22 



RATIO OF WAVE VELOCITIES INDICATING 

 THE EFFECT OF FINITE HEIGHT OF WAVE 



Ch 

 C 



Figure 9, 



Stokes (2) notes: 



The disadvantage of the approximation for the case of a finite as compared with 

 that of an infinite depth is not however quite so great as might at first sight 

 appear. There can be little doubt that in both cases alike the series cease to be 

 convergent when the limiting wave, presenting an edge of 120°, is reached. In 

 the case of an infinite depth, the limit is reached for some determinate ratio of 

 the height of a wave to the length, but clearlj' the same proportion could not be 

 preserved when the depth is much diminished. In fact, high oscillatory waves 

 in shallow water tend to assume the character of a series of disconnected solitary 

 waves, and the greatest possible height depends mainly on the depth of the fluid, 

 being but little influenced by the length of the waves, that is, the distance from 

 crest to crest. To make the comparison fair therefore between the convergency 

 of the series in the cases of a finite and of an infinite depth, we must not suppose 

 the coefficient of cos m<i>IC the same in the two cases for the same length of wave^ 



