28 Mr. E. Gold : Relation between Periodic Variations of 

 independent of X, 

 d 2 P kT 



W = ~ R^£ [El cos (n< +Xl) + 2E2 cos (2nf + 2x ^ 



S — 5 [H sin c-+^)+^ «*"+*>]• 



where p = kpT. 

 Hence 



w = 



= jr = t> • i rEisin(w« + \ 1 )+E 2 sin(2n< + 2X 2 )]+constt. 



a£ ?z±t sin 9 L v y v J 



»= S = + S [^ C ° S ^ + Xl) +^ 2 cos (2^ + 2X 2 )] +constt. 



On this hypothesis, therefore, the phase of the westerly 

 component differs by 180° from that of the presure, i. e. east 



wind and high pressure occnr together. Also since -^-,^-r- 2 



are in general positive, the phase of the N. component differs 

 by 90° from that of pressure, i. e. the N. wind is a maximum 

 when pressure is increasing most rapidly. But approximately 



E=6-3.10 8 cm.; n= OA ^ gA = 7-3.10~ 5 , £T = 8.10 8 (cm./sec.) 2 , 

 ' 24 x 60 x 60 



so that 



JcT 



~ =l-74xl0 4 cm./sec. 



If, further, it is assumed that E] cc sin 2 <f>, E 2 oc sin 3 <£, 

 agreeing approximately with observation, and if the pressure 

 amplitudes at the equator are taken to be 0*6 mm. and 

 1*0 mm. for the diurnal and semi-diurnal waves respectively, 

 it follows that 



u = — 14 sin <f> sin (nt + Xj ) — 23 sin 2 $ sin (2nt + 2X 2 ) 



v = 28 sin <p cos <£ cos (nt + X x ) -f- 34 sin 2 <p cos cf> cos (2nt + 2X 2 ) . 



At the equator v = and the amplitudes of the diurnal and 

 semidiurnal changes in u are 14 and 23 cm./sec._, and are 

 therefore large enough to be observed. 



At St. Helena * (lat. 16° S.) the mean yearly semi-diurnal 

 variation it is given according to observation, by 



m= -22 sin (2nt + 158°) , 



and in v by 



v = 35 sin (2nt + 237°). 

 * J. S. Dines. 



