Convection Currents in the Atmosphere. 457 



Further, the case here considered has been the extreme 

 one of no slipping, whereas in reality the velocity quite 

 near the surface is not on an average Jess than about half of 

 that at a considerable height ; if, then, friction can produce 

 only this reduction close to the ground, it must produce 

 much less at a great height (especially as turbulence 

 diminishes with height J, and hence its effect in reducing 

 the redistribution of mass must be small. 



It thus appears that the effect ot a rise in temperature in 

 a region whose linear dimensions are large in comparison 

 with the height of the atmosphere and small compared with 

 10,000 km. is first to cause an expansion near the ground, 

 lifting up the air above into a tidal wave. This causes 

 a system of horizontal winds in the upper air, and the 

 wave spreads out ; the pressure variation is affected more 

 and more by this the smaller the area. Friction presumably 

 produces little effect on this movement, so that it will be 

 justifiable to omit it in calculating the motion of the upper 

 air and to calculate the surface winds from the upper 

 winds subsequently. A second approximation may then 

 be resorted to if necessary. The velocity can always be 

 neglected in the equation of vertical motion, and the 

 geostrophic condition holds in the upper air if the variation 

 is slow compared with the earth's rotation. 



Comparison with Observation. 



The actual variation of temperature in the atmosphere 

 does not follow the simple exponential law here considered, 

 but the motion arising from any given symmetrical variation 

 of temperature can be found from the results here obtained, 

 provided this variation can be expressed in the form 



JJj/( X ' v > r y) J o(^) e-^e'y'dXdvdy, 

 which is true of most functions met with in practice. 

 Qualitatively such a difference does not seem likely to 

 make much change in the results obtained. The effect 

 of the actual steady falling-off of density with height, 

 instead of the discontinuous change here assumed, is more 

 difficult to predict. From what has been said, however, 

 we should expect that the geostrophic condition would hold 

 except close to the surface in almost all latitudes for the 

 annual and other slow variations ; but for diurnal variations 

 (7 = H ) and semi-diurnal variations (7 = 20) 7 can never be 

 small compared with 2Ocos0, and hence the geostrophic 

 condition cannot hold. This is, on the whole, in accordance 

 Phil. Mag. S. 6. Vol. 34. No. 203. Nov. 1917. 2 K 



