562 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



The constant on the right hand is the same in both the initial and 

 final stages. 



In the case of an adiabatic passage from the initial over to the 

 final stage the temperature T of the elementary mass dm becomes 

 T' and the total potential energy of the whole mass becomes 



(P + I), - C p JT'dm + Constant 



Hence the available kinetic energy in the initial stage is 



-d (P +1) - C p j(T - V) dm. 



§(24) First analysis. The initial stage. The mass of air in the 

 chamber 1 of our fig. i is in neutral equilibrium, and S, is the 

 entropy of the unit of mass. Similarly in the chamber 2 the air has 

 the same volume but a higher entropy, 5 2 , and is in neutral 

 equilibrium. The problem is wholly analogous to that treated 

 previously, only the mass having the smaller entropy now lies 

 alongside the other and not above it. 



The given data of the present problem are: The temperatures 

 T hl and T h2 at the altitude h and the values B, h, p h . From these 

 Ave find the following initial temperature and pressures at the bases 

 of the two masses. 



gh 



To. - T hl 1 + 



V c p 1 hl 



T ° 2= Th2 { 1 + C gh T 



From these and equation (5a) of the preceding chapter, section 20, 

 there results 



117? 



(P + I) a = C v .-.- ._. {T 0l p 0l - T hl p h + T 02 p 02 - 



g 1 + k 2 



— T h2 p h } + Constant. 



The final stage. The mass 2' of higher entropy now occupies the 

 upper part of the whole volume of the trough, the mass 1 having 



