MOVEMENTS OF ATMOSPHERE— GULDBERG AND MOHN 237 



By equation (8) we shall find 



N' 

 tango;' = tang a + (11) 



The last equation shows us that for a stationary but variable cyclone 

 the angle between the gradient and the wind differs from the nor- 

 mal angle a. Suppose that we have U r = 150, 0=48° and k — 

 0.000 10, and consequently in the constant cyclone N = U r sin a 

 = 1 1 1. 5. In one hour N may increase to 115.1, then we find 

 N' — 0.001 and a! = 44. °y. U r is increased by 13.7 and the maxi- 

 mum velocity by about i.5 m . 



Assuming if = o and £' = W that is to say that the cyclone is 

 propagated with the velocity W and in a constant direction, and 

 considering the special case in which M and N are independent of the 

 time and M' = o, N' = o, the equations (5) and (7) show that then 

 U and p are independent of the time and consequently that the 

 pressure is constant at the center during the propagation, and we 

 have from equation (11) a' = a and 



p kUr W 



- = log nat r - * U 2 - — U r sin (<p - a) + C . (12) 



p cos a b r \r ' 



Assuming that at the distance R the pressure P remains constant 

 and that the velocity U can be neglected, the equation is written 



P - p kUr R W 



— = log nat - + £ U 2 + — U r sin (<p - d) . (13) 



p cos a & r r T 



where the influence of the velocity of propagation is represented by 

 the term 



W 



— U r sin (<p — a) 

 r 



which term has its maximum value for 



<p = 90° + a 



and consequently the axis of the isobar makes the angle a with the 

 velocity of propagation. In the direction o b, perpendicular to the 

 axis o a (fig. 50) this term is zero and the pressure has the same value 

 in this direction as in the stationary cyclone. 



