crowded into a pneumatic cushion by some sort of pressure pump; the ordinary air of the room will expand in the same way if the pressure to which it is subjected is relieved.

Thus, let a liter beaker with a sheet of rubber dam tied tightly over the top be placed under the receiver of an air pump. As soon as the pump is set into operation, the inside air will expand with sufficient force to burst the rubber or greatly distend it, as shown in Fig. 35.

Again, let two bottles be arranged as in Fig. 36, one being stoppered air-tight, and the other left uncorked. As soon as the two are placed under the receiver of an air pump and the air is exhausted, the water in A will pass over into B. When the air is readmitted to the receiver, the water will flow back. Explain.

FIG. 35

FIG. 36

B

46. Why hollow bodies are not crushed by atmospheric pressure. The preceding experiments show why the walls of hollow bodies are not crushed in by the enormous forces which the weight of the atmosphere exerts against them. Thus, at normal atmospheric pressure a soap bubble 6 inches in diameter is under a total crushing force of one ton; but the air inside such bodies presses their walls out with as much force as the outside air presses them in. In the experiment of § 35 the inside air was removed by the escaping steam. When this steam was condensed by the cold water, the inside pressure became very small, and the outside pressure then crushed the can. In the experiment shown in Fig. 35 it was the outside pressure which was removed by the air pump, and the pressure of the inside air then burst the rubber.

Illustrations of the expansibility of air

47. Boyle's law. The first man to investigate the exact relation between the change in the pressure exerted by a confined body of gas and its change in volume was an Irishman, Robert Boyle (1627–1691). We shall repeat a modified form

of his experiment much more carefully in the laboratory, but the following will illustrate the method by which he discovered the important law which is now known by his name.

Let mercury be poured into a bent glass tube until it stands at the same level in the closed arm AC as in the open arm BD (Fig. 37). There is now confined in AC a certain volume of air under the pressure of one atmosphere. Call this pressure P1. Let the length AC be measured and called V1. Then let mercury be poured into the long arm until the level in this arm is as many centimeters above the level in the short arm as there are centimeters in the height of the barometer. The confined air is now under a pressure of two atmospheres. Call it P2. Let the new volume A1C(= V2) be measured. It will be found to be just half its former value.

Aī

A-

--D

-B

Hence we learn that doubling the pressure exerted upon a body of gas halves its volume. If we had tripled the pressure, we should have found the volume reduced to one third its initial value, and so on. That is, the pressure which a given quantity of gas at constant temperature exerts against the walls of the containing vessel is inversely proportional to the volume occupied. This may be algebraically stated as follows:

FIG. 37. Method of demonstrating Boyle's law

This is Boyle's law. It may also be expressed in slightly different form. Doubling, tripling, or quadrupling the pressure must double, triple, or quadruple the density, since the volume is made only one half, one third, or one fourth as much, while the mass remains unchanged. Hence the pressure which a gas exerts at constant temperature is directly proportional to its density.*

* A laboratory experiment on Boyle's law should follow this discussion. See, for example, Experiment 8 of "Exercises in Laboratory Physics," by Millikan, Gale, and Davis.

In constructing subaqueous tunnels, the workers are compelled to operate under an air pressure great enough to withstand
the pressure which would force earth and muck into the space where they work. As material is removed (see left end of
picture), powerful jacks press forward a cylindrical shield, inside of which the tunnel lining of cast-iron segments is built
up. A concrete bulkhead separates the compressed-air working chamber at the left from the space at the right, where
atmospheric pressure exists. To enter the high-pressure compartment, the men pass first into the service lock, and remain
there for several minutes, while the air pressure upon them is gradually increased. This is called "compressing" the men.
The blood in this way becomes charged with dissolved air which enters by way of the lungs. To leave the high-pressure
compartment, the men again enter the service lock, while the pressure is gradually lowered to atmospheric to permit the
excess dissolved gases to leave the blood by way of the lungs. If this "decompressing" is done too rapidly, the dissolved
gases escape as bubbles within the blood vessels, causing intense pain and sometimes death. Small cars laden with diggings
of rock, earth, and muck are taken out through the locks as shown at the bottom. (Courtesy of the Popular Science Monthly)

OTTO VON GUERICKE (1602-1686)

German physicist, astronomer, and man of affairs; mayor of Magdeburg; invented the air pump in 1650, and performed many new experiments with liquids and gases; discovered electrostatic repulsion; constructed the famous Magdeburg hemispheres which eight teams of horses could not pull apart (see opposite page 34)

48. Measurement of gas pressure. For measuring gas and steam pressures various types of gauges are used, the Bourdon being one of the best. Fig 38 (2) shows a simple form of this gauge for use with automobile tires. A flattened tube (Fig. 38 (1) ) is bent into the form of an arc, so that when air under pressure enters it the tube tends to straighten. This causes the rack R to turn the pinion P, to which the pointer is attached. These gauges, as well as steam gauges, record whatever pressure exists in excess of the atmospheric pressure. In general, absolute (or total) pressure equals gauge pressure+15 pounds per square inch at sea level.*

30 40

((1) (2)

49. The extent and character of the earth's atmosphere. From the facts of compressibility and expansibility of air we may know that the air, unlike the sea, must become less and less dense as we ascend from the bottom toward the top. Thus, at the summit of Mont Blanc, an altitude of about three miles, where the barometer height is but 38 centimeters, or one half its value at sea level, the density also must, by Boyle's law, be just one half as much as at sea level. How rapidly both density and pressure decrease with altitude is indicated by the curve in Fig. 39.

FIG. 38. Interior of Bourdon type of tire pressure gauge

No balloonist has ascended higher than 8 miles. In 1862 a height of approximately 7 miles was attained by the two daring English aëronauts Glaisher and Coxwell. At this altitude the barometric height is but about 7 inches. Both aëronauts lost the use of their limbs, and Mr. Glaisher became unconscious. Mr. Coxwell barely succeeded in grasping with his teeth the rope which opened a valve and caused the balloon to descend. Again, on May 4, 1927, Captain Gray

*It is recommended that laboratory work on the use of manometers accompany this discussion. See, for example, Experiment 9, of "Exercises in Laboratory Physics," by Millikan, Gale, and Davis.