Atoms are the smallest quantities or chemically indivisible masses of the elements forming the molecules of elements and compounds.

Atoms have weight, the sum of their weights forms the weight of the molecule, and the sum of the weights of the molecules forms the weight of masses, and is the cause of gravity, and of all the phenomena which depend on the mass of a substance.

The elements are characterised, not only by their independent existence, their incapacity of being converted into each other, &c., but also by the weight of their atoms.

Chemical and physical properties depend on the weight, composition, and properties of the molecules forming a substance, and on the weight and properties of the atoms forming the molecules.

This is the substance of those principles of molecular mechanics which lie at the basis of all contemporary physical and chemical constructions since the establishment of the law of Avogadro-Gerhardt. The fecundity of the principles enunciated is seen at every step in all the particular cases forming the present store of chemical data. We will here cite a few examples of the application of the law.

As the weight of an atom must be understood as the minimum quantity of an element entering into the composition of all the molecules formed by it, therefore, in order to find the weight of an atom of oxygen, let us take the molecules of those of its compounds which have already been described, together with the molecules of certain of those carbon compounds which will be described in the [following chapter]:

Molecular
Weight		Amount of
Oxygen		 Molecular
Weight		Amount of
Oxygen
H2O1816HNO36348
N2O4416CO2816
NO3016CO24432
NO24632

The number of substances taken might be considerably increased, but the result would be the same—that is, the molecules of the compounds of oxygen would never be found to contain less than 16 parts by weight of this element, but always n16, where n is a whole number. The molecular weights of the above compounds are found either directly from the density of their vapour or gas, or from their reactions. Thus, the vapour density of nitric acid (as a substance which easily decomposes above its boiling point) cannot be accurately determined, but the fact of its containing one part by weight of hydrogen, and all its properties and reactions, indicate the above molecular composition and no other. In this manner it is very easy to find the atomic weight of all the elements, knowing the molecular weight and composition of their compounds. It may, for instance, be easily proved that less than n12 parts of carbon never enters into the molecules of carbon compounds, and therefore C must be taken as 12, and not as 6 which was the number in use before Gerhardt. In a similar manner the atomic weights now accepted for the elements oxygen, nitrogen, carbon, chlorine, sulphur, &c., were found and indubitably established, and they are even now termed the Gerhardt atomic weights. As regards the metals, many of which do not give a single volatile compound, we shall afterwards see that there are also methods by which their atomic weights may be established, but nevertheless the law of Avogadro-Gerhardt is here also ultimately resorted to, in order to remove any doubt which may be encountered. Thus, for instance, although much that was known concerning the compounds of beryllium necessitated its atomic weight being taken as Be = 9—that is, the oxide as BeO and the chloride BeCl2—still certain analogies gave reason for considering its atomic weight to be Be = 13·5, in which case its oxide would be expressed by the composition Be2O3, and the chloride by BeCl3.[21] It was then found that the vapour density of beryllium chloride was approximately 40, when it became quite clear that its molecular weight was 80, and as this satisfies the formula BeCl2, but does not suit the formula BeCl3, it therefore became necessary to regard the atomic weight of Be as 9 and not as 13½.

With the establishment of a true conception of molecules and atoms, chemical formulæ became direct expressions, not only of composition,[22] but also of molecular weight or vapour density, and consequently of a series of fundamental chemical and physical data, inasmuch as a number of the properties of substances are dependent on their vapour density, or molecular weight and composition. The vapour density D = M/2. For instance, the formula of ethyl ether is C4H10O, corresponding with the molecular weight 74, and the vapour density 37, which is the fact. Therefore, the density of vapours and gases has ceased to be an empirical magnitude obtained by experiment only, and has acquired a rational meaning. It is only necessary to remember that 2 grams of hydrogen, or the molecular weight of this primary gas in grams, occupies, at 0° and 760 mm. pressure, a volume of 22·3 litres (or 22,300 cubic centimetres), in order to directly determine the weights of cubical measures of gases and vapours from their formulæ, because the molecular weights in grams of all other vapours at 0° and 760 mm. occupy the same volume, 22·3 litres. Thus, for example, in the case of carbonic anhydride, CO2, the molecular weight M = 44, hence 44 grams of carbonic anhydride at 0° and 760 mm. occupy a volume of 22·3 litres—consequently, a litre weighs 1·97 gram. By combining the laws of gases—Gay-Lussac's, Mariotte's, and Avogadro-Gerhardt's—we obtain[23] a general formula for gases