MOVEMENTS OF ATMOSPHERE — -GULDBERG AND MOHN 



135 



check the results. Besides it is more convenient to apply the 

 formula 



p I T 



T 



(17) 



and to attribute to m suitable values, which vary with the height 

 of the layer of air. We shall consider then formula (17) as the 

 general formula, when the air experiences a series of transformations. 

 By the aid of formula (6) from § 1 we shall find 



L 



Po 



Po 



consequently we can write 



dp J p \ 1 



= ma \ — J = - 



P \p I Po 



dp 



^8) 



(19) 



C P dp / p p\ \/p\ 



I = m I - — ) = m a 1 I I 



J v„ p \p Po/ L v p» 1 



1 



• (20) 



By integration we find 



ip dp [p p 



v„ P \ P Po 



We shall make use later of formulae (19) and (20). 



Applications 



Let us apply our formula to a mass of air that rises slowly in the 

 atmosphere. 

 Assume 



p c = 760 mm ;/ = 15 mm ;r = 20° 



(1) When the air is not saturated. 

 By the aid of formula (7) of § 1 we find 



x = 0.0125. 

 Substituting this value of x in § 5 formula (4) we find 



m = 3.46. 

 So long as the air is not saturated, the value of x remains constant 

 and consequently the ratio - becomes constant. We have then 



P f 



Po fo \ 273 + r 



273 + t 



