Pressure, Temperature, and Wind in the Atmosphere. 43 



Thus X. of lat. .18°, L is positive near the surface, while 

 between the equator and lat. 18° L is negative. Conse- 

 quently B 1? Gi change sign and become positive' N. of lat. 18°. 

 Thus between the equator and lat. 18° the phase of the 

 upward motion differs from that of the pressure variation 

 by an angle between 180° and 270°, while N. of lat. 18° the 

 difference of phase lies between 90° and 180°. 



2nEk 

 If sin 2 <£ cos <£ = D and ~P/yD = q and the two series 



t/ 



in brackets in the expressions for L, M are denoted by X, Y 



respectively, then, using the condition L = M = for £ = 0, 



we find 



L = D[cos(c~^)-e- z ]+^D[-X cos(c-A/r) — Yosin^-^ + X^ 2 ], 



M=-Dsin(c-^) + g'D[Xosin(t— -^)-Y cos (c-^) + Y*" 2 ] 



where X , Y are the values of X, Y at z = 0. 



Here D and q depend on the latitude but not on the height, 

 while their coefficients depend on the height but not on the 

 latitude. If j3=6. 10~ 6 , c = 0'84, 7/^ = 8. 10 8 , the values 

 of X, Y, c — yjr, e~ z at various heights are as follows : — 



Height in 

 km. 



10 X. 



10 Y. 



10e-z. c—ty. 







1 



7-480 

 9-213 

 9-760 

 9927 

 9-978 

 9-993 



6-297 

 3721 

 2-081 

 1149 

 0-632 

 0-347 



1000 



8-87 

 7-87 

 698 







21° 43' 

 33° 38' 

 40° 1 0' 



'? 



3 



4 



619 43° 46' 

 5-49 45° 44' 



5 









The values of q and DI\ tan <f> in different latitudes are 

 given in the table : 



Lat 0° 15° 30° 45° 60° 



q 1-16 107 068 -061 -697 



lODT^antf, 1*57 1*2 102 056 0"20 



The following table gives for different latitudes and heights 

 the amplitude of the upward motion in mm. /sec, and the 

 excess of phase above that of the variation of pressure. 



