HuNT-^Ow the Action of Waves on Sea-heacheSy 8fc. 275 



wind blows in squalls, and either veers or backs. Assuming, then, 

 that by variation in the wind-pressure waves of translation are 

 generated at sea, and thence travel to the shore, it is of importance 

 to ascertain the form under which they reach the shore. Do they 

 continue to be waves of Mr. Russell's first order, or are they wholly 

 or partially transformed into waves of his second order ? On the 

 reply to this question depends the action which they will exert on the 

 beach, and the point at which they will plunge, if they plunge at all. 

 In a Paper read before the Royal Society, Dr. Rankine writes 

 as follows : — " It is known that in deep water all waves left free 

 from the action of disturbing forces tend ultimately to assume 

 the condition of free rolling waves, whose velocity of advance de- 

 pends on their periodic time It follows that, if a wave is 



raised through the disturbance produced by a solid body, that wave 

 will at first travel with a speed depending on the virtual depth 

 of the original disturbance ; but as it advances to a greater and 

 greater distance from the disturbing body, the velocity of advance 

 will gradually approximate to the terminal velocity corresponding 

 to the periodic time." — {Phil. Mag., vol. xxxvi., p. 55.) According 

 to Dr. Rankine it would seem that a wave of the first order, a wave 

 of translation, may be gradually transformed into a wave of the 

 second order, whose velocity corresponds with its period. A good 

 opportunity of putting this theory to the test presented itself on the 

 occasion of the Torquay regatta of 1883. The wind was fresh from 

 the westward, off shore. The yachts had to round a mark-boat in 

 smooth water, about half a mile off Saltern Cove, in the bight of 

 the bay. Yessels of fifty tons and over in rounding this mark-boat 

 generated waves sufficiently large to toss about the six-ton boat in 

 which I was sailing. It seemed a good opportunity to observe the 

 character of these waves when they reached the shore after travers- 

 ing the half mile of smooth water betwixt the mark-boat and 

 Saltern Cove. The water being smooth there was no doubt as to 

 the exact position of the margin of repose. The large waves 

 generated by the yachts plunged on the beach below, or seawards 

 of the margin of repose, and must therefore have undergone, at 

 least partially, transformation into waves of the second order; 

 unless, indeed, it be contended that they were analogous to Mr. 

 Russell's negative waves of the first order, which, however, seems 

 hardly possible. 



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