454 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



I. The dry stage. Adiabat for dry air. 



log p — m log T = constant. 

 II. The condensation stage. Adiabat for saturated air. 



log p' — — — m log T = constant. 

 P' 



In this way the exact determination of the adiabatic changes of 

 moist air is made dependent on the evaluate m ( if one simple formula. 



§8. PSEUDO-ADIABATS 



The adiabatic change of condition in moist air assumes that the 

 condensed water remains suspended in the air during the expansion 

 and that the mass of air retains its original total constituents 

 unchanged, and that there is therefore no diminution in its total 

 energy by reason of any removal of the results of precipitation. 



But when the mass of the water due to condensation becomes 

 considerable it will partly or entirely separate from the air. 



That change of condition which results from the separation of 

 the precipitation but without addition or subtraction of heat is 

 called pseudo-adiabatic by von Bezold and is accurately studied 

 by him mathematically. 19 The differential equation of the adiabat 

 of the rain stage is, as already given 



0= (c p + £<;) dT - ART dp ' + Td("\ 



but for the case in which the water formed by condensation is 

 immediately separated, this equation changes to the following 

 equation for the pseudo-adiabat: 



= c p dT + xcdT - ART d ^'- + Tdl — ) ■ • • (13) 



In the second member of this equation we can substitute f — y 

 for x or even x 1 — y, that is to say, the original quantity of vapor 

 diminished by the quantity of water that is formed, and we thus 

 obtain 



= ( c - + £c)dT -ycdT - ART?*- + Td(~ 

 p p' \T 



19 Von Bezold. Zur Thermodynamik der Atmosphare. Sitzungsber. der 

 Berl. Akad., 1888. Translated in Mechanics of the Earth's Atmosphere, 

 1891, § 15, p.212. 



