulted from a more extended knowledge of the vapour densities of elements and compounds. Thus the vapour densities of mercury, sulphur, phosphorus, and arsenic, as ascertained by Dumas and Mitscherlich, were plainly inconsistent with chemical analogies and the law of Dulong and Petit. So, too, what appeared to be the vapour densities of sal-ammoniac, phosphorus pentachloride, sulphuric acid, calomel, and of other substances that might be mentioned, were not in accordance with the values demanded by other well-ascertained facts. By the middle of the nineteenth century the hypothesis of Avogadro was practically forgotten and the law of volumes ignored. The atomic weights of the elements, and the system of notation universally employed in England and Germany, were based wholly upon equivalents. The anomalies thus created were clearly pointed out by Gerhardt, and subsequently by Laurent who showed how a consistent and harmonious explanation of the facts could be reached by regarding as true equivalents equal volumes—for example, of steam, ammonia, hydrogen chloride, carbon dioxide, marsh gas, etc.; by assuming, in other words, that equal numbers of the molecules of these various substances are contained in equal volumes of the gases, as contended by Avogadro and Ampère. The simplicity and consistency of the new notation gradually won for it the adhesion of chemists. This adhesion was facilitated by the memorable researches of Williamson on etherification, of Gerhardt on the anhydrides, and by the work of Frankland on the radicals; and it reached its logical conclusion when │Cannizzaro│—on the basis of Avogadro’s hypothesis—discussed, in 1858, the true atomic weights of the metallic elements as distinguished from their equivalent values. In certain of its aspects the new table of atomic weights drawn up by Cannizzaro resembled that originally proposed by Berzelius; but the numbers adopted by the Swedish chemist were founded on no uniform or rational basis, and were frequently inconsistent. [Illustration: STANISLAO CANNIZZARO.]