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quantity of oxygen. He inferred that chromic acid must contain only three atoms of oxygen, as did sulphuric acid SO3; consequently chromic oxide, which contains half the amount of oxygen, must be Cr2O3, and hence ferric oxide must be Fe2O3. The basic oxides must have the general formula MO. To these results he was aided by the law of isomorphism formulated by E. Mitscherlich in 1820; and he confirmed his conclusions by showing the agreement with the law of atomic heat formulated by Dulong and Petit in 1819.

While successfully investigating the solid elements and their compounds gravimetrically, Berzelius was guilty of several inconsistencies in his views on gases. He denied that gaseous atoms could have parts, although compound gases could. This attitude was due to his adherence to the “dualistic theory” of the structure of substances, which he deduced from electrochemical researches. From the behaviour of substances on electrolysis (q.v.) he assumed that all substances had two components, one bearing a negative charge, the other a positive charge. Combination was associated with the coalescence of these charges, and the nature of the resulting compound showed the nature of the residual electricity. For example, positive iron combined with negative oxygen to form positive ferrous oxide; positive sulphur combined with negative oxygen to form negative sulphuric acid; positive ferrous oxide combined with negative sulphuric acid to form neutral ferrous sulphate. Berzelius elevated this theory to an important position in the history of our science. He recognized that if an elementary atom had parts, his theory demanded that these parts should carry different electric charges when they entered into reaction, and the products of the reaction should vary according as a positive or negative atom entered into combination. For instance if the reaction 2H2 + O2 = H2O + H2O be true, the molecules of water should be different, for a negative oxygen atom would combine in one case, and a positive oxygen atom in the other. Hence the gaseous atoms of hydrogen and oxygen could not have parts. A second inconsistency was presented when he was compelled by the researches of Dumas to admit Avogadro’s hypothesis; but here he would only accept it for the elementary gases, and denied it for other substances. It is to be noticed that J. B. Dumas did not adopt the best methods for emphasizing his discoveries. His terminology was vague and provoked caustic criticism from Berzelius; he assumed that all molecules contained two atoms, and consequently the atomic weights deduced from vapour density determinations of sulphur, mercury, arsenic, and phosphorus were quite different from those established by gravimetric and other methods.

Chemists gradually tired of the notion of atomic weights on account of the uncertainty which surrounded them; and the suggestion made by W. H. Wollaston as early as 1814 to deal only with “equivalents,” i.e. the amount of an element which can combine with or replace unit weight of hydrogen, came into favour, being adopted by L. Gmelin in his famous text-book.

Simultaneously with this discussion of the atom and molecule, great controversy was ranging over the constitution of compounds, more particularly over the carbon or organic Atomic and molecular weights.compounds. This subject is discussed in section IV., Organic Chemistry.The gradual accumulation of data referring to organic compounds brought in its train a revival of the discussion of atoms and molecules. A. Laurent and C. F. Gerhardt attempted a solution by investigating chemical reactions. They assumed the atom to be the smallest part of matter which can exist in combination, and the molecule to be the smallest part which can enter into a chemical reaction. Gerhardt found that reactions could be best followed if one assumed the molecular weight of an element or compound to be that weight which occupied the same volume as two unit weights of hydrogen, and this assumption led him to double the equivalents accepted by Gmelin, making H = 1, O = 16, and C = 12, thereby agreeing with Berzelius, and also to halve the values given by Berzelius to many metals. Laurent generally agreed, except when the theory compelled the adoption of formulae containing fractions of atoms; in such cases he regarded the molecular weight as the weight occupying a volume equal to four unit weights of hydrogen. The bases upon which Gerhardt and Laurent founded their views were not sufficiently well grounded to lead to the acceptance of their results; Gerhardt himself returned to Gmelin’s equivalents in his Lehrbuch der Chemie (1853) as they were in such general use.

In 1860 there prevailed such a confusion of hypotheses as to the atom and molecule that a conference was held at Karlsruhe to discuss the situation. At the conclusion of the sitting, Lothar Meyer obtained a paper written by Stanislas Cannizzaro in 1858 wherein was found the final link required for the determination of atomic weights. This link was the full extension of Avogadro’s theory to all substances, Cannizzaro showing that chemical reactions in themselves would not suffice. He chose as his unit of reference the weight of an atom of hydrogen, i.e. the weight contained in a molecule of hydrochloric acid, thus differing from Avogadro who chose the weight of a hydrogen molecule. From a study of the free elements Cannizzaro showed that an element may have more than one molecular weight; for example, the molecular weight of sulphur varied with the temperature. And from the study of compounds he showed that each element occurred in a definite weight or in some multiple of this weight. He called this proportion the “atom,” since it invariably enters compounds without division, and the weight of this atom is the atomic weight. This generalization was of great value inasmuch as it permitted the deduction of the atomic weight of a non-gasifiable element from a study of the densities of its gasifiable compounds.

From the results obtained by Laurent and Gerhardt and their predecessors it immediately followed that, while an element could have but one atomic weight, it could have several equivalent weights. From a detailed study of organic compounds Gerhardt had promulgated a “theory of types” which represented a fusion of the older radical and type theories. This theory brought together, as it were, the most varied compounds, and stimulated inquiry into many fields. According to this theory, an element in a compound had a definite saturation capacity, an idea very old in itself, being framed in the law of multiple Valency.proportions. These saturation capacities were assiduously studied by Sir Edward Frankland, who from the investigation, not of simple inorganic compounds, but of the organo-metallic derivatives, determined the kernel of the theory of valency. Frankland showed that any particular element preferentially combined with a definite number (which might vary between certain limits) of other atoms; for example, some atoms always combined with one atom of oxygen, some with two, while with others two atoms entered into combination with one of oxygen. If an element or radical combined with one atom of hydrogen, it was termed monovalent; if with two (or with one atom of oxygen, which is equivalent to two atoms of hydrogen) it was divalent, and so on. The same views were expressed by Cannizzaro, and also by A. W. von Hofmann, who materially helped the acceptance of the doctrine by the lucid exposition in his Introduction to Modern Chemistry, 1865.

The recognition of the quadrivalency of carbon by A. Kekulé was the forerunner of his celebrated benzene theory in particular, and of the universal application of structural formulae to the representation of the most complex organic compounds equally lucidly as the representation of the simplest salts. Alexander Butlerow named the “structure theory,” and contributed much to the development of the subject. He defined structure “as the manner of the mutual linking of the atoms in the molecule,” but denied that any such structure could give information as to the orientation of the atoms in space. He regarded the chemical properties of a substance as due to (1) the chemical atoms composing it, and (2) the structure, and he asserted that while different compounds might have the same components (isomerism), yet only one compound could have a particular structure. Identity in properties necessitated identity in structure.

While the principle of varying valency laid down by Frankland is still retained, Butlerow’s view that structure had no spatial significance has been modified. The researches of L. Pasteur,