9 \p. 



ON THE ENERGY OF STORMS — -MARGULES 555 



the surrounding air at the same altitude. Under adiabatic condi- 

 tions its temperature in all positions is given by the equation 



' t\* 



pj 



1 dd ndp 



whence ~E~T = ~~T 



d dz p dz 



Let us assume that during the motion of the particle m the pres- 

 sure in the larger mass remains unchanged and that the equation 

 (a) holds good so that we have 



dd _ g_6_ 

 dz = ~ C p T 



If [u] is the density of m but /x that of the surrounding air then 

 there is acting upward on m the accelerating force or buoyancy 



w 



or, since the pressures are the same, 







If we consider m as an elementary mass moving without friction and 

 express its vertical ordinate by z we then have the equation of 

 motion 



d 2 z I \ dd 



dt 2 5 \r""V Cp dz S 



Hence follows the equation of energy, assuming that m has no 

 initial velocity at z 



m I dz\ 2 \ 



I p \k 1 \ 



= m { C p d y 1 - - - j J - g (s - s ) J 



This latter expression is identical with the right-hand side of equa- 

 tion 4 section 14, substituting w^or m, T l for d and h for (z — z ). 



