164 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The constant A is now to be so determined that on the borders of both 

 regions, that is to say for r = R, the movements pass continuously 

 from one into the other. Since now 



u _x dqt.y dW 

 r' dr r dr ' 



_y dq> x dW 

 r' dr~ r dr 



therefore at the boundary we must have 



&<p._d<p\ dW a dW t 



dr " dr dr ' ' dr ' 



This condition is satisfied for the function cp. We have still to bring 

 it about that the corresponding equation shall be satisfied by the 

 function W. Since 



dW n Ac 

 dr ~2Jc r ' 



therefore for r=B we have 



dW i __Xc 

 dr ~2Jc ' ' 



This latter will be the case when we put 

 Therefore we have finally 



dW f A < 2/^N 



i-Z \ m\RJ S 



dr ju 

 or if for abbreviation we put 



^^-XiJ" m 



we obtain 



dW t A 



~dF=J[=2 r 'f( r ) (28) 



The function / (r) can according to equation (26) also be written- 

 This gives / (r) = l for r=0 aud f {r) = (k-c) for r=R 



rC 



