ON THE ENERGY OF STORMS MARGULES 535 



the order of the increasing values of initial entropy. Equal masses 

 of equal entropy can be interchanged at will. 



The available kinetic energy of the system, including the loss 

 by friction, is determined by the relation 



dK + (R) = - d(P + I) = (P + l) a - (P + I) e 



where the index a belongs to the initial and e to the final stage. 

 (P + I) e is the smallest value that the sum total of potential and 

 internal energy can have under adiabatic condition. 



If there be no friction then this equation is to be understood as 

 follows : The largest amount of kinetic energy will be attained when 

 all the masses pass through their respective appropriate positions 

 of equilibrium simultaneously; if this does not occur then the 

 kinetic energy attainable will be less than this which we will desig- 

 nate as "available energy." During the pendulous oscillation 

 of the masses, a part of the potential and of the internal energy 

 is still latent. 2 



If there be friction then the kinetic energy increases and be- 

 comes a larger fraction of the total amount of available energy 

 in proportion as the influence of the friction is smaller; after the 

 masses of air have approached their final positions this fraction 

 diminishes and becomes zero when the final stage is attained. 

 The condition of isentropic change is not precisely fulfilled since 

 the friction produces heat. In our analysis we assume that this 

 heat is again withdrawn from the air-mass. This limitation is of 

 slight importance in the case of atmospheric motions. 



§(3) Of all the different kinds of storms those best known to me 

 are the gusts of wind (the boe-en) which are accompanied by rapid 

 increase of atmospheric pressure and rapid fall of temperature. 

 These were first investigated by Koeppen. Masses of air of unequal 

 temperatures at identical levels are separated by a sharp boundary 

 that advances with the storm wind toward the warmer side. The 

 difference of temperature, which is often io° C. at the surface of 

 the ground, continues up to an altitude of nearly 2000 meters. The 

 pressures at greater altitudes, not far from the boundary, are equal 

 over the warm and cold regions but at the ground they are greater 

 in the cold region. 



Based on this general experience I have formulated the follow- 

 ing problem: Let the mass of air in the lower part of a closed 

 system, A, B, C, D, be initially divided by a screen into two parts 



2 Helmholtz describes the free (freie) energy, F, of any system, the total 

 (gesammt) energy, u, and the latent (gebundene) energy, u — F. — Editor. 



