52 THE NEW WORLD OF SCIENCE 



stancy. Graph No. 6 shows a kink at about 5,500 meters, 

 which is presumably due to a descending current struck at that 

 altitude. Graph No. 7 is that of a balloon followed to a height 

 of 20,000 meters where it apparently developed a leak and 

 failed to ascend further. Graph No. 8 shows the fluctuations 

 which are often found at low altitudes, these fluctuations being 

 undoubtedly due to ascending and descending currents. 



The extreme constancy in the rate of ascent, shown in a great 

 majority of flights, although surprising enough is not as in- 

 explicable as it at first appears, for since the pressure within 

 the balloon due to the tension of the rubber itself is only from 

 five to eight centimeters of water, and since this pressure is at 

 sea level less than I per cent, of the pressure of the atmosphere, 

 it will be seen that the balloon will expand practically freely, 

 that is, as though the walls did not constrain it at all, up to 

 heights of say 10,000 meters where the pressure is about a third 

 of an atmosphere. This means that the ascensional force must 

 be entirely independent of temperature and pressure. 1 For 

 the speeds with which these balloons ascend, namely, about 

 three meters a second, the resistance to motion must be di- 

 rectly proportional to the density of the air and experiment 

 shows it to be nearly proportional to the cross section of the 

 balloon, that is, to the square of the radius. This makes the 

 resistance vary as the cube root of the density, 2 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. 



1 For if / lt d 1 , z ; 1 /> 1 * 1 represent ascensional force, density, volume, 

 pressure and temperature at the surface of the earth, and f 2 , d 2 , v^ /> 2 , t 2 , 

 the corresponding quantities at any given elevation, then since d 2 /d^= 

 /> 2 f 1 //> 1 f 2 (i) and fi/f^v^d^/v^d^ (2) there results from a combination 

 of i and 2 fi/f^tdJv 2 d 2 =p 2 tl/pJ 2 XpJJpJf=ii. 



2 For if R^ is the resistance at the earth's surface and R 2 that at any 

 given altitude, 



which is seen from (i) to equal 



