The atomic theory in chemistry has many points of resemblance to the fluxionary calculus in mathematics. Both give us the ratios of quantities; both reduce investigations that would be otherwise extremely difficult, or almost impossible, to the utmost simplicity; and what is still more curious, both have been subjected to the same kind of ridicule by those who have not put themselves to the trouble of studying them with such attention as to understand them completely. The minute philosopher of Berkeley, mutatis mutandis, might be applied to the atomic theory with as much justice as to the fluxionary calculus; and I have heard more than one individual attempt to throw ridicule upon the atomic theory by nearly the same kind of arguments.

The first chemists, then, who attempted to analyze the salts may be considered as contributing towards laying the foundation of the atomic theory, though they were not themselves aware of the importance of the structure which might have been raised upon their experiments, had they been made with the requisite precision.

Bergman was the first chemist who attempted regular analyses of salts. It was he that first tried to establish regular formulas for the analyses of mineral waters, stones, and ores, by the means of solution and precipitation. Hence a knowledge of the constituents of the salts was necessary, before his formulas could be applied to practice. It was to supply this requisite information that he set about analyzing the salts, and his results were long considered by chemists as exact, and employed by them to determine the results of their analyses. We now know that these analytical results of Bergman are far from accurate; they have accordingly been laid aside as useless: but this knowledge has been derived from the progress of the atomic theory.

The first accurate set of experiments to analyze the salts was made by Wenzel, and published by him in 1777, in a small volume entitled "Lehre von der Verwandschaft der Körper," or, "Theory of the Affinities of Bodies." These analyses of Wenzel are infinitely more accurate than those of Bergman, and indeed in many cases are equally precise with the best which we have even at the present day. Yet the book fell almost dead-born from the press; Wenzel's results never obtained the confidence of chemists, nor is his name ever quoted as an authority. Wenzel was struck with a phenomenon, which had indeed been noticed by preceding chemists; but they had not drawn the advantages from it which it was capable of affording. There are several saline solutions which, when mixed with each other, completely decompose each other, so that two new salts are produced. Thus, if we mix together solutions of nitrate of lead and sulphate of soda in the requisite proportions, the sulphuric acid of the latter salt will combine with the oxide of lead of the former, and will form with it sulphate of lead, which will precipitate to the bottom in the state of an insoluble powder, while the nitric acid formerly united to the oxide of lead, will combine with the soda formerly in union with the sulphuric acid, and form nitrate of soda, which being soluble, will remain in solution in the liquid. Thus, instead of the two old salts,

Sulphate of soda
Nitrate of lead,

we obtain the two new salts,

Sulphate of lead
Nitrate of soda.

If we mix the two salts in the requisite proportions, the decomposition will be complete; but if there be an excess of one of the salts, that excess will still remain in solution without affecting the result. If we suppose the two salts anhydrous, then the proportions necessary for complete decomposition are,

Sulphate of soda 9
Nitrate of lead20·75
29·75

and the quantities of the new salts formed will be