In 1808 Dalton's atomic theory received striking confirmation through the investigations of the French scientist Gay-Lussac, who showed that gases, under similar circumstances of temperature and pressure, always combine in simple proportions by _volume_ when they act on one another, and that when the result of the union is a gas, its volume also is in a simple ratio to the volumes of its components. One of Dalton's friends summed up the result of Gay-Lussac's research in this simple fashion: "His paper is on the combination of gases. He finds that all unite in equal bulks, or two bulks of one to one of another, or three bulks of one to one of another." When Dalton had investigated the relative weights with which elements combine, he had found no simple arithmetical relationship between atomic weight and atomic weight. When two or more compounds of the same elements are formed, Dalton found, however, as we have seen, that the proportion of the element added to form the second or third compound is a multiple by weight of the first quantity. Gay-Lussac now showed that gases, "in whatever proportions they may combine, always give rise to compounds whose elements by volume are multiples of each other."
In 1811 Avogadro, in an essay on the relative masses of atoms, succeeded in further confirming Dalton's theory and in explaining the atomic basis of Gay-Lussac's discovery of simple volume relations in the formation of chemical compounds. According to the Italian scientist the _number_ of molecules in all gases is always the same for equal volumes, or always proportional to the volumes, it being taken for granted that the temperature and pressure are the same for each gas. Dalton had supposed that water is formed by the union of hydrogen and oxygen, atom for atom. Gay-Lussac found that two volumes of hydrogen combined with one volume of oxygen to produce two volumes of water vapor. According to Avogadro the water vapor contains twice as many atoms of hydrogen as of oxygen. One volume of hydrogen has the same number of molecules as one volume of oxygen. When the two volumes combine with one, the combination does not take place, as Dalton had supposed, atom for atom, but each half-molecule of oxygen combines with one molecule of hydrogen. The symbol for water is, therefore, not HO but H{ 2}O.