1883.] 



On the Formation of Ripple-mark. 



39 



dune, considering that region merely as slack water. I feel some 

 doubt as to the view that a regular series of dunes may be formed by 

 uniform current; at any rate, in my experiments the dunes were 

 irregular, and had no definite wave-length. 



His observations on the circumstances which govern the wave- 

 length of ripple-mark are important. He finds that the factors 

 which enter are the amplitude and period of oscillation of the water ; 

 and a third factor is the maximum velocity of the water, which he 

 takes as identical with the ratio between the two others. If the 

 water moves as a whole with a simple harmonic oscillation it is un- 

 doubtedly true that the ratio of amplitude to period is proportional 

 to the maximum velocity, but the vortices quite disturb this relation. 

 The maximum velocity of the water relatively to the bottom must 

 depend upon the intensity of the vortices, and this depends upon the 

 height of the ripple- mark. 



M. Forel finds that the length and breadth of the vessel have no 

 influence on wave-length, but that it diminishes with increasing depth 

 of water. This he attributes to a diminution both of the period and 

 of the amplitude of the oscillation of the water which is in contact 

 with the bottom. The wave-length increases with the coarseness of 

 the sand. 



He remarks that when the ripple-mark is once made, the amplitude 

 of oscillation is without influence on its wave-length. He draws 

 attention to the two limiting velocities, one too great, and the other 

 too small for the formation of ripples, for which values were found 

 in the experiments of § 1. 



M. Forel explains ripple-mark as the confluence of two dunes, 

 formed alternately by the oscillating currents. This theory is 

 undoubtedly correct, if somewhat incomplete. 



The wave-length, he says, is the amplitude of oscillation of a grain 

 of sand " librement transported par Teau." This expression requires 

 further explanation ; if it means the amplitude of oscillation of a 

 particle of water at the bottom, when the oscillation is started, and 

 before the ripples have risen, T am disposed to doubt it. It may 

 mean the distance w T hich an average grain of sand is transported 

 when lying on the surface of other sand, under the like circum- 

 stances ;* if so, ripple-marks formed with a thin layer of sand on a 

 sheet of glass should have a longer wave-length than if the sand be 

 thick ; this I am also disposed to doubt. However this may be, 

 M. Forel considers that the wave-length should vary directly as the 

 amplitude of oscillation, directly as the velocity of the current, 

 inversely as the density of the sand, and inversely as the size of the 

 grains. Considering with M. Forel that the velocity of the current ia 



* I learn by a letter from M. Forel that this is his meaning. 



