164 THE MFX'HANICS OF THE EARTHS ATMOSPHERE. 



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

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

 from one into the other. Since now 



r' dr r <Ir ' 



y da? X dW 

 r dr r dr 



therefore at the l)oundary we must have 



dcp„_djj^ d ]r„ d Tf , 



dr ~ dr dr ~~ dr ' 



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

 it about that the correspoudiug ecjuation shall be satisfied by tbe 

 function W. Since 



dW„ Ic 



therefore for r=E we have 



dW, Xc ^ 

 dr 2k 



This latter will be the case when we ]»ut 



— 2A 

 A=- ^,.i?2-^ 



Therefore we have finally 



dlF,__ X i _2/'r\'^-2 ) 



or if for abbreviation we i)ut 



we obtain 



dW A 



^.=^ ,■./(,■) (2S) 



The function / (>•) can according lo e(j nation (I'd) also be written — 1 

 This gives / (>•) = ! for r=:0 and / (r) = fcl^ for r = R. 



