ON THE ENERGY OF STORMS MARGULES 585 



§(350) Let us consider a system that in its initial stage contains 

 no liquid water. Its internal energy will be 



1^ = C va J Tdm a + C v pj T d mp + L J d mp 

 For the fmal stage this becomes 



T e = C va JT'dm a + C v pJTdm'p + cJTdm' r + L jdm'p 

 Since we assume dm r = therefore dm' p = d mp — d m' r and 

 T e = Cva] T' d m a + C v pj T d mp + L J d mp - 

 - J[L - (C-C v p)T']dm' r . 



The excess of the internal energy in the initial stage over that in 

 the final stage is 



-«T-T."-T> C V J(T -V) dm a + C V J(T - T>) dm. \ 



+ j(L' -RpT)dm' r . . 



We assume further that the density of the writer is infinitely great 

 in comparison with the density of the air (or that the volume of 

 the water is zero). Under this assumption \ e and d\ retain their 

 values when the condensed water falls to the ground. 



If the system is, as before in figure i, composed of a lower por- 

 tion of the mass of atmosphere, extending up to the altitude h, and 

 an upper portion that acts only as a piston of constant weight Bp h , 

 where B is the area of the base; if also the air is at rest in both its 

 initial and its final stages, then for the potential energy of position 

 we have the following expressions, in which the volume and mass 

 integrals are to be extended over the lower portion only. This 

 latter is true also for the mass-integrals in I. The partial pressures 

 are p a and pp. 



P = J dB I pdz + Constant = J (p a + pp) dk+ Constant 



= R a J Tdm a + Rp J Tdmp + Constant 

 P e = R a j T'dm a I Rp f Tdmp + Constant 



= R a J Tdm a + R3 J Tdmp - Rp J Tdm r + Constant 



