I have no time to mention the details of the charming pattern of capillary waves 

 which forms ahead of the obstacle, which is especially prominent if the obstacle is 

 small, like Rayleigh's famous "fish-line" [19], but this can be understood by directly 

 similar arguments. 



9. Waves of greatest height 



I pass now from the frequency spectrum to what I may call the "amplitude 

 spectrum" of water waves. This is best displayed on a diagram (Fig. 4) in which the 

 abscissa is \/h and the ordinate a/A, where a is the vertical height between crest and 

 trough. The wave velocity c for small a/\ is exhibited under the diagram as a reminder. 



Vtqhl 

 0.5 



Figure 4. Amplitude-wavelength diagram for water waves. Under it is shown the wave-velocity 

 versus wavelength diagram for waves of small amplitude (Fig. 1 ) as a reminder. 



Now, there are two kinds of breaking which can limit the possible existence of 

 periodic waves (Fig. 5). At the deep-water end of the scale there is the formation of 

 the "wave of greatest height" which when it occurs as a stationary wave on a stream 

 brings the water locally to rest at its wedge-shaped crest.* Further increase in the 

 energy of these waves goes into spray formation. Stokes [30] predicted this wave and 

 also observed it, writing: "In watching many years ago a grand surf which came rolling 

 in on a sandy beach near the Giant's Causeway, without any storm at the place itself, 

 I recollect being struck with the blunt wedge-like form of the waves where they first 

 lost their flowing outline, and began to show a little broken water at the very summit. 

 It is only I imagine on an oceanic coast, and even there on somewhat rare occasions, 

 that the form of waves of this kind, of nearly the maximum height, can be studied to 



* Values of a/\ for waves of greatest height in Fig. 4 were obtained as follows: for 

 deep-water waves from Michell [25], for the solitary wave from McCowan [24] and for 

 intermediate cases from Kishi [16]. 



23 



