586 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The water that in the final stage is lying on the ground contributes 

 nothing to the P e . The excess of the potential energy of the 

 initial stage over the final stage is 



- d p = p a - p e = R a j(T - V) d m a + R 3 j(T - T>) d m p + 

 + R B §T'dm' r 



If we assume that each portion of the system passes adiabatically 

 over to its final stage, then we have (Q) = o and the available 

 kinetic energy is 



5K + (R)=-5(P+T) = C pa j(T - T>) d m a + 



+ C P p $ (T -T>) d mp +JL>d m' r (F) 



For moist air the final stage of stable equilibrium must be deter- 

 mined under conditions similar to those required for a gas of con- 

 stant composition, i. e., that the strata be so arranged that the 

 entropy increases upward. Assuming that we know the final loca- 

 tion of each mass, then we can determine the pressure p' that the 

 element dm' experiences in its final stage: since we also know the 

 pressure p and temperature T for this element dm in its initial stage, 

 therefore T' and thence U and dm' r are to be computed from the 

 well-known equations for the change of condition of moist air. 



§(35^) We will now substitute a mixture of dry gases a and /? 

 whose composition has a local variability in place of the moist air 

 [whose composition was uniform]. Assume that for each element 



of the mass the ratio — - remains unchanged during the overturn- 

 dmp 



ing. 



The specific heat is determined by the relation 



C p dm = C pa dm a + Cpndm^ • 



The change of the total potential energy due to the overturning 

 process under constant pressure is 



- d (P +T) = J C v (T - V) dm 



= C pa j (J - T>) dm a + C v? J (T - T') dmp 

 For the element dm the values of (T — T') are the same as before 



