ON THE ENERGY OF STORMS MARGULES 549 



tion of equilibrium while P remains unchanged. If the displace- 

 ment of each element of mass proceeds adiabatically, or if there 

 be an internal interchange of heat, then I must increase; after this 

 if the mass is left to itself it strives toward the position of mini- 

 mum I. 



The problem that we would solve by means of equation (6**) is 

 as follows: 



A mass of air in a closed system is at the beginning at rest and has 

 a given initial internal distribution of temperature and pressure. 

 It is set in motion by its tendency toward a condition of stable 

 equilibrium. If there were no friction the individual portions of 

 the mass would oscillate about their positions of equilibrium. In 

 the presence of friction the final condition is attained by the gradual 

 consumption of the kinetic energy. We seek the maximum values 

 of dK. + (R) which we designate as the available kinetic energy 

 of the system. Since the initial values of P and I are known our 

 problem is to compute their values for the final stage. 



No special assumption will be introduced as to the frictional 

 forces; in fact for turbulent motions there is no assumption that 

 can satisfy all demands. Hence the frictional force will not be 

 treated as a part of the pressural force, as is usual nowadays in the 

 treatment of steady motions. The condition (Q) = o demands 

 that the heat generated in the system by friction be immediately 

 withdrawn. But this is not of great importance in atmospheric 

 motions. Even in cases where it is assumed that the addition of 

 heat has no influence on the motion there are more abundant sources 

 of heat than this friction. For the present study the important 

 point is that the heat due to friction shall not give rise to new or 

 additional kinetic energy [during the interval of time under con- 

 sideration]. 



Chapter II 



APPLICATION OF THE EQUATION OF ENERGY TO THE OVERTURNING 

 OF STRATA IN A COLUMN OF AIR 



§(13) The analyses to be executed in this second section will not 

 afford much that is new, they serve only as preparatory to the 

 following sections. 



Consider a column of air of unit area section, in which p and T 



