Carbon forms two oxides. In carbon monoxide, \mathrm{CO}, 12.0 g of carbon is combined with 16.0 g of oxygen; in carbon dioxide, \mathrm{CO_2}, the same 12.0 g of carbon is combined with 32.0 g of oxygen.
Each oxide on its own obeys the law of constant composition. Comparing the two, the masses of oxygen that combine with a fixed mass of carbon are in the ratio 16.0 : 32.0, which is 1 : 2.
Such a simple ratio is not a coincidence; it appears whenever two elements form more than one compound.
Nitrogen and oxygen form several compounds. With 14.0 g of nitrogen, dinitrogen monoxide \mathrm{N_2O} contains 8.0 g of oxygen, nitrogen monoxide \mathrm{NO} 16.0 g and nitrogen dioxide \mathrm{NO_2} 32.0 g, masses in the ratio 1 : 2 : 4.
This is the law of multiple proportions: when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in a ratio of small whole numbers.
John Dalton stated the law in 1803 from data such as these, while he was working out his atomic theory.
In 1808 Dalton published his atomic theory. Every element is made of tiny atoms, and all the atoms of one element are alike in mass and properties, while the atoms of different elements differ.
Compounds form when atoms of different elements join in simple whole-number ratios, and a chemical reaction only rearranges atoms, never creating or destroying them.
Some of these ideas were later refined: atoms are made of smaller particles, and isotopes of one element differ in mass. Its central idea, that matter consists of atoms that are only rearranged in reactions, is still accepted.
The atomic theory explains the laws of chemical combination. Atoms are neither created nor destroyed, so mass is conserved, and every molecule of a compound contains the same atoms, so its composition is constant.
A carbon atom can combine with one oxygen atom or with two, but never with one and a half. That is why the oxygen in \mathrm{CO} and \mathrm{CO_2} is in the ratio 1 : 2.
Counted per nitrogen atom, the oxygen atoms are 1/2 in \mathrm{N_2O}, 1 in \mathrm{NO} and 2 in \mathrm{NO_2}, and 1/2 : 1 : 2 is the same ratio as 1 : 2 : 4.
Water contains hydrogen and oxygen in the mass ratio 1 : 8, so 9.0 g of water holds 1.0 g of hydrogen and 8.0 g of oxygen.
Dalton assumed the simplest formula, \mathrm{HO}, with one atom of each. Then an oxygen atom would be 8 times as heavy as a hydrogen atom. With the formula \mathrm{H_2O}, it would be 16 times as heavy.
Masses alone cannot decide between the two, because they give only the ratio of the masses and not the number of atoms. The answer came from the volumes of reacting gases.