IV A VES. 27 



breakwaters upon the character of waves; but I shall again 

 refer to this subject later on. 



Sir G. B. Airy has shown 1 that when the depth of water is 

 great as compared with the length of a wave as in the case of 

 ordinary waves in the open sea each particle of water in an 

 oscillatory wave describes a circle about its position of rest, in 

 the vertical plane in which the wave is advancing. The motion 

 of particles is therefore forward in that section of the wave 

 which is above the normal water-level, and backward in that 

 which is below it, and they attain their greatest respective for- 

 ward and backward velocities when at the highest part of the 

 crest and lowest part of the trough (see Fig. 6, p. 25). 



The diameters of these circles rapidly decrease with increased 

 depth of water, so that at a depth equal to the length of the 

 wave, crest to crest, the motion of the water-particles is only 

 osV-? f that at the surface, whereas at double that depth it 

 only amounts to ^geWo ^ that a ^ the surface. 



The motion thus diminishes in geometrical progression as 

 the depth below the surface proceeds in arithmetical progres- 

 sion. Let the reader note, however, that the depth of water in 

 which breakwaters are constructed seldom much exceeds one- 

 tenth the length of the waves in heavy seas, at which depth the 

 difference of the horizontal range of particles at the bottom, as 

 compared with that at the surface, is but small. 



The tables 2 on p. 28 give the greatest extent of horizontal 

 and vertical displacement of the particles of water, at different 

 depths, for waves whose length is equal to the depth of the 

 water which they are traversing; and also for waves whose 

 length is ten times as great as the depth of the water which 

 they are traversing ; the greatest horizontal displacement of the 

 particles at the bottom being represented by 2. 



Notwithstanding the rapid diminution in the motion of the 

 particles from the surface downwards, the effect of the bottom 

 upon passing waves is sufficient to cause them to break in con- 

 siderable depths of water. This is more especially the -case 

 when an abrupt change of depth takes place. 



There is a shoal, known as Kiy Bank, off the south coast of 

 Africa, where long ground-swell waves of moderate height, say 

 10 feet to 12 feet trough to crest, are commonly seen to break, 



1 " Tides and Waves." 



2 Extract from Table IV., Airy, " Tides and Waves." 



