Pressure, Temperature, and Wind in the Atmosphere. 47 



If there is a retardation of! phase * with increasing height 

 similar to that for the semi-diurnal pressure wave, then T! 

 is no longer necessarily negligible compared with r 2 , and 

 in fact 



g Tl = -E' sin , 0JT 1 c'0V* r > 



gr 2 = kT 1 sin 2 <j> -^— . 



In this case the difference of phase between the pressure and 

 the temperature variation is 180°— 0, where 



tan<9=-EV/3^-W^. 



If c', ft' have the same values as for the semi-diurnal wave, 

 tan = 5/6 or 6 = 4:0° at the earth's surface, so that the 

 phase-difference would be 140°. 



The agreement of this value with the mean observed value 

 is sufficiently close to suggest that the retardation of phase 

 with increasing height in the semi-diurnal wave is due to 

 frictional influences, and that it is present also in the diurnal 

 wave in the free atmosphere ; and further, that the semi- 

 diurnal variation of temperature in the upper air is a con- 

 sequence of the semi-diurnal pressure variation. 



If the mean amplitude of the pressure variation at the 

 equator is taken as 0'b* mm., the value of E is unity, and 

 with the values of e, /, m, taken above, the values for the 

 temperature variation given in the table on p. 40 have been 

 found. 



The mean temperature amplitude for the places given 

 above is 2°' 8 C, which is rather greater than the theoretical 

 value. 



According to Margules' solution, on the assumption of a 

 given temperature variation and negligible vertical changes, 

 the phases of the variations of pressure and temperature 

 ought to agree. If account is taken of friction, the phases 

 differ slightly, the maximum difference for a large friction 

 constant being 33° f. This is so far from agreement with 

 the observed difference of phase that it appears certain that 

 although the vertical motion may be small compared with 

 the horizontal motion, the atmosphere cannot be treated as 

 an infinitely thin shell in dealing with the diurnal variation 



* The results of observations at higher levels before the reversal of 

 phase is reached give conflicting results. Munich and Peissenberg 

 show an acceleration of phase, the Eiffel Tower a retardation. 



t Margules, Site. Ber, 1893, p. 1386. 





