These results are evidently to be traced to the failure of Berzelius clearly to distinguish atom from equivalent, and to his refusal fully to accept the distinction between atom and molecule enunciated by Avogadro'. To the great French chemists, DUMAS, GERHARDT and LAURENT, is chiefly due the introduction into general use of a system founded on Avogadro's distinction between atoms and molecules. 10. Dumas early accepted Avogadro's hypothesis; from the specific gravities of gases he deduced the relative weights. of the molecules of these gases: in order to gain more information regarding molecular weights he introduced a new method for finding the specific gravities of gases. By this method he determined the molecular weight of sulphur to be 96, and that of phosphorus to be 124; but from the analogy of sulphur compounds with those of oxygen, from various chemical considerations regarding phosphorus compounds, and, I think we must add, from not keeping Avogadro's statement quite distinct from that of Gay Lussac, Dumas convinced himself that these results were incorrect. The molecular weight of mercury also seemed to be abnormal. Dumas knew of exceptions to the law of Dulong and Petit. Mitscherlich's law of isomorphism remained; but Mitscherlich had himself shewn that the same compound might assume more than one crystalline form, how then could trustworthy conclusions regarding atomic structure be deduced from so vague a law? Dumas, and indeed chemists generally, began to despair of the whole theory of atoms; they tried to find relief in equivalents, so called, and in spite of the many difficulties they gradually tended towards an equivalent notation, a notation which nevertheless they could not make thoroughly self-consistent, but which seemed to involve fewer hypotheses than that founded on the theory of atoms. L. Gmelin even regarded the law of fixity of composition 1 For a more detailed account of the work of Berzelius on atomic weights see Ladenburg's Entwickelungsgeschichte der Chemic, pp. 89–100. 2 For a general account of Dumas' influence on chemical theories see his Leçons sur la Philosophie Chimique, republished in 1878. as only true under special conditions. When the affinity between two bodies is small, they may be united, said Gmelin, in almost any proportions, when the affinity is large they tend to combine in fixed proportions. A number may be given to each element representing the relative amount of that element which combines with other elements to form stable and well-marked compounds; this 'combining weight' may be called 'atomic weight,' but it is only a number. Gmelin adopted 8 as the combining weight of oxygen, 6 as that of carbon &c.: the formula of water on his system again became HO. This notation was at best a compromise, and unsatisfactory, but it was very generally adopted for many years. Inorganic chemistry had failed to introduce an accurate and satisfactory theory of chemical structure: it was now the turn of organic chemistry to attempt the task. II. Among the most ardent followers of the new chemistry introduced by Dumas, were two men, whose names are ever to be associated as those of a brilliant pair of students of nature who died all too early for the work which seemed given them to do. Gerhardt and Laurent occupy a prominent place among the modern reformers of chemistry; they introduced order into chemical notation, and system, where system had been conspicuous by its absence'. In criticising the system of so-called equivalent weights Gerhardt adopted the only true method, he studied actually occurring chemical reactions. In a number of reactions between compounds of carbon in which carbon dioxide, water, and ammonia were produced, Gerhardt found that when so-called equivalent weights of the reacting bodies were employed, the quantities of these three compounds evolved could always be represented by whole multiples of the formulæ C,O,, H2O,, and NH, respectively, (C = 6, N=14, O = 8). 1 Laurent's Chemical Method [Cavendish Society Publications] gives a general account of the more important work of these chemists. 238. 27. für pract. Chemie, 27. 439; and Ann. Chim. Phys. [3]7. 129: and 8. He therefore concluded that these formulæ, rather than the commonly accepted formulæ CO,, HO (and NH ̧), must represent equivalent weights of the compounds in question. 2 Similarly he concluded that the equivalent formulæ of sulphur dioxide and carbon monoxide must be SO, and CO, respectively and arguing from these conclusions he thought himself justified in saying that the true equivalents of carbon, sulphur and oxygen are 12, 32, and 16, and not 6, 16, and 8 as generally adopted. Gerhardt likewise applied his acute reasoning powers to an examination of the arguments which determined Berzelius and others to adopt formulæ representing weights of four volumes of many carbon compounds; these arguments he proved to be fallacious. Laurent examined the groundwork on which the systems of equivalent and atomic notation were based. His methods of reasoning were founded on experimentally determined facts, hence their irresistible force. If formulæ are to represent equivalent weights of substances, then said