But in the year 1802 or so, Dalton thought that by the study of chemical combinations it would be possible to determine the relative weights of atoms. Assume that any elementary gas is composed of small, indivisible, equally heavy parts; assume that the weight of an atom of one element is different from that of the atom of any other element; and, lastly, assume that when elements combine the atom of the compound so produced is built up of the atoms of the various elements. Make these assumptions, and it follows that the relative weights of two or more elements which combine together must represent the relative weights of the atoms of these elements.

We know that the fixity of composition of chemical compounds had been established before this time, largely by the labours of Black and Lavoisier. Fixity of composition had however been called in question by Berthollet, who held that elements combine together in very varying quantities; that, in fact, in place of there being two or three, or a few definite compounds of, say, iron and oxygen, there exists a graduated series of such bodies; and that the amount of iron which combines with oxygen depends chiefly on such physical conditions as the temperature, the pressure, etc., under which the chemical action occurs. But by the date of the publication of the first part of Dalton's "New System," the long dispute between Berthollet and Proust regarding fixity of composition of compounds had nearly closed in favour of the latter chemist, who strongly upheld the affirmative side of the argument. But if Dalton's assumptions are correct, it is evident that when two elements form more than one compound, the quantity of element A in one of these must be a simple multiple of the quantity in the other of these compounds; because there must be a greater number of atoms of element A in the atom of one compound than in that of the other compound, and an elementary atom is assumed to be indivisible. Hence it follows that if one element be taken as a standard, it must be possible to affix to any other element a certain number which shall express the smallest quantity of that element which combines with one part by weight of the standard element; and this number shall also represent how many times the atom of the given element is heavier than the atom of the standard element, the weight of which has been taken to be one. If this element forms two compounds with the standard element, the amount of this element in the second compound must be expressed by a simple multiple of the number assigned to this element, because it is not possible, according to the fundamental assumptions of the theory, to form a compound by the combination of fractions of elementary atoms.

By pondering on the facts regarding chemical combinations which had been established by various workers previous to the year 1802, Dalton had apparently come to such conclusions as those now indicated.

In his paper on the properties of the gases constituting the atmosphere, read to the Manchester Society on November 12, 1802, he stated that one hundred measures of common air would combine with thirty-six measures of "nitrous gas" in a narrow tube to produce an oxide of nitrogen, but with seventy-two measures of the same gas in a wide vessel to produce another oxide of nitrogen. These facts, he says, "clearly point out the theory of the process: the elements of oxygen may combine with a certain portion of nitrous gas, or with twice that portion, but with no intermediate quantity."

In the concluding paragraph of his paper on absorption of gases by liquids, read on October 21, 1803, we found (see p. 116) that he had got so far in his inquiry into the "relative weights of the ultimate particles of bodies" as to give a table of twenty-one such weights. About this time Dalton made analyses of two gaseous compounds of carbon—olefiant gas and carburetted hydrogen or marsh-gas. He found that both are compounds of carbon and hydrogen; that in one 4.3 parts by weight of carbon are combined with one part by weight of hydrogen, and in the other the same amount (4.3) of carbon is combined with two parts by weight of hydrogen.[8]

This was a striking confirmation of his views regarding combination in multiple proportions, which views followed as a necessary deduction from the atomic hypothesis. From this time he continued to develop and extend this hypothesis, and in the year 1808 he published his "New System of Chemical Philosophy."

The first detailed account of the atomic theory was however given to the chemical world the year before Dalton's book appeared. During a conversation with Dalton in the autumn of 1804 Dr. Thomas Thomson learned the fundamental points of the new theory, and in the third edition of his "System of Chemistry," published in 1807, he gave an account of Dalton's views regarding the composition of bodies.

In the same year a paper by Thomson appeared in the Philosophical Transactions, wherein it was experimentally proved that oxalic acid combines with strontia to form two distinct compounds, one of which contains twice as much oxalic acid as the other, the amount of strontia being the same in both. Analyses of the oxalates of potash, published about the same time by Wollaston, afforded another illustration of the law of multiple proportions, and drew the attention of chemists to Dalton's theory. But the new theory was opposed by several very eminent chemists, notably by Sir Humphry Davy. In the autumn of 1807 Wollaston, Thomson and Davy were present at the dinner of the Royal Society Club, at the Crown and Anchor, in the Strand. After dinner, these three chemists discussed the new theory for an hour and a half, Wollaston and Thomson trying to convince Davy of the truth of Dalton's theory; but "so far from being convinced, he went away, if possible, more prejudiced against it than ever."

Soon after this Wollaston succeeded in convincing Mr. Davis Gilbert (afterwards President of the Royal Society) of the justness of the atomic theory, and he in turn so placed the facts and the reasoning before Davy, that from this time he became a supporter of the new theory.

In order that the atomic theory should be fruitful of results, it was now necessary that the values of the atomic weights of many elements should be carefully determined.