120 HEIGHT OF THE HOMOGENEOUS ATMOSPHERE. 



70. Mass of the Earth's Atmosphere. By means 

 of the barometer, some idea may be formed of the mass of 

 air and vapor surrounding the earth, since the weight of the 

 whole atmosphere is equal to that of a stratum of mercury 

 about 29.9 inches thick covering the globe. Suppose the 

 earth to be a sphere of radius r, and that h is the height of 

 the barometric column at all points of its surface. Then 

 the mass of the atmosphere is approximately equivalent to 

 the mass 4:rar% of mercury, where a is the density of the 

 mercury. 



Let p be the mean density of the earth ; then, 

 the mass of the atmosphere : the mass of the earth 



= 3<rh : pr. 



Taking a = 13.568 (Art. 47), and p = 5.5,* and sup- 

 posing the height of the barometric column h to be 30 

 inches, which is probably near the average height at sea- 

 level,! it will be found that the above ratio of the mass of 

 the atmosphere to that of the earth is about 



71. The Height of the Homogeneous Atmosphere. 



If the atmosphere were of the same density throughout 

 as at the surface of the earth, its height I would be approx- 

 imately obtained from the following equation, 



ah = pi, (1) 



where o and p are the densities of mercury and air respect- 

 ively, and h is the height of the barometric column. From 

 Art. 70, and Art. 33, Sch., we have 



o = 13.568x768p = 10420.224p, 



* There ia some doubt about the accuracy of this value ; the value deduced by 

 the Astronomer Royal at the Harton Colliery in 1864 is 6.6- Phil. Trans., 1856. 

 t See Bncy. Brit., Vol IH., p. 88. 



