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MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 219 



Make 



c c' = d a, a a' = d s, c a = r, c' a' = r + d r; 

 the angles c' c a = <p and c a a' = <p. 

 We have 



a c b = — d (p, 

 e a = — d r 

 ad = ae — bf 

 a' d = b e + a' f 



By substituting the values of these quantities we shall find 



(7) 



(8) 



Supposing that U r cos (p is constant and that the angle <f' * s con_ 

 stant and equal to a as in permanent cyclones, then by integration 

 and determining the arbitrary constants so that <p = o for r = r Q 

 we shall have 



U r cos a 



r 

 tang a log. nat. — — <p 

 r n 



= W r sin <p . (9) 



By this equation we can determine the angle <p that alimentary 

 air must describe in order to reach the interior limit of the cyclone. 



The equations that we have developed apply also to the upper 

 strata of an anti-cyclone where the barometric minimum occurs. 



First example. 



r 



r 



= 6 ; <p = 20° 



By equation (9) we calculate the following values: 



a = 40° 50° 60° 70° 



W 



jy = 0.44 0.57 0.68 0.77 



