TENSION AND PRESSURE.

35

will assume, a cubic foot of gas, and, excepting the very small fluctuations caused by variations of temperature, this volume is constant. Connected with the reservoir is a pressure-gauge similar to those you may see on any steam-boiler, and by this we can measure the tension of the confined gas. By means of this pump we can force air or any other gas into the chamber, and as we work the pump our gauge shows an ever-increasing tension; and here, lest you should be confused by the two terms tension and pressure applied to the same manifestation of energy, let me call your attention to the obvious distinction between the condition of permanent elasticity or tension of a mass of gas, and either the outward pressure which in consequence of its tension the gas exerts on every surface exposed to its action, or the external pressure by which the tension is balanced and the mass of gas confined within a limited volume. Still, as in a state of rest, the tension everywhere exactly balances the pressure, the two terms are frequently interchangeable, although it is usual to estimate pressure as so many pounds on a square inch, and to measure tension by the height of the column of mercury which it is capable of sustaining. Either of these measures, however, can always be easily reduced to the other.

Now, what relation does the tension of the air in this copper vessel sustain to the quantity of air (measured, of course, by its weight) which the chamber contains? The law of Mariotte, as we have already stated it, enables us to answer this question. We already know that if we force two cubic feet of air into one cubic foot, the pressure exerted on this mass of gas, and therefore the tension of the gas, must be doubled. If we force three cubic feet into one cubic foot, both the pressure and the tension must be trebled, etc. In other

words, the tension of a mass of gas confined under a constant volume will be proportional to the quantity— that is, to the weight-of gas so confined, and conversely the weight must be proportional to the tension. But, as you see, this is merely another mode of stating the same general property of aëriform matter which we have called the law of Mariotte. If it is true that the volume of a constant weight of any gas is inversely proportional to the pressure to which it is exposed, it must also be true that the tension of a constant volume of the same gas is directly proportional to its weight.

Consider a further consequence of the property of aëriform matter we have been discussing, which exhibits still another phase of the law of Mariotte. According to the well-known principle of Archimedes, every object immersed in the atmosphere is buoyed up by a force exactly equal to the weight of air it displaces. This force, which produces such a marked effect in the ascension of a balloon, cannot be neglected in any scientific investigation in which it becomes necessary to determine weights with great accuracy. It is, however, a variable force, because, since the tension of the atmosphere as shown by the barometer is continually varying, the weight of air displaced in any case must also vary. But, working as we must amid this variableness, the law of Mariotte comes to our aid and enables us to predict what must be the effect in any given case; for as the weight of a constant volume of gas is directly proportional to its tension, so the weight of air displaced by a body of invariable dimensions must be proportional to the heights of the barometer column which at different times measures the tension of the atmosphere.

In this discussion of Mariotte's law, we have necessarily assumed that all the conditions which may modify

MOLECULAR MOTION.

37

the volume or density of a mass of gas were constant, except only the one we have been studying. It is, however, a familiar fact that the condition of our atmosphere may be modified by several causes, and of these temperature produces even a greater effect than the ordinary variations of pressure. To the influence of temperature on the condition of a gas we must next give our attention; but, before we attack this somewhat difficult problem, let me point out to you that the law of Mariotte or Boyle is most closely related to the law of Avogadro. The one law is found to hold just as far as the other, and any deviation from the one is accompanied by a corresponding deviation from the other. So close, indeed, is the connection, that we can not resist the conviction that the two laws are merely different phases of one and the same condition of matter; and our molecular theory explains this connection in the following way:

The molecules of a body are not isolated masses in a fixed position, all at rest, but, like the planets, they are in constant motion. The greatest length of path over which this motion can ever extend must be exceedingly short, so short, indeed, that, if the path could be traced, it would be wholly imperceptible to our senses, even when aided by the most powerful instruments. But, nevertheless, the motion is none the less real, and none the less capable of producing mechanical effects. In a gas the motions of the molecules are supposed to take place in straight lines, the molecules hurrying to and fro across the containing vessel, striking against its walls, or else encountering their neighbors, rebounding and continuing on their course in a new direction, according to the well-known laws which

govern the impact of elastic bodies. Of course, in such a system, all the molecules are not moving with the same velocity at the same time; but they have a certain mean velocity, which determines what we call the temperature of the body, and the higher the temperature the greater is this mean velocity; moreover, the mean velocity of the molecules of each substance is always the same at the same temperature. It varies, however, for different substances, and, for any given temperature, the less the density of the gas the greater is this velocity, although, as we shall hereafter see, the velocities of the molecules of two different gases are inversely proportional, not simply to their densities, but to the square roots of these quantities. We are able to calculate for each gas at least approximately what this velocity must be for any temperature, and, in the case of hydrogen gas, the value at the temperature of freezing water is about 6,097 feet per second. The internal energy, therefore, in a pound of hydrogen gas at the freezing-point is as great as that of a pound-ball moving 6,097 feet per second, and the energy in an equal volume (a little over 6.6 cubic yards when the barometer is at 30 inches) of any other true gas is equally great under the same conditions; a greater molecular weight compensating in every case for a less molecular velocity. Let us now bring together the two remarkable results already reached in this lecture.

One cubic inch of every gas, when the barometer marks 30 inches, and the thermometer 32° Fahr., contains 1023 molecules.

Mean velocity of hydrogen molecules, under same conditions, 6,097 feet per second.

It is evident, then, that every mass of gas must contain a large amount of internal energy, and this

WHAT THERMOMETERS TELL US.

39

energy is made manifest in many ways, especially in what we call the permanent tension of the gas. Every surface in contact with a mass of gas is being constantly bombarded by the molecules, and hence the great pressure which results. Now, the greater the number of molecules in a given space, the greater will be the number of impacts on a given surface in a given. time, and therefore the greater will be the energy of the molecular bombardment. Evidently, then, according to the molecular theory, the pressure of the same gas on a given surface ought to be exactly proportional to the number of molecules in a given volume; or, what amounts to the same thing, to the weight of the given volume; and this is the very characteristic property of aëriform matter, which we have called the law of Mariotte.

Another effect of molecular motion is that condition of matter which the word temperature, just used, denotes. There are few scientific terms more difficult to define than this common word temperature. In ordinary language we apply the terms hot or cold to other bodies according as they are in a condition to impart heat to, or abstract it from, our own, and the various degrees of hot or cold are what we call, in general, temperature. Two bodies have the same temperature if, when placed together, neither of them gives or loses heat; and, when, under the same conditions, one body loses while the other gains heat, that body which gives out heat is said to have the higher temperature.

Increased temperature tested in this way is found to be accompanied by an increase of volume, and we employ this change of volume as the measure of temperature. This is the simple principle of a thermome

ter.

The essential part of this instrument is a glass bulb, connected with a fine tube, and filled with mer