split them, and so, were we large enough, we might be able to crack the earth; but we have made sufficient advance since the days of the old controversy to know that questions of this sort, in the present state of knowledge, are both irrelevant and absurd. The molecules are to the physicist definite units, in the same sense that the planets are units to the astronomer. The geologist tears the earth to pieces, and so does the chemist deal with the molecules, but to the astronomer the earth is a unit, and so is the molecule to the physicist. The word molecule, which means simply a small mass of matter, expresses our modern conception far better than the old word atom, which is derived from the Greek a, privative, and réμvw, and means, therefore, indivisible. In the paper just referred to, Sir W. Thompson used the word atom in the sense of molecule, and this must be borne in mind in reading his article. We shall give to the word atom an utterly different signification, which we must be careful not to confound with that of molecule. In our modern chemistry, the two terms stand for wholly different ideas, and, as we shall see, the atom is the unit of the chemist in the same sense that the molecule is the unit of the physicist. But we will not anticipate. It is sufficient for the present if we have gained a clear conception of what the word molecule means, and I have dwelt thus at length on the definition because I am anxious to give you the same clear conviction of their existence which I have myself. As I have said before, they are to me just as much real magnitudes as the planets, or, to use the words of Thompson, "pieces of matter of measurable dimensions, with shape, motion, and laws of action, intelligible subjects of scientific investigation."1

1 See Lecture on Molecules, by Prof. Maxwell, Nature, Sept. 25, 1873.

LECTURE II.

THE MOLECULAR CONDITION OF THE THREE STATES OF MATTER THE GAS, THE LIQUID, AND THE SOLID.

IN my first lecture I endeavored to give you some conception of the meaning of the word molecule, and this meaning I illustrated by a number of phenomena, which not only indicate that molecules are real magnitudes, but which also give us some idea of their absolute size.

Avogadro's law declares that all gases contain, under like conditions of temperature and pressure, the same number of molecules in the same volume; and, if we can rely on the calculations of Thompson, which are based on the well-known theorem of molecular mechanics deduced by Clausius, this number is about one hundred thousand million million million, or 1023 to a cubic inch. Of course, as the volume of a given quantity of gas varies with its temperature and pressure, the number of molecules contained in a given volume must vary in the same way; and the above calculation is based on the assumption that the temperature is at the freezing-point, and the pressure of the air, as indicated by the barometer, thirty inches. The law only holds, moreover, when the substances are in the condition of perfect gases. It does not apply to solids or liquids, and not even to that half-way state between liquids and gases which Dr. Andrews has recently so admirably

defined. In the state of perfect gas, it is assumed that the molecules are so widely separated that they exert no action upon each other, but the moment the gas is so far condensed that the molecules are brought within the sphere of their mutual attraction, then, although the aëriform state is still retained, we no longer find that

A

B

FIG. 5.-Barometer.

the law rigidly holds; and when, by the condensation, the state of the substance is changed to that of a liquid or a solid, all traces of the law disappear. In order that you may gain a clear conception of this relation, I shall ask your attention in this lecture to the explanation which our molecular theory gives of the characteristic properties of the three conditions of matter, the gas, the liquid, and the solid. We begin with the gas, because its mechanical condition is, theoretically at least, by far the simplest of the three.

Every one of my audience must be familiar with the fact that every gas is in a state of constant tension, tending to expand indefinitely into space. In the

case of our atmosphere, this tension is so great that the air at the level of the sea exerts a pressure of between

EXPANSIVE ENERGY IN GASES.

39

fourteen and fifteen pounds on every square inch of surface-about a ton on a square foot.

It is this pressure which. sustains the column of mercury in the tube of a barometer (Fig. 5); and since, by the laws of hydrostatics, the height of this column of mercury depends on the pressure of the air, rising and falling in the same proportion as the pressure increases or diminishes, we use the barometer as a measure of the pressure, and, instead of estimating its amount as so many pounds to the square inch, we more frequently describe it by the height in inches (or centimetres) of the mercury-column, which it is capable of sustaining in the tube of a barometer. The tension of the air is balanced by the force of gravitation, in consequence of which the lower stratum of the air in which we live is pressed upon by the whole weight of the superincumbent mass. The moment, however, the external pressure is relieved, the peculiar mechanical condition of the gas becomes evident.

Hanging under this large glass receiver is a small rubber bag (a common toy balloon), partially distended with air (Fig. 6). The air confined within the bag is exerting the great tension of which I have spoken, but the mass remains quiescent, because this tension is exactly balanced by the pressure of the atmosphere on the exterior surface of the bag. You see, however, that, as we remove, by means of this air-pump, the air from the receiver, and thus relieve the external pressure, the bag slowly expands, until it almost completely fills the bell. There can, then, be no doubt that there exists within this mass of gas a great amount of energy, and since this energy exactly balances the atmospheric pressure, it must be equal to that pressure.

But I wish to show you more than this, for not only

is it true that the bag expands as the pressure is relieved, but it is also true that the gas in the bag expands in exactly the same proportion as the external pressure.

diminishes. In order to prove this, I will now place under this same glass one of those small gasometers, which are used by the itinerant showmen in our streets for measuring what they call the volume of the lungs, while under this tall bell at the side I have arranged a barometer-tube for measuring the external pressure. The two receivers are connected together by rubber hose, so as to form essentially one vessel, and both are connected with the air-pump.

We will begin by blowing air into the gasometer until the scale marks 100 cubic inches, and, noticing after adjusting the apparatus that the barometer stands at 30 inches, we will now proceed to exhaust the air, at the same time carefully watching the barometer. . . . It has now fallen to 15 inches; that is, the pressure on