118 DENSITY OF THE ATMOSPHERE. SECT. XV. 



heights above the earth be taken in increasing arithmetical 

 progression, that is, if they increase by equal quantities, as by a 

 foot or a mile, the densities of the strata of air, or the heights of 

 the barometer which are proportionate to them, will decrease in 

 geometrical progression. For example, at the level of the sea if 

 the mean height of the barometer be 29*922 inches, at the height 

 of 18,000 feet it will be 14-961 inches, or one half as great ; at 

 the height of 36,000 feet it will be one-fourth as great ; at 54,000 

 feet it will be one-eighth, and so on. Sir John Herschel has shown 

 that the actual decrease is much more rapid, and that, in any hypo- 

 thesis that has been formed with regard to the divisibility of the 

 aerial atoms, a vacuum exists at the height of 80 or 90 miles above 

 the earth's surface, inconceivably more perfect than any that can be 

 produced in the best air-pumps. Indeed the decrease in density is 

 so rapid that three-fourths of all the air contained in the atmosphere 

 is within four miles of the earth ; and, as its superficial extent is 

 200 millions of square miles, its relative thickness is less than 

 that of a sheet of paper when compared with its breadth. The air 

 even on mountain tops is sufficiently rare to diminish the intensity 

 of sound, to affect respiration, and to occasion a loss of muscular 

 strength. The blood burst from the lips and ears of M. de 

 Humboldt as he ascended the Andes ; and he experienced the 

 same difficulty in kindling and maintaining a fire at great heights 

 which Marco Polo, the Venetian, felt on the mountains of 

 Central Asia. M. Gay-Lussac ascended in a balloon to the 

 height of 4'36 miles, and he suffered greatly from the rarity of 

 the air. It is true that at the height of thirty-seven miles the 

 atmosphere is still dense enough to reflect the rays of the sun when 

 18 below the horizon ; but the tails of comets show that extremely 

 attenuated matter is capable of reflecting light. And although, 

 at the height of fifty miles, the bursting of the meteor of 1783 

 was heard on earth like the report of a cannon, it only proves 

 the immensity of the explosion of a mass half a mile in diameter, 

 which could produce a sound capable of penetrating air three 

 thousand times more rare than that we breathe. But even these 

 heights are extremely small when compared with the radius of 

 the earth. 



The density of the air is modified by various circumstances, 

 chiefly by changes of temperature, because heat dilates the air 

 and cold contracts it, varying ^ of the whole bulk when at 32 



