VI. OP THE FLOOD TIDE. 9 



out of its place and carried forward -with the velocity of the surrounding particles ; 

 it is urged still on, until the particles which have displaced it have made room for 

 themselves behind it, and then the power diminishes." It finally settles down 

 quietly in its new place. This is the motmi of migration of an individual particle 

 of water. (P. 315.) 



This is the migratory motion, or motion of translation of the water particles in the 

 wave of the first order of Mr. Russell's classification ; and I shall aim to show, 

 directly, that this is the only wave action to be considered, the only one the process 

 of which applies to the present investigation. 



This motion of the water particle is resolved into two components, a vertical 

 motion and a longitudinal motion. " First, the particles begin to • rise, scarcely 

 advancing; they next advance as well as rise; they cease to rise but continue 

 advancing ; they are retarded and come to rest, descending to their original level." 

 (P. 342.) This is the course of the water particle, as observed by Mr. Russell, by 

 means, as I said before, of visible particles suspended in the water, a mode of 

 investigation precisely analogous to the case of nature, where matter held in sus- 

 pension, as sand, is transported by the moving water, and brought under the 

 influence of the wave action. " The wave is thus a receptacle of moving power," 

 (p. 347,) "a vehicle for the transmission of mechanical force." (P. 361.) During 

 the translation of the particle, the greatest height accompanied by the progressive 

 motion is at the top of the wave, or in the middle, corresponding to the greatest 

 height, or crest, of the wave. Now when, in travelling along a gradually shoaUng 

 channel, approaching a slojsing coast, the depth of the water diminishes to an 

 equality with the height of the wave, the wave breaks, or falls to pieces, " the 

 particles in the ridge of the wave pass forward out of it, fall over, and the wave 

 becomes a surge or broken foam, a disintegrated heap of particles, having lost all 

 continuity." (P. 352.) The velocity with which the particles pass forward out of 

 the wave, or are trajected, in other words the velocity of translation, is in propor- 

 tion to the height of the wave. The mechanical power exerted is, therefore, in 

 proportion to the height of the wave. This is so apparent to every one who has 

 watched the surf, in dififerent stages of violence, that it is hardly worth while to 

 state it. 



The wave I have described here is the positive wave of the first order ; that is, the 

 wave which makes its appearance in a form wholly raised above the general level 

 of the fluid. And it is this form of wave that is to be seen at all times breaking 

 upon an alluvial coast, and there only; it is the final wave which, inside of, and be- 

 yond, all others, comes into actual contact with the beach, and defines the inner 

 limit of the water. This form of wave follows upon the destruction of the waves 

 of the sea, as they break upon the shore, as may be observed at any time on the 

 sea-shore, and to the greatest advantage upon the long, gently sloping, and shallow 

 beaches. " One of the common sea waves approaches the shore, consisting of a 

 negative or hollow part, and of a positive part raised above the level." As the 

 water becomes more shallow the positive part increases in height, this increase goes 

 on with the diminution of depth, until at length the wave breaks, and its crest falls 

 forward into the hollow in front. (P. 373.) But it does not cease to travel, though 

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