MOVEMENT OF AIR IN ANTICYCLONES POCKELS 599 



value zero so that the condition (Ic) consists of two, one for each 

 region, i. e., 



iJL YA = r r for r < R (IC) 



dr 



d (rV n ) 

 dr 



= for r > R (Ic") 



The continuity condition (Ic) alone determines V n as a function of 

 r; if then we substitute this function in (lb') we shall obtain a 

 differential equation for V t ; finally the equation (la') serves for 

 the determination of the distribution of pressure after we have 

 substituted therein the functions found for V n and V t . The com- 

 plete solution therefore demands the integration of three ordinary 

 linear differential equations of the first order for the inner region and 

 three others for the outer region ; in this solution the integration con- 

 stants are to be so determined that both V n and V t as also p are con- 

 tinuous at the boundary between the two regions, i. e., for r=R, 

 since at the passage from the inner to the outer region both the 

 velocity and direction of the current of air, as also the pressure of 

 the air, must change continuously. 



In the manner thus indicated we first find 



V n = - 1 r riorr <R (1) 



where the constant of integration must be zero because other- 

 wise V n in the center of the system of winds would become infinite; 

 furthermore 



constant , ^ _ 

 V n = £( r r > R, 



r 



and the constant of integration is — %yR 2 so that V n shall remain 

 continuous when r = R, hence 



R 2 

 Vn-hT ~ iorr>R 



In the case of a cyclone the sign of y is to be taken oppositely from 

 that in this equation for the anticyclone. Now the differential 

 equation (lb') becomes 



forr<i? =1 r(— r + v t) + kV t +- r*r (Ha) 



iorr>R =l r R'( d ll .l + Yl) + kVt+lrXR 2 .- (lib) 

 2 \ dr r r 2 / 2 r 



