OF THE UNITED STATES ARMY. 



139 



as the cube root of the density,- which means that at a height of 

 6,000 meters, where the density is about one half, the resistance is 

 .83, of what it would be at the surface. If, as is approximately true 

 for these speeds, the resistance varies as the square of the velocity, 



Uniform rate of ascent of pilot balloon up to ii,ooo meters. 



or the velocity as the square root of the resistance, this would mean 

 that the velocity should vary as the sixth root of the density. In 



2 For if Ri is the resistance at the earth's surface and R2 that at any 

 given altitude, 



Ri ^ vM 



which is seen from (i) to equal 



m 



