MOVEMENT OF AIR IN ANTICYCLONES POCKELS 



60 1 



tance; we thus arrive at Oberbeck's solution. 3 In the case to be 

 considered by us of an anticyclone, or a positive y, C is to be put 

 zero in order that V t be not infinite when r = o ; on the other hand 

 the exponential function in the expression (2') is to be retained 

 since its exponent is negative and it therefore disappears when 

 r = a. It is because he omitted the exponential function in his 

 general solution that Oberbeck could not apply his solution to the 

 anticyclones. 



In order that the expressions for V t namely (2) with C = o and 

 (2') may be equal to each other when r = R, as is required by the 

 continuity of the velocity, we must have 



2 {k + r ) 2k r 



whence the following value results 



C" = 



fXR 2 



2k~WVr) 



h/ r 



Finally, as the complete solution for the velocity components we 

 obtain 



n 2 / 



► for r < R 



(3) 



1 R 2 



2 r 



_ _ 1 r j & 



1 2 " k r 



The exponent 



\ k+ r J J 



► torr>R (3') 



kfr 2 



3 Oberbeck (Annalen, 1882, XVII, p. 143) subjects the quantity — 7- =c 

 to the condition c < k in order to obtain an infinitely large value of the 

 velocity at the center and a deflection of the direction of the wind to the 

 left instead of to the right of the gradient. But this is attained by the con- 

 dition c <2k; for the velocity (logarithmic) becomes infinitely large when 

 c = 2k and the angular deviation remains in general always between the 

 limits + tg- x l/k and + n/2, which latter value is attained at the center 

 as soon as c > k. 



