308 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



for the motion of the atmosphere on the rotating sphere that result 

 from small variations of the temperature t 



gr-RTo ~=^-2y c sin a? 



,15 _Jb 



— RTo ..'. =':^ — 2 K C COS 00 



(10) 



— RTo — ^ . ='— +2i'asiii (jj-{-2ybcosco 



r sin oo;) A ^t 



,1^ ;)t "^ V^r i^.To / ' ,1/- r sin cj.lcy r sin ci9,iA 



If K=(), these give the corr'^sponding equations for the sphere at 

 rest. 



VII. THE ATMOSPHERE WITHIN A SPHERICAL SHELL AT REST. 



As in the first computation in the second section for the case of a 

 plane we shall assume only horizontal motions. jNIoreover the radius 

 of the sphere *S^ will be assumed very large in proportion to the height 

 of the stratum of air. If in equation (10) we substitute S instead of r, 

 put a=0 and v=0 and eliminate h and c from the last three equations, 

 there results 



S^ f'd'^r ,-)-f\ 1 ,1 /,1f . \ cl-f 



ieiT.O^-c^>srn^^V^'^"^>«m^a^^=^ ' '^^^^ 



Single daily wave. The wave of temperature 

 T = A sin fc) sin [Jit + A) 

 causes a wave of pressure 



f =B sin cj sin {nt + A) 

 where A and B have the relation 



\R1\, ~-.; -"^R To 



2 TT 



With To = 273'^, 7i= 91 y (m y tn ^ = radius of the earth, and^o = 



760 mm., a variation of temperature of 1° on the equator will produce 

 a variation of pressure at the equator of 10.4 mm. B will be equallj' 

 large for the spherical shell as for a plane wave of the same periodic 

 time, when we assume the wave length for the plane to be equal to the 

 circumference of the circle of 45° latitude on the sphere. 

 Double daily icave. For the temperature wave 

 r = A sin "^oo sin (2 nt + 2 A) 

 we obtain the pressure wave 



£ = J5 sin '^CD sin (2 nt + 2 A) 



