VII. 



THE ENERGY OF THE BILLOWS AND THE WIND. 



By Prof. H. Vox Helmholtz. 



Iii my communication to the Academy on July 25, 1889, I called atten- 

 tion to the fact that a plane surface of water above which a steady wind 

 is blowing is in a state of unstable equilibrium an 1 that the origin of 

 large waves or billows of water is essentially due to this circumstance. 

 I have there also shown that the same process must be repeated at the 

 boundary of two strata of air of different densities gliding over each 

 other, but that in this case it can assume much larger dimensions and 

 without doubt has an important meaning as a cause of nonperiodic 

 meteorological phenomena. 



The importance of these processes has induced me to investigate still 

 more thoroughly the relations of the energy and its distribution between 

 the air and the water; at first, however, as before, with the limitation 

 to stationary waves in which the motions of the particles of water only 

 take place parallel to a vertical plane in which the coordinates are re- 

 spectively (x) vertical and (y) horizontal. Since however we can 

 only solve even this special problem by the development into a converging 

 series whose higher terms rapidly diminish in magnitude but offer com- 

 paratively complex forms therefore the conclusions that we may have 

 drawn from a knowledge of the first largest term of such a serk s are 

 necessarily always limited to waves of slight altitude and cause the 

 correctness of many more important generalizations to appear doubtful. 



Many of these difficulties have been surmounted in that I have been 

 able to reduce the law of stationary rectilinear waves to a problem of 

 minima, in which the variable quantities are the potential and actual 

 energies of the moving fluids. From this problem in variations many 

 general conclusions can be deduced as to the decrease and increase of 

 the energy, and the difference between stable and unstable equilibrium 

 of the surface of water. 



Theoretically considered, there arises here a rather new problem in 

 so far as we have to do, not with the difference between stable and un- 



* From the Sitzungsberichte of the Royal Prussian Academy of Sciences at Berlin. 

 1890, vol. vn, pp. 853-872. Wiedemann, Ammlev, 1890. xli, pp. 641-G62. 

 112 



