174 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



When the whirlwinds have great dimensions, we cannot neglect 

 the work of friction. Assuming that the trajectories of the par- 

 ticles of air are logarithmic spirals, we can calculate the barometric 

 depression as we have done in paragraphs 12 and 14 (see figures 

 9, 10, 11) where the whirlwind of great velocity shows a baro- 

 metric depression equal to 32.9 mm for a radius equal to 2 degrees 

 of a great circle and with a maximum velocity equal to 50 meters 

 per second. The whirlwind of average velocity shows a barometric 

 depression equal to 34.9 mm for a radius equal to 20 degrees and with 

 a maximum velocity equal to 16 m. p. s. In the last case the work 

 of the friction is much greater than in the first, because the distance 

 traversed is ten times longer. 



Considering table I, we shall see that barometric depressions can 

 be produced by different states of the atmosphere. The two whirl- 

 winds, in which the barometric depressions do not sensibly differ, are 

 distinguished by their maximum velocities, and it is necessary to 

 seek the explanation of this difference in the lengths of the radii 

 of the vertical currents that produce the horizontal velocities. 

 The whirlwind of great velocity belongs to a vertical current whose 

 radius is probably several tenths of a degree, but whose initial verti- 

 cal velocity is very great. The other whirlwind of average velocity 

 belongs to a vertical current whose radius extends over several 

 degrees and whose initial vertical velocity is not great. 



The length of the radius of the vertical current, which we can 

 assume proportional to the distance from the center to the point 

 where the velocity attains its maximum value, plays an important 

 part in the theory of whirlwinds. Comparing two whirlwinds 

 having the same barometric depression, that which has the shorter 

 radius has the greater velocity and consequently is the most violent. 

 Comparing two whirlwinds with the same maximum velocity, that 

 which has the shorter radius has the greater gradient and the smaller 

 depression. 



The physical cause that determines the length of the radius de- 

 pends on the difference in the condition of the ascending air and of 

 the surrounding atmosphere. 



