Pressure, Temperature, and Wind in the Atmosphere. 31 



III. 



If the motion in the pressure- wave is resisted by a force 

 proportional to the velocity, the equations of motion become 



^ + 2 nv cos 6 + lu= - -p *. T , [Ei cos (nt + Xi) + 2E 2 cos (2nt + 2\ 2 )] 

 dt r K sin 9 L v 



dv 



2nwcos 



* + /b = - § [H sin (ni + x ° + S 2 sin (2re< + 2X2> ] • 



If we write 



ATE, AT BEi _ 



Rsin<£ *' R B</> 

 2w cos </> = «, a 2 + n 2 4- 1 2 = X l9 2an = Y l5 

 then for the diurnal terms in w and t> we obtain 



Wl = + -^ x 2 ~Y 2 — J Sm ' x ^ 



v= i — X'—Y* F cos (^ +x i' f ^2), 

 where 



Hn/? _ -^xXx + ftYQ 



Tan ^" ^(aY^nXJ + /3 l {aX l - «Y,) 



*»„ a - +*QgiX 1 + « 1 Y l ) 



"^^i-^Yj-aXj+AlfiXx-aYO' 



those values of # l5 2 being taken which give to sin 6, cos 6 

 the same signs as the numerator and denominator of these 

 fractions : the radicals in w l5 Vj are then, and only then, to 

 be taken with the + sign. For the semi-diurnal terms write 



2*T _ *TdE 2 



and we get 





