METEOROLOGICAL WORK 53 



If, as is approximately true for these speeds, the resistance 

 varies as the square of the velocity, 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 other words, since 

 the sixth root of 2 is 1.13, at a height of 6,000 meters, the 

 velocity should be about 13 per cent, greater than at the surface. 

 Such an increase in velocity would be very easily observable in 

 the experimental data. The fact that it is not found there is 

 due to the wholly fortuitous circumstance that the slow dif- 

 fusion of hydrogen through the walls, as observation by Blair 

 and Sherry has shown, is just sufficient, with the balloons here 

 used, to retard the ascensional rate enough to make it quite ex- 

 actly constant. 



This makes it possible, provided one could always duplicate 

 the size and weight of his balloon, to obtain a very exact de- 

 termination of wind velocity and direction by a one-theodolite 

 method, the height being always known from the time and the 

 known rate of ascent. 



When, however, the weight and inflation of the balloons are 

 varied, as they must be in practice, since the balloons vary in 

 weight from twenty to thirty-five grams, and since it is con- 

 venient also to vary the filling according as low altitude or high 

 altitude wind-data are desired, it is found that no accurate 

 formula can be found for computing the speed in terms of the 

 ascensional force, the weight to be lifted, and a single invariable 

 constant. For approximate work, however, the one-theodolite 

 method, because of its convenience and because of the imprac- 

 ticability of measuring an accurate base line at the front, is 

 much in use, and one of the advances made in the meteoro- 

 logical work of the army during the past year has consisted in 

 developing with the aid of the large amount of data available, 

 a general formula for the rate of ascent in terms of the ascen- 

 sional force and the weight to be lifted, which though far from 

 accurate is more reliable than that which has heretofore been 

 used. The formula heretofore used is that of Dines, namely, 



