Pressure, Temperature, and Wind in the Atmosphere. 41 

 where 



But C 2 = Aj sin </> = B 2 tan c/>, 



d = B 2 tan </> — | F sin <£, A 2 = — B 2 sec (j> + § F sin 2 <£, 



where F = EifeTj/nr. 



Also 1/r is small compared with y or c/3 and ?iV is small 

 compared with </, while kTyr is about 1*3. 



Therefore, neglecting the small terms and eliminating 

 A l5 C 1? A 2 , C 2 , we obtain 



tan <j> ^ - Bj tan c/>(y + *i) + § F7 sin - /frjr B 2 tan = 0, 

 tan ^ 2 - B 3 tan 0( 7 + ^) - J F/3 ^ sin + fl^B, tan c/> = 0. 



The solution of these equations is 



Bj = \ F cos + IV [P cos i/r + Q sin ^J, 

 B 2 = r l> z [-Qcos^ + Psin^], 



where Z = I ydz. 



But the vertical velocity must vanish at the earth's surface, 

 so that d = Co = for z=0. 

 Therefore P~=Q = 0, and 



A 1 = 0, A 2 = -£F(2 + 3 cos 2 </>), 



B, = §Fcos</>, B 2 = 0, 

 Ci = 0, C 2 =0. 



The motion is therefore exactly the same as that found in 

 Section II. 



In order to proceed to a further approximation and to 

 obtain values for C l5 C 2 , put 



B 1 = B/ + fFcos0, 



A 2 = A 2 '-iF(2 + 3cos 2 0), 

 so that A 2 ' = — B/ sec <£, i\ = B/ tan <j>. 



