122 DECREASE OF DENSITY OF THE ATMOSPHERE. 



r + z r 8 



or ' "289F = ~ (r+) 2 ' 



.-. z = r(V289 l); 

 = 5.6r+ 

 = 22000 miles (approximately). 



REM. The actual height of the atmosphere, however, is 

 possibly much lower than this, for its temperature has been 

 found, by experiments made in balloons, to diminish with 

 great rapidity during an ascent; it is therefore very likely 

 that, at a height less than 5r, the air may be liquefied by 

 extreme cold, and in that case its external surface would be 

 of the same kind as the surfaces of known inelastic fluids. 

 (Besant's Hydromechanics, p. 120.) 



73. Decrease of Density of the Atmosphere. 



(1) When the force of gravity is constant. 



Take a vertical column of the atmosphere, and let it be 

 divided into an indefinite number of horizontal strata of 

 equal thickness, so that the density of the air may be uni- 

 form throughout the same stratum. Let the weight of the 

 whole column from the top of the atmosphere to the earth 

 = a, that of the whole column above the lowest stratum = 

 b, that of the column above the second = c, and so on. 

 Then b, c, d, etc., are the forces respectively which compress 

 the first, second, third, etc. strata, which, as they are of 

 equal thickness, are as their weights, a b, b c, c d, 

 etc. Hence we have 



a b : b c :: b : c\ 



.*. a : b :: b : c. 



In the same way, it may be shown that 



b : c :: c : d, 

 and so on. Hence, b, c f d, etc., and therefore the densities 



