ON THE ENERGY OF STORMS — -MARGULES 571 



whence we obtain the mass-integral of (T — T') as follows: 



r 



»J0 



(T - V) fidz = K .{T* (p 0x - Ph ) 



gh 

 R 



[ ph+1 iSL x (p °*- ph)dx ]} 



.(A) 



This expression multiplied by the factor C p dx and integrated 

 throughout the whole length / gives the available kinetic energy 

 of the whole syst.em. But since we take the true average tempera- 

 ture T* instead of the barometric average temperature therefore 

 we first substitute 



Pox - Ph = Ph 



gh 



RT* 2 \ RT* 



gh + 1 



. . (B) 



and remark that in the first member, on the right hand side of the 

 integral (/L), both terms of (B) as the serial development of p ox —p h 

 are to be used, but in the last member of (^4) only the linear 

 term in h or the first term of (B) need be considered, if we desire 

 to go only as far in the result as terms of the order 



T */_fM a 



\RT*J 



For r* we choose a linear function of the length in which r 

 is small relative to unity so that 



T*( 1 +T 



I 



1 



T* T* 



* x x o 



1 - T- 



This gives for the last term in the integral (^4) 



i p 



I Ji- 



(Po x ~ Ph) dx = p h 



gh Ix 

 RT* \ I 



2lx 



and for the complete integral (A) 



J. g °\RT*/ \ 2 / 2 / 2P j 



