390 HERMANN VON HELMHOLTZ 



communicated his theoretical conclusions, and the comparison 

 of them with his observations, to the Academy of Berlin, on 

 July 17, 1890, with the title ' The Energy of the Waves and 

 Wind ', as the continuation and completion of his two earlier 

 works on atmospheric motion. 



In his earlier investigations Helmholtz had shown that a 

 level surface of water, over which a wind is blowing evenly, 

 will be in a state of unstable equilibrium, and that the origin 

 of the waves of water must be ascribed to this very circum- 

 stance. Further, the same process must occur at the border 

 of layers of air of different densities that slide over one 

 another ; but will here assume much greater dimensions, and 

 has an essentially causative significance in the irregular 

 phenomena of meteorology. This determined him to investi- 

 gate the relations of energy, and its distribution between air 

 and water, more exactly in his memoir on the energy of waves 

 and wind, while still confining himself to the case of stationary 

 waves, in which the movements of the water particles can 

 only proceed parallel to a vertical plane. He refers the laws 

 of stationary rectilinear waves back to a minimal problem, in 

 which the potential and kinetic energy of the moving fluids 

 are the variables, and is able to formulate conclusions as to 

 the increase and decrease of the energy, and the difference 

 between stable and unstable equilibrium of the surface of the 

 water. In this difference of the state of equilibrium, the 

 masses in question are no longer at rest, but are in persistent, 

 though stationary, motion. 



Till now it had proved impossible to lay down any general 

 law for moving systems, comparable with that for resting 

 bodies, as expressed in the statement that stable equilibrium 

 involves a minimum of potential energy. Helmholtz finds 

 the minimal law for stationary waves with constant amounts 

 of current to be that the variation of difference between 

 potential and kinetic energy disappears, so that stable equi- 

 librium of a stationary wave-form corresponds under all 

 possible variations of such a form with a minimum of such 

 a difference. If, on the other hand, the same magnitude 

 becomes a maximum with another form of curve, the con- 

 dition of equality of pressure on either side of the limiting 

 surface is at least temporarily fulfilled, but any disturbances, 



