MOVEMENTS OF ATMOSPHERE— GULDBERG AND MOHN 127 



§ 4. Variation of pressure with altitude 



According to the theory of the equilibrium of fluids the increase 

 of pressure per unit of length is equal to the force which acts on 

 the unit of volume. Let g designate the force of gravity per unit 

 of mass and z ttfe height, we shall have: 



dp 



T*=-s» (1) 



Introducing the value of p given by equation (6) of § i we shall 



have 



dp gdz 



— =-*—- (2) 



p aT 



(i) The virtual temperature remains constant. 



In this case designating by p the pressure at the surface of the 

 earth we shall find by integration. 



J± (3) 



p = p e T ° 



in which e is the base of the system of Napierian logarithms. 



(2) The virtual temperature decreases proportionally to the height. 



By introducing T = T — <xz in equation (2) we shall find, by 



writing m =— - — 

 oca 



T =T - — (4) 



am 



a 

 z =-m(T - T) (5) 



/-(£)" (6) 



M>- S \Y m 



p \ ami J 



As to the variation of the pressure of the vapor of water we can 

 adopt various hypotheses. We shall consider only the following 

 formula : 



j-gy (8) 



