LIMIT TO THE HEIGHT OF THE ATMOSPHERE. 121 



and taking h = 30 inches, we have, by solving (1) for I, 



I = n - = 26050 feet, 

 P 



which is a little less than 5 miles. 



72. Necessary Limit to the Height of the At- 

 mosphere. Since the attraction of the earth diminishes 

 at a distance from its surface (Anal. Mechs., Art. 133a), it 

 is clear that the atmosphere is very far from being of uni- 

 form density throughout, and therefore the result in Art 71 

 is very far from the truth. A limit can -be found, however, 

 to the height of the atmosphere from the consideration that, 

 beyond a certain distance from the earth's centre, its attrac- 

 tion will be unable to retain the particles of air in the cir- 

 cular paths which they describe about the earth, since the 

 centrifugal force must exceed the force of gravity. 



Let w be the earth's angular velocity, and r its radius. 

 Then the centrifugal force of a particle m of air on the 



earth's surface is mwV, and this is equal to ^ - [Anal. 



Mechs., Art. 199, (3)] ; therefore, at a height z above the 

 surface, the centrifugal force mw 2 (r + z) 



mg r -\- z 

 ~ 289 ^~ 



The earth's attraction at the same height (Anal. Mechs., 

 Art. 133) 



mgr 2 



and, in order that the particle may be retained in its path, 

 these two forces must equal each other. 



mg r -f z _ 

 **' 289 ~7~ ~ 



