"314 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The Slim of the series of sines in the value of s is — 



For the equator 0.15 



For latitude 30° 0.38 



For latitude 45° 0.42 



For latitude 60° 0.32 



Again we find a minimum at the equator; the maximum of the press- 

 ure amplitude lies between latitudes 30° and 45°; the diminution in the 

 higher latitudes is greater than in the previous examples, but still slow 

 in comparison with the diminution of the temperature amplitude. Ac- 

 cording to equations (12) and (126) the greatest pressureaud highest tem- 

 perature occur simultaneously. 



IX. ROTATING SPHERE : SEMIDIURNAL WAVE. 



If in the differential equations (10a), for the horizontal motions on a 

 rotating sphere, we put 



T=A {00) sin {2nt+2X) 

 €=E {cj) siu {2nt-\-2X) 

 b=(p{cj)cos{2nt+2X) 

 c=il- (a9)sin (2m^+2A) 

 there results : 



dE J2 cos 00 

 BTo doj sin oo 

 ^~ 2nS sin^ go 



dE , 2E 



^^ ~i — cos CO 4- . 



BTodoo sm co 



^~~2n8 siu^Gj 



After the elimination of q) and ^', and when we again put A = ytttt 

 there remains 



^2 sin^ c»9— ^sin(i9COSGj+^(4A-sin*(i94-2sin2cj— 8)=4A-A(cj)sin'*<i?.(13) 



If we assume that A{oo) = C sin^ oo, we have then to do with the same 

 problem as in the computation of the semidiurnal tide in an ocean of 

 constant depth. Assuming 



E{co)=ay-\-a28\u^ oo+a^i sin* co-{-ae sin^ CO -{■ 



there results 



ao=0, «2=0, a4 apparently undetermined. 



(4xC-8)«6-(3x4-2)fl4-4A-C=0 ) 

 (i^+6i)a,+4-(*'+3i)«,+2+4A-rt,=:0[> .... (13a) 

 i=4, 6, 8 . . . ) 



_ai+2_ 4A" 



«. i{i+3)-i{i+Gf-^ 

 ai+2 



