MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 191 



By integration we find 



r U = £ a r 2 + b (2) 



where a and b denote two constants that we can determine in the 

 following manner: 



Let the given velocity of the exterior air be U l at the distance r x 

 and assume the velocity of the interior mass equal to zero at the 

 distance r , we find 



and 



* a = ~2 — T7'> o = - — — 2 



r. r — rJ 



U = 1 . ~ . U t (3) 



r n- - r n - 



It is quite probable that in nature the radius r is equal to zero and 

 we shall then have 



U - I • U t (4) 



' i 



Hence, the current of air rotates with a constant angular velocity (see 



§14). 



In order to determine the gradient and the pressure, we distinguish 

 two cases in the northern hemisphere. 



(i) Rotation contrary to the sun. 



In the cyclones of the northern hemisphere the rotation takes 

 place contrary to the apparent diurnal motions of the sun, the grad- 

 ient is directed toward the center, the centrifugal force and the 

 deflecting force of the rotation of the earth are directed outward. 

 We have then 



u U 2 



- G = — + 2 a) sin 9 . U (5) 



P r 



By writing /xG = — and introducing the value of U given in equa- 

 dr 



tion (4) we find by integration, p being the pressure at the center 



where U = o, 



P ~ Po = % (U 2 + 2 co sin 6 . U r) (6) 



P 



(2) Rotation with the sun. 



In the anti-cyclones of the northern hemisphere the rotation takes 

 place with the apparent diurnal motion of the sun; the gradient 



