58S SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5 1 



We assume that dQ is positive when dp is negative 



therefore R — XC p is positive 



and also that X < n (3) 



and that cooling accompanies expansion as X is positive. . . (4) 



and finally assume that X is constant (5) 



If T and p belong to the initial stage of a mass then by the 

 expansion or transition to a smaller pressure p we have 



• tApJ :-- (la) 



tO]JL-C„^(r.-D . . (2a) 



Consider a vertical column filled with this gas at rest: Let p and 

 T at the altitude z have the same values that a particle would have 

 when ascending [adiabatically] from the base (p and T ) to this 

 altitude. 



The distribution of temperature in this column is now given by 

 the above equation (1) by the condition of equilibrium (a) [§13], 

 and b)' the equation of condition for clastic gases p = RTfi. 

 Combining these we obtain 



1 op g 1 1 or 



pJz = R T = X ' f ~dz 

 whence 



8 T eX X c 



az K k L p 



With this fictitious gas, and for any given distribution of tempera- 

 ture in the vertical column, we can carry through a process similar 

 to that considered in our preceding second chapter (§§ T3-22) 

 and find that for ascending particles (or diminishing pressure) the 

 diminution of temperature just given in equation (6) belongs to 

 the condition of neutral equilibrium, and that a more rapid diminu- 

 tion of temperature corresponds to unstable equilibrium. In the 

 first case the vertical temperature gradient is smaller than thai 

 for neutral equilibrium of dry air. 



