WAVE-CURBEFTS ON SHALLOW-SEA. FAITNAS. 263 



the disturbances of the air does not extend beyond the depth of a 

 few fathoms," and that " below this surface- stratum there is no 

 other movement except the quiet flow of ocean-currents " 

 ('Introduction to the Study of Fishes,' p. 298). 



In a paper published in the ' Transactions of the Devonshire 

 Association ' in 1883 I described a glass bottle trawled in 

 40 fathoms in the English Channel, and endeavoured to prove, 

 from its condition and contents, that it had been subjected to 

 alternate periods of wave-disturbance and of repose (" The Sub- 

 marine Greology of the English Channel off the Coast of South 

 Devon," Part III., Trans. Dev. Assoc, vol. xv. pp. 359-365). 

 Professor Gr. Gr. Stokes, Sec. U.S., has been so good as to peruse the 

 paper referred to, and to farour me with a letter on the subject of 

 wave-disturbance on the sea-bottom, from which the following is 

 an extract. Eeferring to waves with a period of 17 seconds (such 

 as hf had himself had an opportunity of observing), and acting 

 at a depth of 40 fathoms, Professor Stokes writes : — 



" Lensfield Cottage, Cambridge, 

 18 Jan., 1884. 



"... I find for the velocity of propagation of the waves 

 87*14 feet per second in the deep, and 73'05 in the shoal, or 

 59'41 miles per hour in the deep, and 49* 13 in the shoal. Also, 

 for the ratio of the velocity at the bottom to the velocity at the 

 surface 0"5332 to 1. As to the actual velocity at the surface, that 

 will depend on the height we assign to the waves. Taking it as 

 eight feet above or below mean level in the shoal, 16 feet from crest 

 to trough in all, I find a velocity of 1*989 miles per hour at the sur- 

 face, and 1"036, say 1 mile, an hour at the bottom. The height 

 may, however, well be greater than what I have assumed, and the 

 velocity will be greater in proportion. 



" But even a velocity of only 1 mile per hour might make a 

 material difference if combined with a tidal current. Thus, sup- 

 pose we had a tidal current running 2 miles an hour, approxi- 

 mately in the same direction as the waves are travelling in, or in 

 the contrary direction. Then, whereas with the tide alone we 

 should have a steady current of 2 miles, and with the waves alone a 

 reciprocating flow of 1 mile, with the two together we should have 

 a flow rapidly changing between 1 mile and 3 miles. Now, taking 

 the resistance to vary as the square of the velocity, the 3-mile 

 current would have two and a quarter times as much power to roll 

 over a shell or bottle as the tidal current alone ; and, moreover, this 



