Ratio of the Length and Height of Sea Waves. Ill 



its maximum height to final disappearance or extinction, 

 that the ratio of height and length must, in this view, vary 

 through all the degrees observed in waves. 



But what is meant by the decline or the subsidence of a 

 wave since the actual bulk or magnitude is neither mea- 

 surable by its height nor its length, but by the area of a 

 cross section ? A volume of water has been raised to a 

 certain height above the ordinary level ; and in declining its 

 height must decrease until the curve of its profile gets 

 flattened out to a straight line. In what manner is the 

 length thereby affected ? Inquiry will, I think, show that 

 the length is not only relatively increased (which it would 

 be by remaining constant while the height alone decreased), 

 but itself increases — that is, absolutely, in the act of the 

 wave's subsidence. 



Now, although we cannot accompany a wave in its onward 

 progress across a sea to note the changes it undergoes in its 

 transit, yet be it remembered that the same laws which 

 influence deep-sea waves, however vast, likewise direct the 

 movement of the smallest ripples^ scanning which the eye 

 may under favourable circumstances take in at a glance the 

 phenomena here indicated. 



For instance, if a fresh breeze be blowing on a smaU piece 

 of water so as to produce a series of riplets, and these travel 

 into a part which is sheltered from the wind, it will be 

 observed that at genesis the wave is steepest — i.e., the ratio of 

 the length to the height smaU, and that as long as the wind 

 has a direct active influence in sustaining them the height 

 preserves a large proportion to the length. As soon^ however, 

 as the direct support of the wind ceases the wave begins to 

 decline by, be it observed, spreading out in length and 

 decreasing in height. The annexed diagram is made from 

 observation in a spot favourably situated. The genesis of 

 the riplet is at A (Fig. 1); from A to B, the point of matu- 

 rity, it increases in size, the ratio of height to length being 

 greatest during increase. In the mature stage (from B to C) 

 the same ratio is maintained. At C, however, the wind has 

 ceased its support, and thence to D the wave gradually sub- 

 sides to extinction — i.e., until the height becomes indefinitely 

 smaU, and the length indefinitely great — in other words, the 

 surface becomes flat. 



Such a diagram may be said to represent the life of a sea 

 wave in miniature, for although it is the facsimile of the 



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