Laurent, a standard must be adopted. But it had been frequently shewn that the quantities represented by so-called combining weights were not always mutually equivalent. Power of neutralising unit weight of standard substance might be adopted as the reaction on which to base the system, but this method could be applied only to a limited number of substances. The idea of equivalency is associated with function; What is a given substance capable of doing?: this question must be answered before the equivalent of the substance can be determined. But in one action certain weights of two bodies. may be equivalent, while altogether different weights of the same bodies are equivalent in another reaction. Laurent affirmed that it was possible to found a systematic notation on equivalent weights assigned to the elements. Thus, in ferrous oxide 28 parts by weight of iron are combined with 8 parts by weight of oxygen,-let Fe = 28, then ferrous sulphate is represented by the formula Fe,SO,; but in ferric oxide there are 2.28 (i.e. 186) parts by weight of iron for every 8 parts by weight of oxygen,-let fe = 18,6, then the formula for ferric sulphate is fe, SO,: the formulæ Fe, SO, and fe, SO, represent strictly equivalent quantities of the two sulphates of iron. So also if the composition of potassiumhydrogen sulphate is expressed by the formula KHSO1, then, in a system of notation founded on equivalent weights, the composition of the double sulphate of potassium and aluminium is represented by the formula K Al, SO, (Al = 27′3). But such a notation is inconvenient, and it frequently conceals most important facts; e.g. in a strictly equivalent notation the differences between monobasic and polybasic acids disappear. Laurent returned to the generalisation of Avogadro and made that the basis of his system; he clearly distinguished between molecules and atoms, and he applied the law of equal volumes and equal numbers to molecules only. He admitted that apparent exceptions to the Avogadrean law existede.g. the molecules of sulphuric acid and salammoniac vapour appeared to occupy twice the volume occupied by the molecule of hydrogen;-but he said that this hypothesis generalised the facts better than any other which had been proposed. Laurent founded his system on an atomic basis, and a fundamental point was the distinction between atom and molecule. He adopted formulæ representing two volumes: the facts of 'nascent' action he explained by the conception of atoms as distinct from molecules. Molecule he defined to be 'the 'amount of a gaseous substance which occupies twice the ' volume occupied by an atom of hydrogen,' or, 'the smallest 'amount of a substance capable of taking part in a chemical 'reaction.' Atom he defined as 'the smallest amount of an 'element which enters into the composition of a compound.' Here we have the application of the term molecule to elements and compounds alike, while atom is used of elements only. Equivalents are the amounts of bodies which are of equal value in performing a stated action. Gerhardt and Laurent adopted the laws of atomic heat and isomorphism as aids in determinations of atomic weights. division of 12. Chemical evidence in favour of the elementary molecules during chemical changes was accumulated by Brodie, Wurtz, Williamson and others, but the work of these chemists will be referred to in more detail when we come to speak of the chemical methods for determining molecular weights (see pp. 72-77). Thus, at last, we have arrived at a clear separation between the meanings of the terms atom, molecule, equivalent. The system now adopted in chemistry is essentially that of Gerhardt and Laurent; it is founded on the conception of atoms and molecules. Dalton's fundamental idea has been amply confirmed by modern research. We have maintained the idea of equivalency, but we no longer speak, as Wollaston did, of the equivalent of an element; we compare the elementary atoms among themselves and arrange them in groups all the members of each of which are equivalent in respect of a certain definite action they are capable of performing. A true and fundamental conception once gained in science is never lost, it may be largely modified, it may even appear at times to be abandoned, but it develops slowly and bears much fruit at last. The vicissitudes in the fortunes of a truly scientific idea are aptly illustrated by the history of the atomic theory. After a period of dormancy of more than 2000 years, the atomic theory was revived and rendered definite by Dalton, was firmly established on an experimental basis by Berzelius, was almost abandoned by the school founded by the same chemist, was rehabilitated and again nearly despaired of by Dumas, was largely advanced by Avogadro, was subdivided and its parts clearly distinguished by Gerhardt and Laurent, and is now the foundation-stone of a great and ever-increasing edifice. 13. Thus far I have dealt with the development of the atomic and molecular theory regarded almost entirely from the chemical point of view. So great however is the importance of clearly perceiving the position which this theory occupies in modern chemistry, and of realising the nature of the |