p' (he~ vz km _ 



p l I v ty 



Convection Currents in the Atmosphere. 127 



it usually is, then in (12) only the terms involving- g need be 

 considered. With sufficient accuracy, then, 



-ugX j h %~ m % -'#?«-"J.(V)^- ■ • • (14) 



In each case the ratio of the second part to the first is of 

 order \/i/, so that the second part may be omitted. 

 Then 



U= -*\q \- ^— jr {e~ vz - e~ mz ) + ^~ ze~ mz \ J x (Xr)^ 



* tvdy — kv r ) v y 2iy ) 



. . . (15) 

 y=-^<^ [*«--+ ^-- # }jo(Xr)^, (16) 



V= (^'^ + ^-^)J (^)^. (17) 



If 6 were zero, the pressure would reach its maximum an 

 eighth of a period after the temperature minimum, and the 

 maximum outward velocity at a small height would be a 

 quarter of a period after the temperature minimum, and an 

 eighth of a period after the pressure maximum. The phases 

 would be the same at all points. 



If the radius be a large multiple of 1000 km., the co- 

 efficients are all small. Hence the daily motion does not 

 penetrate far into the interior of a continent. 



In the case of an annual period, these approximations are 

 always justifiable even for the largest continents. In both 

 cases the relation p' =go~' holds. An amplitude of 1° C. 

 in the temperature variation corresponds to one of about 

 0*42 mm. in the pressure variation. 



