Convection Currents in the Atmosphere. 125 



From these we can deduce 



cmg+ ~y l Ae- mz j J (X,r)e*y*. 



Hence 



r 4 1 



— p = - 



( v 2 — X 2 



— k ce~ mz f J {\r)e 1 ^ 



+ L«-**J (Xr)^, (5) 



where L is an arbitrary constant. 



As the horizontal motion is all radial, we can put 



u=XJ cos <fi and t , = Usin<£, 



where U is independent of 0. Then the first two equations 

 of motion give 



t7 U-/,V 2 U+^U=-|;(^-iwv), .... (6) 



and the last gives 



lylv _ U S7 2 w = g*Y - ^ (£' - i ***y V) , . . . (7) 



while 



Po 



1 7 xt \ I vq — T i\i 





