524 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



to raise its temperature from T\ to T 2 but also the additional 

 quantity needed for the evaporation of the water taken up by that 

 kilogram of air. 



In the case of adiabatic change of condition along the path 

 P 2 p 2 the condensation of vapor causes the vertical temperature 

 decrease to be smaller than in dry air. The ratio of the masses 

 of saturated vapor and dry air in any given volume is nearly o.oi 

 at 1 5 C. If we neglect small quantities of this order of magnitude 

 as compared with unity then we have 



Idx - C p [(dz) - dt] 



where dx is the mass of vapor condensed per kilogram of dry air 

 along the path dz; Idx is the corresponding amount of heat of evap- 

 oration ; — dz the corresponding change of temperature in satur- 

 ated moist air and — (dz) the corresponding change of temperature 

 in dry air. 



The complete treatment of a cycle for moist air requires a great 

 display of formulae. But we can with dry air imitate all that is 

 important and thus the process becomes more perspicuous. 



Instead of adding the heat required for evaporation at the point 

 P 2 on the lower path, where it would be used to warm the air ascend- 

 ing along the path P 2 p 2 (that is to say, in diminishing the vertical 

 diminution of temperature) — we arrange a graduated series of 

 sources of heat along the path P 2 p 2 so as to cause a prescribed tem- 

 perature to prevail along this whole path so that the change — dt 

 occurs in the distance dz. If the change of temperature is to be 

 — (dz) for adiabatic conditions then the quantity of heat to be 

 added will be dQ = C p [(dz) — dz] where we write dQ instead of 

 Idx. 



We now imagine the following cycle: 



(1) Movement along the path P x P 2 and heat added at P 2 as in 

 previous case. 



(2) Heat added along the path P 2 p 2 in such a manner that the 

 temperature at every altitude has a prescribed value. Equilibrium 

 between gravity and the vertical diminution of pressure. 



(3) and (4) as before. 



The conditions of the second step in this cycle are for the added 

 heat 



AT 

 dQ = C p dT - — dp 



