THEORY OF CYCLONES VON BEZOLD 353 



must be satisfied and the problem consists essentially in the dis- 

 cussion of this equation. 



Consider a special isobar and let its radius be r c , the radius of 

 curvature of the inertia curve r it and the velocity of the wind along 

 the isobar v, then for a particle of air whose mass is m moving along 

 the isobar in the prescribed manner we have 



and 



Let the whole process go on at the geographic latitude <p and for 

 simplicity assume that this latitude is the same for all points of the 

 cyclone, which of course cannot be the case but will cause no great 

 error if we assume an average value for <p; finally, let T be the length 

 of the siderial day expressed in seconds of mean solar time, then we 

 have 10 



v T 



Ti = 



or 



whence 



4 % sin <p 



4tz mv 

 Pi = — T -sin? 



V 2 4:7C 



r ■■= m[ — + -jr v sin <p 



4 x 

 Put k = 0.0001458 = — and r = m y, where y is the acceleration 



communicated to the mass m by the gradient force F , then the pre- 

 ceding equation assumes the simpler form 



v 2 

 y = — + vksiri(p (6) 



c 



But for the acceleration y we also have the equation 



10 Sprung: Lehrbuch, p. 24. 



