Pressure, Temperature, and Wind in the Atmosphere. 33 



Therefore from the equator to lat. 30°, 6 1 increases from 



/ V / J 2 \ 



180° + tan" 1 - to 270°, and 6 2 from tan" 1 ^-! 1+ _-. Ho 90°. 

 n 2n\ 3/r / 



From lat. 30° to the pole both 1 and 2 increase at first, and 

 after reaching a maximum value diminish very slightly 

 indeed to their values at the pole, which are approximately 



90° — tan -1 - in excess of their values at lat. 30°. 

 n 



At lat. 30° the amplitudes of w, and v 1 are equal, and each 



n 

 is 12 , cm. /sec. The maximum value of the ratio vjiii is 



+ <l+W4/^ 1 +5?) 



If E 2 = F sin 3 (f> as before, and the amplitude is 1 mm. at 

 the equator, 



2^Fsin 2 <£r(2 + 3cos 2 <£)4^y>i 2 y . ,_ , , .. , . , 

 w 2 =- -jj- K g ~Y 2 J sin ( 2r ^ + 2 ^ + ^\)> 



10AT?2Fsin 2 c6cos6rl + 9/ 2 /100>i 2 -H , n 

 r 2 = g- 2L — — I ~x72-Zy7-J cos (2n*+2X«+W 



~;{Z 2 + 4 n 2 (l4-4cos 2 </))} 

 tan ^ ~ * (3 cos 2 > - 2) {±n 2 sin 2 + / 2 ) ' 



Z{3Z 2 4-4tt 2 (7 + 3cos 2 <ft)} 

 tan ^ 9 - 2<* 2 + 20n 2 sin 2 £) * 



Thus ^ increases from 180 4- tan -1 — at the equator to 



270°, when cos 2 = 2/3, and afterwards changes very little ; 

 a|t 2 increases from the equator to the pole, but is always less 

 than 90°. 



The ratio v 2 /u 2 increases from zero at the equator to a 

 value slightly greater than unity when cos 2 (/> = 2/3, i. e. in 

 lat. 55°. Afterwards it diminishes very little and is always 

 greater than unity. 



The following table* gives the values of u, v, &c. in 

 cm./sec. for different latitudes, and for 1 = 0, \n, n : — 



* Cf. Margules, Sitzunc/sberichte tier k. Ah. der Wissenschafteu Wien. 

 Bd. cii. Abth. ii. Dec. 18U3, pp. 1383, 1386. 



Phil. Mag. S. 6. Vol. 19. No. 109. Jan. 1910. D 



