308 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



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

 from small variations of the temperature r 



(10) 



-RT ^ - = C -r-2vGG08 GO 



_7?y — r Jl£ — -=^+2fasin oj-\-2v b gosgj 



de_dr.{2_ g x Ja 3 (ft sin a?) ?c =Q 



dt dt \r R%) Jr r sin oodoo rsmcod^ 



If j/=0, these give the corresponding 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. Moreover the radius 

 of the sphere 8 will be assumed very large in proportion to the height 

 of the stratum of air. If in equation (10) we substitute 8 instead of r, 

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

 there results 



Single daily wave. The wave of temperature 



r = A sin oo sin {nt + A) 

 causes a wave of pressure 



e = B sin &> sin (nt + A) 

 where A and B have the relation 



\BT —^) ~ A B T 



7T 



With T = 213°, n = 04 y 60 y 60 ^ = ra,hus °f tne earth, andjp = 



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 equally 

 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 wave. For the temperature wave 



r = A sin 2 co sin (2 nt + 2 A) 

 we obtain the pressure wave 



e = B sin 2 co sin (2 nt + 2 A) 



