TEMPERATURE OF ASCENDING CURRENTS VON BEZOLD 335 



then its weight must be P = mg if we consider the mass as enclosed 

 within an enclosure that has no weight and as located within a 

 vacuous space such as the receiver of an air pump and at a place 

 where the acceleration of gravity is g. Under these suppositions 

 the full amouiit of work required to raise this weight through the 

 vertical distance h would be mgh or that which Schmidt considers 

 necessary under the conditions existing in the atmosphere. But 

 this volume of air thus imagined cut out of the atmosphere, is in 

 fact surrounded by air. Consequently its weight in the atmosphere 

 is 



P' = gm — gm' = g (m — m') 



where m' is the mass of the air displaced by it. But since the baro- 

 metric pressure within the enclosed mass is the same as that in its 

 immediate neighborhood therefore 



1 + at a +t 



m' = m = m, 



1 + at' a +f 



where t is the temperature of the mass and t' that of the surrounding 

 air and where 



This latter value can be either positive or negative or zero according 

 as t is smaller or larger or equal to f. Hence no work is done in 

 lifting the enclosed air unless its mass is colder than that of the 

 surrounding air. If it is warmer then it has a buoyancy and it 

 rises of itself through the surrounding cool air which flows in to fill 

 its place, and thus the center of gravity of the whole system sinks 

 exactly as the theory of equilibrium demands. 



But under all circumstances the absolute value of P' is much 

 smaller than m g, so that for a mass of air rising through the altitude 

 h (and whose ascent indeed never occurs alone in the atmosphere 

 but only in connection with other air descending at some other place, 

 tli us forming a connected whole) it is never allowable to introduce 

 mg h into the computations as representing the work done. 



But even when work is really done in lifting, which can only occur 

 when ascending air is cooler than the descending, as in the case of 

 cyclones with cold centers, still the work is exceedingly slight in com- 



