In short, all the formulæ are what are called _two-volume formulæ_; that is, the relative molecular weights of the substances occupy the same volume as two relative parts by weight of hydrogen. Hence their vapour densities—referred to hydrogen as unity—are the halves respectively of their molecular weights. Steam is 9 times, hydrogen chloride 18.25 times, and ammonia 8.5 times heavier than hydrogen, when measured under identical conditions of temperature and pressure. The quantities expressed by the formulæ H2, H2O, HCl, NH3, occupy the same volume. This is equally true of the quantities expressed by O2, N2, Cl2, etc. These expressions signify that the molecules of the elements of hydrogen, oxygen, nitrogen, and chlorine consist each of 2 atoms of the respective substances: the molecule of water consists of 3 atoms—2 of hydrogen and 1 of oxygen; the molecule of hydrogen chloride of 2 atoms—1 of hydrogen and 1 of chlorine; whereas the molecule of ammonia contains 4 atoms—1 atom of nitrogen and 3 atoms of hydrogen.
Certain of the elementary bodies are, as already stated, capable of existing in different allotropic states. Thus there is a modification of oxygen known as _ozone_. This substance has long been recognised as being formed from air under the influence of the electric discharge. It was the subject of study by Schönbein as far back as 1839; but that it was a condensed form of oxygen and not a peroxide of hydrogen—as was at one time surmised—was first established by Andrews and Tait. The degree of its condensation was definitely ascertained by Soret by observing its rate of diffusion, from which, on the basis of Graham’s law, its density could be inferred. It was found to be 1½ times that of ordinary oxygen. Hence, if the molecule of oxygen consists of 2 atoms, that of ozone consists of 3 atoms. The chemical symbol of ozone is, therefore, O3.
It has been found also that the molecule of sulphur, in the state of solution, contains eight atoms. This complex molecule in the gaseous state gradually breaks down as the temperature is increased, and at temperatures above 850° contains, like its analogue oxygen, only two atoms. The molecules of phosphorus and arsenic, in the gaseous state, are each found to consist of four atoms. On the other hand, the molecules of mercury, zinc, and cadmium each consist of only one atom. As will be shown later, Kundt and Warburg established, in 1875, the fact that mercury vapour is a monatomic gas, by determining the rate at which sound is propagated through it. In the same way it was shown that helium, argon, and its congeners are also, as already stated, monatomic gases.