I propose therefore to begin at the beginning, and, taking the simplest case, that of dead or inorganic matter, show how the material universe is built up by the operation of the all-pervading law of polarity. What does matter consist of? Of molecules, and molecules are made up of atoms, and these are held together or parted, and built up into the various forms of the material universe, primarily by polar forces.

Let me endeavour to make this intelligible to the intelligent but unscientific reader. Suppose the Pyramid of Cheops shown for the first time to a giant whose eye was on such a scale that he could just discern it as a separate object. He might make all sorts of ingenious conjectures as to its nature, but if microscopes had been invented in Giant-land and he looked through one, he would find that it was built up, layer by layer, on a regular plan and in determinate lines and angles, by molecules, or what seemed to him almost infinitely small masses, of squared stone. For pyramid write crystal, and we may see by the human sense, aided by human instruments and human reason, a similar structure built up in the same way by minute particles. Or again, divide and subdivide our iron filings until we reach the limit of possible mechanical division discernible by the microscope; each one remains essentially a bar of iron, as capable of being magnetised, and showing the same qualities and behaviour under chemical tests as the original bar of iron from which the filings were taken. This carries us a long way down towards the infinitely small, for mechanical division and microscopic visibility can be carried down to magnitudes which are of the order of 1/100000th of an inch.

But this is only the first step; to understand our molecules we must ascertain whether they are infinitely divisible, and whether they are continuous, expanding by being spread out thinner and thinner like gold-beater’s skin: or are they separate bodies with intervals between them, like little planets forming one solar system and revolving in space by fixed laws. Ancient science guessed at the former solution and embodied it in the maxim ‘that nature abhors a vacuum’: modern science proves the latter.

In the first place bodies combine only in fixed proportions, which is a necessary consequence if they consist of definite indivisible particles, but inconceivable if the substance of each is indefinitely divisible. Thus water is formed in one way and one only: by uniting one volume or molecule of oxygen with two of hydrogen, and any excess of one or the other is left out and remains uncombined. But if the molecules could be divided into halves, quarters, and so on indefinitely, there can be no reason why their union should take place always in this one proportion and this only.

A still more conclusive proof is furnished by the behaviour of substances which exist in the form of gases. If a jar is filled with one gas, a second and third gas can be poured into it as readily as into a vacuum, the result being that the pressure on the sides of the jar is exactly equal to the sum of the separate pressures of each separate gas. This evidently means that the first gas does not occupy the whole space, but that its particles are like a battalion of soldiers in loose skirmishing order, with such intervals between each unit that a second and third battalion can be marched in and placed on the same ground, without disturbing the formation, and with the result only of increasing the intensity of the fire.

Now gas is matter as much as solids or liquids, and in the familiar instance of water we see that it is merely a question of more or less heat whether the same matter exists as ice, water, or steam. The number and nature of the molecules is not changed, only in the one case they are close to one another and solidly linked together; in the other, further removed and free to move about one another, though still held together as a mass by their mutual attractions; and in the third, still further apart, so that their mutual attraction is lost and they dart about, each with its own proper motion, bombarding the surface which contains them, and by the resultant of their impacts producing pressure.

In this latter and simpler form of gas the following laws are found to prevail universally for all substances. Under like conditions volumes vary directly as the temperature and inversely as the pressure. That is to say, the pressure which contains them remaining the same, equal volumes of air, steam, or any other substance in the state of gas, expand into twice the volume if the temperature is doubled, three times if it is tripled, and so on; contracting in the same way if the temperature is lowered. If on the other hand the temperature remains constant, the volume is reduced to one half or one third, if the pressure is doubled or tripled. From these laws the further grand generalisation has been arrived at, that all substances existing in the form of gas contain the same number of molecules in the same volume.

This, which is known as the Law of Avogadro, from the Italian chemist by whom it was first discovered, is the fundamental law of modern chemistry, and the key to all certain and scientific knowledge of the constitution of matter and of the domain of the infinitely small, just as much as the law of gravity is to action of matter in the mass, and the resulting conditions and motions of mechanics and astronomy.

This conclusion obviously follows from it, that difference of weight in different substances arises not from one having more molecules in the same volume than another, but from the molecules themselves being heavier. If we weigh a gallon or litre of hydrogen gas, which is the lightest known substance, and then weighing an equal volume of oxygen gas find that it is sixteen times heavier, we know for certain that the molecule or ultimate particle of oxygen is sixteen times heavier than that of hydrogen.

It is evident that in this way the molecules of all simple substances which can exist in the form of pure gas can be weighed, and their weight expressed in terms of the unit which is generally adopted, that of the molecule of the lightest known substance, hydrogen. But science, not content with this achievement, wants to know not the relative weight only, but the absolute dimensions, qualities, and motions of these little bodies; and whether, although they cannot be divided further by mechanical means, and while retaining the qualities of the substances they build up, they are really ultimate and indivisible particles or themselves composites.