Denudation of the Lake District. 475 



the height of the wave and the depth of the ocean. In a certain time 

 the water first raised above the general level of the ocean imme- 

 diately over the elevated area would run off, leaving the surface of 

 the ocean there at its original level ; and when this should be com- 

 pleted the posterior boundary of k the wave would be immediately 

 over the periphery of the elevated area. During the same time the 

 front of the wave would move on through a certain space, still form- 

 ing a circle of which the centre would be immediately over that of 

 the elevated area. Thus the whole wave would at the instant now 

 referred to be comprised between two concentric circles, the 

 distance between which would be the breadth of the wave. After- 

 wards, as the front or anterior boundary of the wave spread out- 

 wards, so would the posterior boundary move forward in a similar 

 manner, always preserving the annular form just mentioned. As 

 the wave diverged its height would gradually diminish till it be- 

 came finally insensible. 



The motion of the wave here spoken of is altogether distinct 

 from the motion of translation of the aqueous particles. This 

 latter motion, however, accompanies the former in the kind of wave 

 here described, producing a current like that of a tidal river oppo- 

 site to the usual course of the stream. Each particle begins to 

 move onward the instant when the anterior boundary of the wave 

 has reached it, but its motion being always slower than that of the 

 wave, it will afterwards be overtaken by the posterior boundary of 

 the wave, which will then leave the fluid particle behind and at 

 rest. Thus, at any proposed point, the current will begin when the 

 front of the wave reaches that point, will increase there till the 

 highest part of the wave is directly over it, and will then gradually 

 decrease till the posterior boundary of the wave has reached the 

 point in question, where the current will then cease altogether. 

 There will be no reflexion of this great solitary wave unless it meet 

 with some obstruction in the course of its motion. 



We are indebted to Mr. Russel for our knowledge of the pro- 

 perties of these great waves of translation. He has further ascer- 

 tained, experimentally, that the velocity of the wave is equal to that 

 which would be acquired in vacuum by a stone falling under the 

 action of gravity through a height equal to half the depth of the 

 ocean measured from the crest of the wave. He has also found 

 that the velocity of the current at any point is independent of the 

 depth of that point, being the same at the bottom as at the surface*. 

 From these data it is easy to calculate the velocity of the current 

 which attends the wave, when the depth of the ocean and original 

 height of the wave are known. And hence it appears that there is 

 no difficulty in accounting for a current of twenty-five or thirty 



* Mr. Russel's experiments were made with much smaller waves and at 

 much smaller depths than those above spoken of ; but he expresses a con- 

 viction (and, as the author conceives, a well-founded conviction) that the 

 same results will hold for much greater depths than those experimented 

 with. 



