Pressure, Temperature, and Wind in the Atmosphere. 29 



The phase of the semi-diurnal pressure variation is about 

 150°, so that the agreement with the simple theory is 

 remarkable. The amplitude of v is, however, much greater 

 than that calculated from the expression given above. 



The semi-diurnal variation near lat. 48° has been calcu- 

 lated by Hann* from observations on Santis, Obir, &c. The 

 values given by him are 



M=-20sin(2n* + 177°) 

 t> = 43 sin (2nt + 246°), 



and here also, while there is a fair agreement in phase with 

 the theoretical value, the amplitude of v is too large. 



II. 



If the effect of the Earth's rotation be taken into account, 

 while the vertical motion and the friction are still neglected, 

 the equations become 



-j- +2wu cos <£= — -— = — [EiCosCwt + Xi) 



+ 2E 2 cos (2nt + 2\ 2 )] 



+ |^ 2 sin(2^ + 2\ 2 )l 

 The solution of these equations is 



E 1 + 2sin^cos0-^ 1 



u = A cos at + B sin at =—. — ; -z ; 0-7 — sm(nt + \ } ) 



nRsm<f> 1 — 4cos-(/> 



jrv 2E 2 + sin cos 6 °- 2 - 



~^sin(2^ + 2X 2 ) 



2nR sin </> sin 2 cf> 



/lT 2E 1 cot«#, + g 1 



v= — B cos at + A sin at-\- -^ — z : ^-~- cos (?it + \i) 



?iK 1 — 4 cos- 



?^E 

 -.m 2E 2 cot </>H--^t 



+ S ^T^ c03(2re ' +2X2) ' 



where a= 2n cos <j>. 



* ilfe*. Ze#. 1903, p. 503. The amplitudes given by Hann are double 

 because be has taken S.-N., W.-E. 



