MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 1 () 7 



away from the axis. The gradient G in a horizontal plane is found 

 by the formula 



G = i a = _* vdv = p_ a i^ (io) 



[i d x fi d x n R 4 



Consider a horizontal plane at the distance z = z = — h, and study 



the phenomena on this plane. 



Writing 



(1 x 



V = ^ and £ = - and D = \ p V 2 



we shall have 



u = - — ; — — • V n ; G = - 



1 + f 2 ° ' // /* (1 + e 2 ) 2 



The horizontal velocity has a maximum u when £ = i and 

 m = £ V . The horizontal gradient has a maximum 



£ m when £ = i/y~ 

 and 



16 ft h 



Choosing as the parameters D expressed in millimeters and the dis- 

 tance of the axis x = h, where the horizontal velocity has its 

 maximum, as expressed in degrees of a great circle, we shall find 



The maximum horizontal velocity U = V 51.5 D 



The maximum horizontal gradient G m = 0.65 — ° 



x 



The distance from G m to the vertical axis x m = 0.58:r 



The height of the horizontal axis h = x 



The absolute maximum velocity 1 7 = 2 U 



By the aid of the preceding formulas we have calculated the fol- 

 lowing table in which D denotes the barometric difference: 



£ 0.5 



U : U 0.80 



G :G m 0.99 



D :D 0.20 



