55° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



are functions of the altitude z only. The condition of hydrostatic 

 equilibrium is 



1 dp 

 * ji dz 

 or 



1 dj> _ _g_ 

 pdz" RT J 



(«) 



The analysis is simplified by the assumption that g is independent 

 of z whence the potential equation becomes 



W = gz (/?) 



Let us distinguish between a lower part of the column having a 

 mass M extending to the altitude h and a higher mass M h . Let 

 overturnings of the strata take place in M whereby // is changed 

 but the pressure 



p h = s M h (r) 



on the upper boundary of M remains constant. 



Let Z be the altitude of the center of gravity of M h then during 

 all changes Z — h remains unchanged, since M h rises and falls like 

 a solid piston. 



The potential energy of position for the whole column of air is 



gz/idz = gz/idz + gM h z 

 *J *J 



P 



By utilizing the relation (a) we have 



C h CPh C h 



gz/xdz=- zdp= pdz-hp h 



J J v J 



P - pdz + (Z - h) p h = R§ Tdm + Constant . (1) 



where the integral in the last part of the equation is to be extended 

 over the whole of the lower mass M. 

 The internal energy of the column is 



I = C v JTdm + Constant (2) 



Overturning of the strata can occur spontaneously whenever the 



