Pressure, Temperature, and Wind in the Atmosphere. 37 



This diminution is probably due in part to the greater re- 

 sistance to motion near the earth's surface ; it may be due in 

 part also to a change in the phase of the semi-diurnal 

 temperature variation in the free atmosphere. 



The value of E is taken to be independent of the height 

 because the amplitude of the pressure variation jh € is found 

 from observation to be nearly proportional to p lt With this 

 value of! e the quantities ?/, v, w, r must be given by 



^^Ajcosx + Agsin ^, 

 ^Bicosx+Bosinx, 

 w = Cx cos x + ^2 sin %, 

 t = t 1 cos% + To sin%. 



Substitution in the equations of motion leads to the follow- 

 ing equations for A l5 Bj, &c. 



— 2/2 Aj + 2n cos cj>B 2 -\-2n sin c/)C 2 = 0, 



2£T, 



2nA 2 +2n cos </>B 1 + 2/i sin (f>Ci~ — E sin 2 c/>, 



3&T 



— 2/2 cos Ao— 2/iBi = — -E sin 2 6 cos 6. 



r 



— 2n cos <f>A : + 2 nB 2 =0 



— 2/isin^Ao — 2?iC 1 =#t 2 , 



-2n sin 0A! +2nC 2 =0T 1 +E£T 1 <;#r* sin 3 (/>, 



whence 



^ Tl =-E//lV^-^sin 3 c/), 



(jr 2 — -siiKpLH ocos-</)J. 



If the diminution of phase is taken to be 8° for 300 m. 

 (Eiffel Tower) and 40° tor 3000 m. (Sonnblick), c = 0'84, 

 /3 = 6 . 10 -6 cm. -1 nearly. Also r=6'3 . 10 s cm. nearly, so 

 that Tj is large compared with t 2 at the earth's surface. 

 The phase of the semi-diurnal temperature variation is 

 therefore 90° less than that of the semi-diurnal pressure 

 variation ; the difference diminishes with increasing height 

 and with 0. 



