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J. L. Proust formulated (1797) what is now known as the law of definite proportions, which states that the proportions by weight of the elements forming any given compound are definite and invariable. John Dalton proposed (c.1810) an atomic theory in which all atoms of an element have exactly the same weight. He made many measurements of the combining weights of the elements in various compounds. By postulating that simple compounds always contain one atom of each element present, he assigned relative atomic weights to many elements, assigning a weight of 1 to hydrogen as the basis of his scale. He thought that water had the formula HO, and since he found by experiment that 8 weights of oxygen combine with 1 weight of hydrogen, he assigned an atomic weight of 8 to oxygen. Dalton also formulated the law of multiple proportions, which states that when two elements combine in more than one proportion by weight to form two or more distinct compounds, their weight proportions in those compounds are related to one another in simple ratios. Dalton's work sparked an interest in determining atomic weights, even though some of his results : such as that for oxygen : were soon shown to be incorrect.
While Dalton was working on weight relationships in compounds, J. L. Gay-Lussac was experimenting with the chemical reactions of gases, and he found that, when under the same conditions of temperature and pressure, gases react in simple whole-number ratios by volume. Avogadro proposed (1811) a theory of gases that holds that equal volumes of two gases at the same temperature and pressure contain the same number of particles, and that these basic particles are not always single atoms. This theory was rejected by Dalton and many other chemists.
P. L. Dulong and A. T. Petit discovered (1819) a specific-heat method for determining the approximate atomic weight of elements. Among the first chemists to work out a systematic group of atomic weights (c.1830) was J. J. Berzelius, who was influenced in his choice of formulas for compounds by the method of Dulong and Petit. He attributed the formula H2O to water and determined an atomic weight of 16 for oxygen. J. S. Stas later refined many of Berzelius's weights. Stanislao Cannizzaro applied Avogadro's theories to reconcile atomic weights used by organic and inorganic chemists.
The availability of fairly accurate atomic weights and the search for some relationship between atomic weight and chemical properties led to J. A. R. Newlands's table of "atomic numbers" (1865), in which he noted that if the elements were arranged in order of increasing atomic weight "the eighth element, starting from a given one, is a kind of repetition of the first." He called this the law of octaves. Such investigations led to the statement of the periodic law, which was discovered independently (1869) by D. I. Mendeleev in Russia and J. L. Meyer in Germany. T. W. Richards did important work on atomic weights (after 1883) and revised some of Stas's values.
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