ON THE ENERGY OF STORMS— MARGULES 



551 



center of gravity sinks thereby; the available kinetic energy in the 

 initial stage is 



dK + (R) = - d (P + I) 

 and for (Q) = o this becomes 



- C p j d T dm, 



which is in the ratio C p /R or 1. 41/0. 41 = 3.44 larger than the 

 work done by gravity ; the principal part of the kinetic energy is 

 derived from the internal energy. 



Let T and T' be the temperatures of the elementary mass dm and 

 T* and T*' the average temperatures of the whole mass M at the 

 initial and final stages, respectively, then we have 



8 K + (R) = C p J (T - T') dm = C p (T* - T*') M . (3) ( 



Under the condition here given, kinetic energy is available; that 

 is to say, when by adiabatic overturning of the layers the average 

 temperature of the whole mass of air sinks, then the condition is 

 not stable. 



§(14) Computation of the available kinetic energy in the case of any 

 change of position of a layer. 



Let the thin layer m t (see fig. 2) 

 that initially lay beneath M 2 be adi- 

 abatically brought to lie above M 2 . 

 In this case nothing changes in the 

 lower mass M since the upper mass 

 M 2 acts like a piston of constant 





M. 



A 



M 



o 



ft, 



M , 



FIG.2. 



weight. Let the layers of the mass 

 M 2 retain the same consecutive or- 

 der. The kinetic energy that is 

 available when the mass m t ascends 



in small particles and spreads out over M 2 ,is now to be computed 

 from equation (3). 



Let p x and T l be the initial pressure and temperature of m t ; 

 p h and T\ the same quantities at the end. Then 



T' = T 



1 1 1 1 



Ph 



Pi 



Pi = P h + g M 2 



Let p 2 , T 2 and p' 2 , T' 2 be the corresponding pairs of values for 

 a stratum dM 2 , then from the adiabatic condition and from 



