Stated in the form of a law, Gay-Lussac's discovery was :—The weights of equal volumes of both simple and compound gases are proportional to their combining weights (or, to use Dalton's term, their atomic weights), or to rational multiples of the latter. This law appeared as if it ought to have some simple relation to Dalton's Jaws ; but there is an apparent difficulty in reconciling them, which was surmounted in 1811 by Amadeo Avogadro, Professor of Physics in Turin. The difficulty is this :—

Imagine a given volume, say a cubic inch, to be filled with oxygen; suppose it to contain a very large but unknown number of atoms of oxygen, which we will call «. This oxygen, if mixed with twice its volume of hydrogen, or two cubic inches, and made to combine with it (which can be done by heating the mixture with an electric spark), yields nothing but water ; and neither of the gases remains uncombined in excess. Let us suppose that n atoms of oxygen combine with 2« atoms of hydrogen; and as water also, according to Dalton, consists of atoms, there will be n atoms of water formed by their union. But experiment shows that the water, in the state of water-gas or steam, has a volume equal to that of the hydrogen from which it was formed; that is, n atoms of water-gas inhabit a volume equal to that inhabited by 2n atoms of hydrogen. From this it would appear that equal volumes of gases do not contain equal numbers of atoms ; and while some chemists supposed, with Dalton, that water consists of one atom of oxygen in union with one atom of hydrogen, others imagined that two atoms of hydrogen were present for each atom of oxygen, basing their conclusions on the fact that two volumes of hydrogen combine with one volume of oxygen, and considering it probable that equal volumes of gases contain equal numbers of atoms. This last probability was maintained by Avogadro, and he defended his doctrine by the following suggestion.