Pressure, Temperature, and Wind in the Atmosphere. 35 



The agreement with the observed results is only approxi- 

 mate, but it must be remembered that the variations are 

 affected by vertical convection of air, and this cannot be 

 altogether eliminated by taking the difference between the 

 variations in oppositely directed components, because the 

 winds from opposite directions do not occur with the same 

 frequency and strength, nor under the same conditions of 

 temperature and insolation. Vertical convection would tend 

 to diminish the difference of phase between u and v, and the 

 fact that this is the case in the above example may be taken 

 as evidence that a considerable convection effect exists in the 

 wind records from mountain peaks. 



IV. 



In the preceding sections the equation of continuity has 

 been neglected, the assumption being tacitly made that the 

 temperature variation and perhaps the small vertical motion 

 would be such as to satisfy it. In this section it will be 

 shown that if account be taken of the observed change in the 

 pressure variation with change of altitude, the temperature 

 variation which must be associated with the pressure varia- 

 tion according to the hydrodynamical equations, is in fair 

 agreement with the observed temperature variation. It will 

 also be shown that the vertical velocity is small, of the order 

 10 ~ 2 , compared with the horizontal velocity, and that between 

 the equator and lat. 18° the maximum upward velocity in 

 the semi-diurnal wave occurs before the passage of the trough 

 of the pressure-wave, while between lat. 18° and the pole 

 the maximum upward velocity occurs after the trough of the 

 pressure-wave has passed. 



Margules* has dealt very fully with the oscillations of the 

 atmosphere, and has deduced the pressure-waves resulting 

 from given temperature-waves. The inherent difficulties of 

 the problem are, however, so great that it is impossible to 

 solve the whole system of equations in this way, and conse- 

 quently the vertical velocity and the equation for the vertical 

 motion were neglected by him. But if the pressure variation 

 is taken as given by observation, the whole system of equa- 

 tions can be solved by approximation, and it is by this method 

 that the results of the present section are reached. 



The equations for the small oscillations of the atmosphere, 



* Sitziuu)$berichte Akad. Whs. Wlen, 1690, 1892, 1893, Bd. 99, 101, 

 102. 



D2 



