204 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



the same mass of air passes from the horizontal current to the ver- 

 tical current is expressed by the formula 



7T r 2 w = 2 u r h U cos 4> 

 whence 



w n = — U n cos <l> (1) 



2 h TT 



- U cos (p 



JlZin 



JtCax. x < 



In cyclones of the second order the ratio h/r is probably so small 

 that we can neglect the vertical velocity and the vertical depression 



E which belongs to the 



accelerated motion of 

 the vertical current. The 

 rotation of the cyclonic 

 motion is determined by 

 the deflecting force T 

 (fig. 26) of the rotation of 

 the earth. We have as- 

 sumed that the cyclonic 

 system has a barometric 

 minimum at the surface 

 of the earth and a ba- 

 nc 26 rometric maximum in 



the upper strata. It 

 follows that the rotation in the upper strata is opposed to that at 

 the surface of the earth. The intermediate vertical current which 

 joins the two horizontal currents is consequently rectilinear. The 

 phenomena are inverse to those of the anti-cyclones. However, the 

 little that we know about the motions of the cirrus clouds seems to 

 indicate that the axes of rotation of the lower current and of the 

 upper current do not lie in the same vertical line. 



As parameters of the cyclonic system we can choose the depres- 

 sion D and the radius r which 

 depend on the physical state 

 of the air. We can approxi- 

 mately establish the follow- 

 ing relations between the max- 

 imum velocity U and the gra- 

 dient C . Assume that the gradient curve (fig. 27) is composed 

 of a straight line and of a curve whose equation is 



G= a + a ' 

 r r 3 



fig. 27 



