554 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



pressure, temperature, and entropy for a normal condition of the 

 air, then for any other pair of values, p and T, the entropy for a 

 unit mass is 



T p 



S = 5 + Cplog— - -Rlogp 



For a column at rest we have from equation (a) 

 dS C p dT Rdp C p /dT 



dz T dz p dz T \ dz C p 



whence it follows that stable equilibrium exists when S increases 

 with the altitude, but unstable when S diminishes with increasing 

 altitude. 



This result also holds good for sudden changes of temperature 



T 



at special localities ; in such cases S 2 — S t = C p log 2 ; the entropy 



* 1 

 increases with the altitude when T 2 > 7\ arid the warmer layer lies 



above the colder. 



§(18) Potential temperature. Helmholtz and von Bezold* define 

 the potential temperature T of a mass whose actual temperature is 

 T and pressure p as being that temperature which the mass will 

 attain when brought adiabatically to the normal pressure P. Henc e 

 we have 



_ / P\k dT - 



T= T \~ ) dS = C p ^= S = C p log T + Constant. 



■\\ 



The equilibrium is stable if the layers are arranged to succeed eacl 

 other upward in the order of increasing potential temperature or 

 increasing entropy. 



§(19) Buoyancy of an elementary mass of air that has a temperature 

 different from that of its surroundings. 



In a mass of air at rest where T is a function of the altitude only, 

 we will introduce a foreign particle of air m, which has the tempera- 

 ture # at the altitude z but always the same pressure p as that of 



*See the article by Dr. L. A. Bauer, reprinted as No. XXII of this col- 

 lection. — C A. 



