PAPER BY PROF. HELMHOLTZ. Ill 



It is sufficient to have proven that for one form of wave billows due 

 to wind are possible, which billows have a less store of energy than 

 the same wind would have over a plane boundary surface. Hence it 

 follows that the condition of rectilinear flow with plane boundary sur- 

 face appears at first as a condition of indifferent or neutral equilibrium, 

 when we consider only the lower powers of small quantities. But if 

 we consider the terms of higher degree, then this condition is one of 

 unstable equilibrium, in view of certain disturbances that correspond to 

 stationary waves between definite limits as to wave-length; but on the 

 other hand is a condition of stable equilibrium when we consider shorter 

 waves. 



This result is evidently of great importance for the origin of waves. 

 It follows from this, as we everywhere see confirmed in nature, that 

 even the most uniform wind can not blow over a plane surface of water 

 without on the slightest disturbance causing waves of a certain length, 

 which for a given height acquire regular form and speed of propaga- 

 tion. If the wind increases then the heights of all these waves in- 

 crease, the shorter ones among them break foaming, so that new longer 

 cues of less height can be formed. 



The greater energy that is necessary in this case in order to push the 

 shorter waves up higher becomes possible in that the previous feebler 

 wind had already given a part of its energy to the mass of water, and 

 the new stronger wind finds this i)art already i^resent there. 



Breaking, foaming atmospheric billows cause mixture of strata in 

 the mass of air. Since the elevations of the air-waves in the atmos- 

 phere can amount to many hundred metres, therefore precipitation can 

 often occur in them which then itself causes more rapid and higher 

 ascent. Waves of smaller and smallest wave-length are theoretically 

 possible. But it is to be considered that perfectly sliarp limits between 

 atmosi)heric strata having different motions certainly seldom occur, 

 and therefore in by far the greater number of cases only those waves 

 will develop whose wave-length is very long compared with the thick- 

 ness ot the layer of transition. 



The circumstance that the same wind can excite waves of different 

 lengths and velocities, will cause interferences to occur between the 

 waves, and also higher and lower wave summits to follow each other 

 interchangeably. This is a process observed often enough on the 

 shore of the ocean. But where two wave summits of different groups 

 of waves reenforce each other a height will easily be attained at 

 which they break into foam, and thereby, as in the analogous case 

 of the production of sonorous combination tones, longer waves can 

 be formed which, when they are favored by the strength of the wind, 

 can also grow larger. This is one of the processes by which waves of 

 great length can arise. 



