Pressure, Temperature, and Wind in the Atmosphere. 45 

 Writing as before 



u = A 1 cos % + A 2 sin ^, 

 v = Bj cos % + Bo sin ^, 

 2u = d cos %+ G 2 sin ^, 

 t = r x cos % + t 2 sin x, 



where ^ = ?i£-f-\, we obtain the following equations for A x &c 



— nA 1 + 2n sin <£ C 2 + 2« cos (/> Bo = 0, 



— nA 2 + 2/i sin (/> d + 2/icos (/> B^-— nF' sin <£, 



— 2/icos</>A 2 — nB x = — 2/iF' sin cj)cos<j>, 



— 2n cos $ A x +nB 2 = 



— 2/i sin </> A 2 — wCi = <7 T 2 — kTi sin 2 </> -^ - , 



— 2?i sin (/> A^wC^ — <7 T i> 

 where F' = E ' W \ 



From these we find 



C 2 = — fr9Ti (l — " 1 cos 2 (/>), 



A 2 = — ., ,'/T 2 sind>-f .IF'smtf) l + 4cos 2 <£) + ., -x^- 



4 



B x = — //To sin cos (/> — n F' sin <j> cos (4 cos 2 cf> — 2) 



4 ,rp • o , , BE' 



— «- Al, sin COS ffl ^— , 



C 1 =^- i /T 2 (l-4cos 2 c/))-f;F / sin 2 (/)(l + 4cos- 2 (/)) 



-,, 1 AT 1 sin 2 6(l-4cos 2 0)^-. 

 The continuity equation gives 

 v , • o , ,/2 # VijdC x , 1 3(Bisin0), Co A 



_, Tl+ (^ 7 _,v + ao s+ i a»«itu. a 0- 



