SAND-WAVES IN TIDAL CURRENTS 337 



current of a given velocity the pumping action! 

 of the eddy will become too weak before the direct 

 current becomes too strong. Therefore the growth 

 in height of the sand-wave will be arrested when 

 the upward velocity, or pumping action, of the 

 eddy in the trough is not greater than the rate of 

 subsidence of the sand-grains. If this reasoning 

 be correct, the large heights which the cliffs of the 

 Mississippi sand-reefs can maintain is partly due 

 to the heterogeneity of the material, hence their 

 being characteristic of recent sediments. 



The measurements which I have made are suffi- 

 cient to give a rough indication of the relation of 

 velocity of current to the length of the sand-waves 

 which it produces. The measurements about to be 

 quoted are those where there is sufficient depth 

 of water to admit of full development of the waves. 

 For two slow streams, taking the mean, I found that 

 a current of o'695 foo^ P^^ second produced waves 

 with a length of 5- 7 5 inches. In the estuary of the 

 Dovey a current of 2' 93 feet per second produced 

 waves with a length of 1248 inches, so that the 

 increase in length was much more rapid than the 

 increase in velocity. The length of the sand-waves 

 in the estuary was 2 17 times as great as that 

 in the slow streams. If the length increased pro- 

 portionally to the square of the velocity, then the 



