Careful experiments reveal the following law: _The volume of a given mass of gas at constant temperature is inversely proportional to the pressure to which it is subjected_. This law is often expressed mathematically. _P/P´ = V´/V_, or _PV = P´V´_. Since doubling the pressure reduces the volume one-half, it doubles the density. Tripling the pressure triples the density. We therefore have _P/P´ = D/D´_ or the density of a gas directly proportional to its pressure. [Illustration: FIG. 38.--Height and density of the air.] =59. Height of the Atmosphere.=--From its properties of _compression_ and _expansion_, the air varies in density and pressure as one ascends in it. At a height of 3 miles the pressure is reduced to about one-half. This is an indication that one-half of the air is below this level. Balloonists have gone to a height of 7 miles, Glaser and Coxwell in England in 1862 and Berson in France in 1901. The atmosphere has been explored to a height of 30,500 meters (18.95 miles) by sending up self-registering barometers in small balloons which burst at great altitudes. A parachute protects the instruments from breakage from too rapid fall. This height of 30,500 meters was reached by a balloon sent up by William R. Blair, at Huron, South Dakota, September 1, 1910. At a height of 35 miles, the density is estimated at 1/30,000 of its value at sea-level. (See Fig. 38.) It is believed that some rarefied air exists for a considerable distance above this point, some estimates placing the extent at 100 miles, and others from 200 to 500 miles. Evidences of some air at such heights are shown by: (a) the height at which meteors first appear, (b) the height of the Aurora Borealis, and (c), the distance that the sun is below the horizon when the last traces of color disappear from the sky in the evening. Although the exact limits of the atmosphere are unknown, the weight of a column of air 1 sq. cm. in cross-section, and extending _upward as high as the atmosphere_, may be accurately computed. For this column of air exactly balances the column of mercury in the tube of the barometer. Below sea-level, the air increases rapidly in density and it is estimated that at a depth of 35 miles, the density of the air would be a thousand times that at the earth's surface, or more than that of water. Important Topics 1. Evidence of compressibility of gases and incompressibility of liquids. 2. Boyle's Law. Proof, applications. 3. Extent of the atmosphere--three evidences. Exercises 1. Mention three illustrations of the compressibility and expansibility of air that you know from your own experience. 2. Increasing the pressure increases the amount of a gas that will be absorbed by a liquid? Explain this. Have you ever observed this fact? Where?