While Dalton’s theory could not give information about the absolute weights in grams of the atoms of various elements, it could say something about the relative atomic weights, _i.e._, the ratios of the weights of the different kinds of atoms, although it is true that these ratios could not always be determined with certainty. If, for example, the ratio between the oxygen and hydrogen in water is found to be as eight to one, then the weight ratio between the oxygen atom and the hydrogen atom will be as eight to one, if the water molecule is composed of one oxygen atom and one hydrogen atom (as Dalton supposed, see Fig. 2). But it will be as sixteen to one, if the water molecule is composed of one oxygen and two hydrogen atoms (as we now know to be the case). On the other hand, a ratio of seven to one will be compatible with the experimental ratio of eight to one only if we assume that the water molecule consists of fifteen atoms, eight of oxygen and seven of hydrogen, a very improbable hypothesis. In another case let us compare the quantities of oxygen and of hydrogen which are compounded with the same quantities of carbon in the two substances, carbon monoxide and methane respectively. On the assumption that the molecules in question have a simple structure, we can draw conclusions about the ratio of the atomic weights of hydrogen and oxygen. Now, if a ratio such as seven to one or fourteen to one is obtained while the analysis of water gives eight to one or sixteen to one, then either the structure of the molecule is more complicated than was assumed, or the analyses must be improved by more careful experiments. We can thus understand that the atomic theory can serve as a controlling influence on the analysis of chemical compounds. In order to choose between the different possible ratios of atomic weights, for example, the eight to one or the sixteen to one in the case of oxygen and hydrogen, Dalton had to make certain arbitrary assumptions. The first of these is that two elements of which only one compound is known appear with but one atom each in a molecule. Partly on account of this assumption and partly on account of the incompleteness of his analyses, Dalton’s values of the ratios of the atomic weights of the atoms and his pictures of the structure of molecules differ from those of the present day, as is obvious from Fig. 2. A much firmer foundation for the choice made appears later in the _Avogadro Law_; starting with the fact that different gases show great similarity in their physical conduct—for instance, all expand by an increase of ¹⁄₂₇₃ of their volume with an increase in temperature from 0° C. to 1° C.—the Italian, Avogadro, in 1811, put forward the hypothesis that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. A few examples suffice to show the usefulness of this rule.