314 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The sum of the series of sines in the value of s is— 1 



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) aud (126) the greatest pressure and highest tem- 

 perature occur simultaneously. 



IX. ROTATING SPHERE : SEMI-DIURNAL WAVE. 



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

 rotating sphere, we put 



t—A (go) sin (2nt+2X) 

 s=E(go) sin (2nt+2\) 

 b=q> (co)cos(2n«+2A) 

 c=ip (go) sin (2nt+ 2A) 

 there results : 



dE _2 cos go 

 _RT d,Go sin go 

 ™~2nS sin 2 go 



dE 2E 



lilodGO siu GO 



"~~2nS sin 2 co 



n 2 8 2 

 After the elimination of cp and ip, and when we again put Jc=„ 7f r 



there remains 



d?E . . dE 



j^ sin 2 oo— j^ sin gocos go+ E(4ksin i co+2 sin 2 co-S)=ikA(Go)sm i go . (13) 



If we assume that A(go) = G sin 2 go, 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( go)= a -f a-z si n 2 go -f a 4 sin 4 &?+a 6 sin 6 go + 



there results 



a =0, « 2 =0, a 4 apparently undetermined, 



(4x6-8)a 6 -(3x4-2)fl. 4 -4fcC=0 ) 

 (i 2 +6i)a i+i — (i 2 4-3i)Oi + 2+4ftaj=0 > .... (13a) 

 t==4, 6, 8 . . . ) 



_ai+2_ 4fe 



a i i(i + 3)-i(i + G)<m± 



(1x4-1 



