Convection Currents in the Atmosphere. 121 



Hence 



P0 U P - V*-7T 2 /l 2 I 



(pm+ \y 2 )k _ . tt.v 



_ \c ,i_/ ce mz gin e i y t 



ly I 

 + L*-«<*sinyV*, (13) 



where L is an arbitrary constant. 



To find the velocities we have now to solve 



-du z _ 2 1 BV 1 fy' ~) 



d£ 3 d<£ /o o# 



du zr72 i z 3 V ljy ± _ | ' (14) 



where both the right sides are now known. 



The boundary conditions to be satisfied are : — 



(1) There shall be no motion when z is very large. 



(2) u and w shall both vanish when z = 0. This is the 



condition that there shall be no slipping at the 

 boundary. The motion of the ocean is thus 

 neglected. 



The solutions are therefore 



anr — c/v-\-kiy(v 2 —Tr 2 jl 2 ) + y 2 ttx ltf _ e _ mz , 



U= ~T (v 2 -7r 2 /l 2 )\iy-k(v 2 -7r 2 jl 2 )} bcos T ey{e V ~ e > 



ctq-mk 77 CZ TTX ,, 



ty t 2mk I 



-^^cos^e^ie-^-e-™), (15) 



t iy t v J 



— qv + kiyiv 2 — tt 2 I 2 ) ■+ y 2 . ttx .. N 



{v 1 — r K 2 i 2, )\iy — k{y z ~7T z i 1 )) I K J 



qocb . itx ., m . 

 + ~— ain^^*(tf— *' I -rf-"'). (161 



