Generation, Growth and Propagation of Waves 67 



"The second state of the development of wave motion is to be observed 

 when the velocity of the wind acting on the smooth water has increased to 

 two miles an hour (90 cm/sec). Small waves then begin to rise uniformly 

 over the whole surface of the water, these are waves of the second order. 

 Capillary waves disappear from the ridges of these waves, but are to be found 

 sheltered in the wave troughs between them and on the anterior slopes of 

 these waves. The regularity of the distribution of these secondary waves 

 over the surface is remarkable; they begin with about an inch of amplitude 

 and a couple of inches long; they enlarge as the velocity or duration of the 

 wave increases; by and by the coterminal waves unite; the ridges increase, 

 and if the wind increases the waves become cusped, and are regular waves 

 of the second order (gravity waves). They continue enlarging their dimensions, 

 and the depth to which they produce the agitation increases simultaneously 

 with their magnitude, the surface becomes extensively covered with waves 

 of nearly uniform magnitude." Scott Russell's wave of the first order is the 

 "solitary wave." 



Similar observations were made by Apstein (see Kruemmel, 1911, p. 57) 

 aboard the "Valdivia" and on the research steamer "Poseidon" in the open 

 ocean, partly by means of photographs of the ocean surface taken from 

 a very short distance. Mostly several kinds of waves were present 

 simultaneously. The capillary waves cover all areas hit by the wind; their 

 length is about 2-3 cm, their crests are, without exception, slightly curved; 

 the shape of these wave crests, which have a length of about 9-15 cm, make 

 the water surface look to be covered with irregular "rhombic corrugations". 

 Beside these "elementary" waves appear, as next larger size, waves of 

 6-12 cm length and, following these, waves of 18-25 cm, also 30 cm length. 

 At a wind speed of 100 cm/sec, waves several metres long appear, and the 

 length of the crest is at an average 3-5 times the wave length. Until longer 

 wave crests and regular wave trains are formed, the water surface has the 

 appearance of a piece of crepe paper rather than of a sheet of corrugated 

 iron. 



All these observations deal rather with the qualitative aspect of the process 

 of wave formation, whereas the quantitative indications are mostly based 

 on estimates and not on instrumental measurements. Jeffreys made a few 

 more exact observations of this kind on ponds near Cambridge, in order 

 to test the theoretical results. He observed, with wind speeds of less that 

 104 cm/sec, small disturbances which did not have the characteristics of 

 waves. Only beyond this limit did the first distinct waves appear and at wind 

 speeds of 104, 110 and 116 cm/sec the wave length was 80, 8-8 and 9-8 cm. 

 Stanton, on the contrary, found in wave tanks, with wind velocity of 

 250 cm/sec, wave lengths of only 6 cm. More thorough systematical in- 

 vestigations, taking into account all factors which might influence wave 

 formation, would be most desirable, the more so as the theory of the process 



