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

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.

31

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

LAW OF MARIOTTE.

33

the outside of the gasometer has been reduced to onehalf, and the scale of the instrument shows me that the volume of the air in the interior has become 200 cubic inches; that is, has doubled. But let us continue the exhaustion. . . . The barometer now marks 10 inches, showing that the pressure has been reduced to onethird. The gasometer now contains 300 cubic inches of gas. The volume, then, has trebled. . . . Pushing the experiment still further, we have now the barometer standing at 7 inches, and the scale of the gasometer shows that the volume of the inclosed air has become 400 cubic inches. The pressure has been reduced to one-fourth, and the volume of the air has quadrupled; and so we might go on. Let, now, the atmosphere reënter the apparatus, and at once the air in the gasometer shrinks to its original volume, while the barometer goes back to 30 inches.

. .

We might next take a condensing-pump, and, arranging our apparatus so as to resist the ever-increasing pressure, as the air was forced into the receivers, we should find that, when the barometer marked 60 inches, the scale of the gasometer would show 50 cubic inches, and that, when the mercury column had risen to 120 inches, the air in the gasometer would have shrunk to 25 cubic inches; and so on. There are, however, obvious mechanical difficulties, which make this phase of the experiment unsuitable for a large lecture-room, and what we have seen is sufficient to illustrate the general principle which I wished to enforce. The principle, in a few words, is this:

The volume of a confined mass of gas is inversely proportional to the pressure to which it is exposed: the smaller the pressure the larger the volume, and the greater the pressure the less the volume.

This principle holds true not only with air, but also with every kind of aëriform matter. If, instead of using that mixture of oxygen and nitrogen we call air, we had introduced into the gasometer 100 cubic inches of pure oxygen or of pure nitrogen, or of any other true gas, we should have obtained precisely the same effect. The results of the experiment are not in the least degree influenced by the nature of the gas employed; and, assuming that we start with the same gas-volumes, the resulting volumes are the same at each stage of the experiment. In every case the volume varies inversely as the pressure. The principle thus developed is one of the most important laws of physical science. It was discovered by the chemist Boyle in England in 1662, and verified by the Abbé Mariotte in France somewhat later, and is by some called the law of Mariotte, and by others the law of Boyle.

It is always important to look at the phenomena of Nature from different sides, for otherwise we shall be liable to mistake their true relations when we see them under unusual aspects. So, in order that we may the more fully comprehend the bearing of the law of Mariotte on the philosophy of chemistry, it will be well for us to study this important principle from a point of view somewhat different from that we have just presented.

Both in the rubber bag and in the small gasometer we experimented with the constant quantity of gas which we at first introduced, and we measured its varying volume with the changing pressure. But more frequently we have to deal with a constant volume of gas, and to consider what quantity of gas-measured by its weight-a given vessel holds under different pressures. Here is a strong copper reservoir holding, we