250 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



On the other hand, for the ascending branch we obtain a value 



)/' — g c 

 " h ' 



if for the sake of simplicity the difference of temperature prevailing 

 above and below be equally distributed throughout the whole height. 



This simplification is, of course, not strictly correct since the ascend- 

 ing branch of the two stages certainly includes in itself several stages, 

 e. #., the dry stage, the rain or snow stage, and perhaps also the hail 

 stage, or all together. Still the method of computation of the average 

 gradient as given here in the formula is the only method that we can 

 apply when we have only one upper and one lower station. The follow- 

 ing considerations however remain applicable at least in a general 

 way when we can apply more rigorous formula. 



Namely, for purely adiabatic change in any case we have t a <t d , and 



therefore also 



n' <^n". 



We attain to the same result also when we simply consider that the 

 vertical gradient within the condensation stage is materially smaller 

 than in the dry stage. When, therefore, the greatest gradient coming 

 into consideration in the ascending branch is n"=v, then the average 

 of all must certainly be smaller. 



Therefore, in purely adiabatic ascent and descent and passage into the 

 condensation stage the mean vertical temperature gradient in the ascending 

 branch is always smaller than in the descending. 



If now we imagine regions of ascending and descending currents 

 alternately passing over one and the same point of the earth's surface, 

 we thus obtain for the mean vertical temperature gradient above that 

 point a value n that certainly lies between n' and n" therefore satisfies 

 the condition, 



n' < n < n" , 



wherein n"= v is nearly constant, n' however varies within wide limits 

 according to the initial temperature and the initial quantity of aqueous 

 vapor contained in the air. 



Therefore, under the assumption of adiabatic changes, in moist air that 

 reaches the point of condensation, the mean vertical temperature gradient 

 is always smaller than in dry air. 



We see from this that the consideration of the condensation alone 

 already suffices to explain at least the direction of the departure of the 

 observed vertical temperature gradients from those computed under the 

 assumption of dry air, even if we retain the assumption of purely 

 adiabatic changes. But this latter assumption is in fact certainly never 

 fulfilled exactly, and it is therefore necessary to examine more accu- 

 rately the influence that the departure to one side or the other from this 

 normal process may have upon the vertical temperature gradient. 



