484. One of the most obvious properties of matter is weight, and air may be shewn to possess this. It would seem a natural process to test this by first weighing an empty bladder, and then weighing this bladder full of air; Aristotle is said to have done so, and, finding the same result in the two cases, to have inferred that air has no weight. But here we have the operation of a cause of error to which we drew attention in Art. 444; the additional weight of air in the bladder is counterbalanced by the buoyancy of the atmosphere exerted on the inflated bladder. The experiment must then be made in a manner which avoids this cause of error. Take a flask of glass or metal, and exhaust it of air by the aid of a machine to be described hereafter, called the air-pump; then weigh the exhausted flask. Admit the air to the flask and weigh it again. Then the difference between the two results gives us the weight of the air which the flask will hold. As we have said in Art. 462 the weight of a cubic foot of air under ordinary circumstances is about 1 ounces. We spoke of exhausting the flask of air; but in practice we cannot draw out all the air, though we may contrive to leave only a quantity which is quite inappreciable. Again, the experiment may be carried a step further. For not only can we draw air out of a vessel, but we can force into it any quantity of air we please. Thus we can increase the amount of air in the vessel, and we shall find that as we do so we increase the weight of the air in the same proportion.

485. Again, the resistance which air opposes to motions through it is an evidence that it has the properties of matter; we are very sensible of this resistance when we run. The reaction of the air when they strike it with their wings enables birds to fly; in a space void of air they could not fly. Wind is air in motion, and the powerful effects of high winds are merely the consequences of matter in violent motion.

486. It is usual to remark that air possesses the property of matter which we call impenetrability. Invert a tumbler and press it below the surface of water; then it is easy to see that the water does not get to the highest part

of the tumbler. If a small cork be floating on that part of the water over which the tumbler was placed, the cork will not reach the highest part of the tumbler. The air in the tumbler is indeed compressed into less space than it originally occupied, and so the water occupies part of the tumbler; but the air remains in the upper part of the tumbler and excludes the water from it.

XLIII. PRESSURE OF THE ATMOSPHERE.

487. If we put air in a vessel furnished with a moveable piston we find that we can push in the piston and compress the air to any extent we please. If we wish to keep the air in this compressed state we must retain the piston in its place by a suitable force; if we diminish that force the air pushes the piston back through some space, and if we remove all the force the air resumes its original dimensions. There must be some relation then between the force which we apply to the piston, and the volume occupied by the compressed air; this relation we shall consider in the next Chapter after some necessary preliminaries in the present.

488. We know that air requires the exercise of some constraint to confine it within the space it occupies, and so we naturally suppose that there must be some pressure acting on the apparently unconstrained air around us, and we soon find that this pressure must be supplied by the atmosphere itself; any stratum of air has to support the pressure produced by the weight of all the strata above it. A very important experiment serves to demonstrate the existence of the pressure of the atmosphere, and to measure its amount.

489. To measure the pressure of the atmosphere.

Take a glass tube a yard long, open at one end and closed at the other; fill it with mercury and place a finger over the open end to prevent the escape of the mercury. Invert the tube, put the end closed by the finger below the surface of a vessel containing mercury, and withdraw the finger. Some of the mercury will fall out of the tube,

A

G

leaving a vacuum, that is an empty space, at the top of the tube. In the diagram let AB denote the tube, EF the surface of the mercury in the vessel, and G the surface of the mercury in the tube. It is found that the height of G above the level of EF is about 30 inches, so long as the place at which the experiment is made is not much above the level of the sea; but even at the same place the height is always fluctuating slightly according to the state of the temperature and the weather. The column of mercury above the level of EF is supported by the pressure of the atmosphere on the surface of the mercury in the vessel; this pressure is transmitted through the mercury in the vessel, and into the tube by means of the end B. The principle is the same as in Art. 420; we may imagine two tubes, one containing mercury of about 30 inches high, and the other extending upwards as far as the atmosphere extends, and the columns of mercury and of air would produce the same pressure at their lowest points: the column of mercury must be supposed to be in a tube closed at the top so as to relieve it from the pressure of the atmosphere above it.

E

B

D

490. As we ascend to a height above the level of the sea the pressure of the atmosphere diminishes, and so the height of the column of mercury diminishes. If the atmosphere were throughout of the same density there would be a diminution of about one inch in the mercury for every 900 feet of ascent; but the fact is that the higher we ascend the less is the density of the atmosphere, and so the diminution of the column of mercury is not in exact proportion to the ascent.

491. We see then that the pressure of the atmosphere under ordinary circumstances on a square inch of surface is equal to the pressure of a column of mercury of the height 30 inches standing on one square inch as base: thus

the pressure is equal to the weight of 30 cubic inches of mercury, that is about 15 pounds.

492. In the propositions which we have given with respect to liquids in equilibrium in open vessels we have supposed that no pressure was exerted on the upper surfaces. But we now see that the atmosphere will exert a pressure, which under ordinary circumstances is about 15 pounds on a square inch; and hence it is necessary to advert to the principal results formerly obtained, in order to ascertain whether they still hold.

(1) The upper surface of a liquid will still be a horizontal plane as in Art. 358; for the pressure of the atmosphere being of the same amount on every square inch of the surface will not disturb the horizontal surface.

(2) Suppose a small area taken inside a vessel containing liquid; then the pressure will be the weight of a certain column of liquid extending up to the surface, increased by the amount of pressure due to the atmosphere; see Arts. 362 and 363.

(3) In Arts. 376...378 we have found the pressure of liquid on a vertical side of a vessel, and the point at which the pressure may be supposed to act. Now if we consider the pressure of the atmosphere we must observe that it will act in the same manner on the two faces of the vertical side; on one face the atmosphere would be in contact with the vertical side, and on the other face the pressure will be transmitted through the liquid. Thus on the whole the pressure of the atmosphere merely supplies two equal opposing forces which balance each other and leave our former result unaffected.

(4) The principle of Chapter XXX. that liquids stand at a level will still hold when we regard the pressure of the atmosphere.

(5) The result obtained at the end of Art. 420 will still hold when we regard the pressure of the atmosphere; for practically the pressure of the atmosphere at the levels AB and CD will be the same, supposing these levels only slightly different.

XLIV. RELATION BETWEEN PRESSURE
AND VOLUME.

493. Two important principles were established with respect to liquids in Chapters XXVI. and XXVII.; namely, that pressure applied to the surface of a liquid in a vessel is transmitted unaltered in amount throughout the liquid, and that the pressure at any point is the same in all directions round the point. Now these two principles hold for air and gases as well as for liquids, as may be shewn by the same reasoning and experiments as have been already used; thus they hold for all fluids.

494. We are now about to explain the relation which holds between the volume and the pressure for the case of compressible fluids, that is for the case of air and the gases.

Take a glass tube and bend it so that the two branches shall be parallel. Let A, the end of the shorter branch, be closed, and B, E the end of the longer branch, open. Pour into the tube a smalĺ quantity of mercury, and, by withdrawing air or adding mercury, make the mercury in the two branches stand at the same level C and D; let this level meet the vertical straight line MPQ at M. Thus in AD we have a quantity of mercury sustaining the pressure of

B

A

M

the atmosphere; for the pressure at C is produced by the atmosphere, and this pressure is transmitted to D. We will suppose this pressure to be of its ordinary amount, so that it is measured by 30 inches of mercury. Pour more mercury into the tube at B, and suppose the mercury to rise to E in the longer branch and to F in the shorter branch. Let the level of E meet the vertical straight line MPQ at Q, and let the level of F meet this straight line at P. Then the air which formerly occupied the space represented by AD is now compressed into the space