ON THE ENERGY OF STORMS MARGULES 553 



By substituting this in equation (4), the linear term in h disappears 

 and there remains 



- d (P + I) = gW *U 3 (a - -L) (4a) 



This value is positive and gives the kinetic energy made available 

 by the overturning of m t provided 



£ dT ^ g 



a > -°- or - — > — • 

 C p dz C p 



In this case the equilibrium of the column of air is unstable. 



If a <g/C p then with every adiabatic overturning of any layer 

 there is associated an increase of the total potential energy P -f I 

 and the equilibrium of the column of air is stable. In the limiting 

 case a = g/C p and the equilibrium is neutral. 



§(16) Discontinuous distribution of temperature. If at the bound- 

 ary between m x and M 2 the temperature passes suddenly from 7\ to 

 T 2 it will suffice to assume M 2 to be of an order of magnitude similar 

 to m t whence we will now indicate it by m 2 . The interchange of 

 positions of m x and m 2 gives us 



-8(9 + I) = C p {m 1 (T 1 - T\)+m 2 (T 2 - T> 2 )\ 



gm 2 \ K 



V. = T, 1 - 



Pi 



hence when p is the pressure at the boundary and gm is small in 

 comparison with p we have 



-3(P + I) =w 1 m 2 1 -(r i -T 2 ) .... (46) 

 P 



which corresponds to unstable equilibrium when the warmer mass 

 lies below. 



§(17) The entropy as the criterion of stable equilibrium in a column 

 of air of uniform constant constitution. 



The condition for stable equilibrium can be expressed very simply 

 when we make use of the entropy. If P, 6, 5 are respectively the 



