By the middle of the nineteenth century the system of symbolical notation suggested by Berzelius was everywhere current; and, stripped largely of its dualistic associations, this system still remains the most generally convenient method of expressing the composition, analogies, and numerical relations of substances. During the middle of the last century philosophic chemists, although subscribing, with hardly an exception, to the doctrine of definite combining proportions, were by no means agreed as to the sufficiency of Dalton’s explanation of the experimental laws of chemical combination; and the hypothesis of atoms in the Daltonian sense was not universally accepted. To some the atomic theory of Dalton, which assumed that the combining proportion was identical with the relative weight of the atom, was unnecessary as an explanation of the laws of combination. Or at most it was only one out of a variety of molecular conditions in which matter might exist. Consequently some chemists were in the habit of drawing a distinction between _chemical_ atoms and _physical_ atoms. The chemical atom was identical with the Daltonian atom but this was by no means the same as the physical atom of Democritus or Leucippus. The view in 1850, in fact, was not very dissimilar from that to which recent experimental inquiry has led. But it can hardly be said that the doubts were dependent upon valid experimental evidence; they arose rather from the erroneous interpretation of imperfectly ascertained facts—upon the supposed inconsistencies of the law of Gay Lussac with the hypotheses of Avogadro and Ampère. As soon as the facts were clearly perceived and the inconsistencies reconciled we heard less of the supposed distinction between the chemical and the physical atom. It is only within quite recent time, and as the result of entirely new lines of inquiry, that the distinction has been revived. In the early part of the last century attempts were made by Berzelius to classify the chemical elements according to their electro-chemical relations, and by Thomson according as they were “supporters” or “non-supporters of combustion.” It was soon perceived that Thomson’s system had no philosophical basis, and it quickly fell into disuse. After the discovery of isomorphism, an endeavour was made by Graham to arrange the simple bodies in accordance with their natural relations, and even before 1850 the various elements were grouped by him very much as now.