DECREASE OF DENSITY OF THE ATMOSPHERE. 123 



of the successive strata, form a series of terms in geometric 

 progression, which is decreasing since a is greater than b, 

 and therefore b greater than c, and so on ; and as the strata 

 all have the same thickness, the heights of the several strata 

 above the earth's surface increase in arithmetic progression. 

 Hence, 



If a series of heights be taken in arithmetic pro- 

 gression, when the force of gravity is constant, the 

 densities of the air decrease in geometric progression. 



SCH. By barometric observations at diiferent altitudes, 

 it is found that at the height of 3| miles above the earth's 

 surface, the air is about one-half as dense as it is at the 

 surface. Forming therefore an arithmetic series, with 3| 

 for the common difference, to denote the heights, and a 

 geometric series with \ for the common ratio, to denote 

 densities, we have 



Heights, 3$, 7, 10$, 14, 17$, 21, 24}, 28, 31$, 35, etc. 

 Densities, $, $, $, ^, ^, ^, T $ 



That is, according to this law, at the height of 35 miles 

 the air is less than a thousandth part as dense as it is at the 

 surface of the earth. 



(2) When the force of gravity varies inversely as the 

 square of the distance from the earth's centre. 



Let r be the radins of the earth, p' the density at the sur- 

 face of the earth, p the density at a height z, and h the 

 height of a homogeneous atmosphere. Then, since the 

 density varies as the compressing force, and this varies as 

 the weight, we have 



p' : dp :: hp'g : g-^- ^ (- p dz), 



ur 2 



where a and -~- r , are the measures of the earth's attrac- 

 (r + zY 



