MOVEMENTS OF ATMOSPHERE — GULDBERG AND MOHN 201 



In nature the velocity is represented by a curve, and at the point 

 where U = U , the variation of the velocity is zero. Consequently 

 the angle of inclination is equal to the normal angle a for the maxi- 

 mum velocity. Choosing D and r as the parameters of the sys- 

 tem we shall f have 



The maximum gradient G = — - 



n-u • i v tt P COS a D o 



The maximum velocity U Q = - . — - 



p k r 



(10) 



In the neighborhood of the equator with p = 0.1199, a = o and 



k = 0.00002, we have U = 51 — °; assuming that the system of par- 



allels has a breadth of 2r = 20 and that the total depression is 2 mm 

 we shall find G n = o.2 mm and U = 10 meters. 



Variable Latitude 



We employ the same notation as in §11, and we consider only the 

 case in which the gradient coincides with the meridian. Take the 

 origin at the equator, and write the latitude 



& = Xx 

 where 



9 n 



X " : ± W ' 180 



Here the sign plus indicates that the gradient is directed toward 

 the north and the sign minus that the gradient is directed toward 

 the south. Assuming that the velocity is expressed by equation 

 (2), we again find equations (3) and (4). 



Eliminating G from these equations we shall have 



d (tang (p) 

 U cos <p -j = 2 o) sin (9 - (k + c) tang <[> ■ ■ ( n ) 



Introducing & in place of sin 6, we see that equation (11) is satisfied 

 by 



tan ^ = drb ( *- £) (12) 



e = -^- (13) 



k + c 



