8 14 STUDIES FOR STUDENTS 



will fail to move the sand grains, and hence cannot build ripples, 

 while higher velocities agitate the whole mass of sand so violently 

 that no ripples can form. (8) The formation of ripples is initiated 

 by some obstacle or inequality on the surface of the sand, behind 

 which sand grains accumulate in the eddy caused by its presence; 

 this leaves a furrow on either side of the initial ridge, due to the 

 abstraction of sand accumulated in the ridge; and these furrows 

 in their turn cause additional ridges to develop on their outer mar- 

 gins, and so on. (9) In a given locality, ripple marks almost 

 always form with the same spacing, regardless of the varying 

 intensity of winds and waves affecting the water body; this is in 

 consequence of laws 7 and 6 stated above. (10) The depth at 

 which ripple marks may form is limited by the depth to which 

 wave action may extend with sufficient energy to move the bottom 

 sands; hence it depends on the size of the waves, and therefore in 

 part indirectly on the size of the water body; in the Rhone, the 

 limiting depth is a few decimeters; in Lake Geneva, some ten 

 meters; and in the ocean, from 20 to 188 meters, according to 

 Lyell and Siau. Forel revised De Candolle's law regarding the 

 relation of ripple spacing to the amplitude of the friction-producing 

 movement to read: "The breadth of the ripples, or the distance 

 from one crest to another, is the length of the path followed during 

 a single oscillation by a grain of sand freely transported by the 

 water." The length of this path varies directly as the horizontal 

 amplitude of the oscillatory movement of the water, directly as 

 the velocity of that movement, inversely as the density of the sand, 

 and inversely as the size of the sand grains. 



Darwin's paper "On the Formation of Ripple-Mark in Sand" 

 is especially noteworthy for its careful analysis of the vortices 

 which are so important a factor in the construction of the ripples. 1 

 When symmetrical oscillation ripples were subjected to the action 

 of a steady current, Darwin noticed that not only did sand grains 

 migrate up the weather slope of each ripple with the current, but 

 that they also ascended the lee slopes, apparently against the cur- 

 rent. This proved conclusively the existence of vortices. Darwin 



x G. H. Darwin, "On the Formation of Ripple-Mark in Sand," Proc. Roy. Soc. 

 London, XXXVI (1883), 18-43. 



