This conception has been much used since Laurent's time, but it has for the most part been applied to the atoms of the elements.

Hydrogen being taken as the standard substance, the elements have been divided into groups, in accordance with the number of hydrogen atoms with which one atom of each element is found to combine. Thus certain elements combine with hydrogen only in the proportion of one atom with one atom; others combine in the proportion of one atom with two atoms of hydrogen; others in the proportion of one atom with three atoms of hydrogen, and so on.

The adjective monovalent, divalent, trivalent, etc., is prefixed to an element to denote that the atom of this element combines with one, or two, or three, etc., atoms of hydrogen to form a compound molecule.

Let us consider what is implied in this statement—"The nitrogen atom is trivalent." This statement, if amplified, would run thus: "One atom of nitrogen combines with three atoms of hydrogen to form a compound molecule." Now, this implies (1) that the atomic weight of nitrogen is known, and (2) that the molecular weight, and the number of nitrogen and hydrogen atoms in the molecule, of a compound of nitrogen and hydrogen are also known.

But before the atomic weight of an element can be determined, it is necessary (as we found on p. 146) to obtain, analyze, and take the specific gravities of a series of gaseous compounds of that element. The smallest amount of the element (referred to hydrogen as unity) in the molecule of any one of these gases will then be the atomic weight of the element.

When it is said that "the molecular weight, and the number of nitrogen and hydrogen atoms in the molecule, of a compound of nitrogen and hydrogen are known," the statement implies that the compound in question has been obtained in a pure state, has been analyzed carefully, has been gasefied, and that a known volume of the gas has been weighed. When therefore we say that "the nitrogen atom is trivalent," we sum up a large amount of knowledge which has been gained by laborious experiment.

This classification of the elements into groups of equivalent atoms—which we owe to Frankland, Williamson, Odling, and especially to Kekulé—has been of much service especially in advancing the systematic study of the compounds of carbon. It helps to render more precise the conception which has so long been gaining ground of the molecule as a definite structure.

A monovalent element is regarded as one the atom of which acts on and is acted on by only one atom of hydrogen in a molecule; a divalent as one, the atom of which acts on and is acted on by two atoms of hydrogen—or other monovalent element—in a molecule; a trivalent element as one, the atom of which acts on and is acted on by three atoms of hydrogen—or other monovalent element—in a molecule; and so on.

The fact that there often exist several compounds of carbon, the molecules of which are composed of the same numbers of the same atoms, finds a partial explanation by the aid of this conception of the elementary atom as a little particle of matter capable of binding to itself a certain limited number of other atoms to form a compound molecule. For if the observed properties of a compound are associated with a certain definite arrangement of the elementary atoms within the molecules of that compound, it would seem that any alteration in this arrangement ought to be accompanied by an alteration in the properties of the compound; in other words, the existence of more than one compound of the same elements united in the same proportions becomes possible and probable.

I have said that such compounds exist: let me give a few examples.