138 G. K. GILEERT RIPPLE-MAKKS AND CROSS-BEDDING 



being horizontal, and close to the bottom the ellipses are nearly flat, so 

 that the water merely swings forward and back. It is in this oscillating 

 current, periodically reversed, that the sand-rii)ples are formed. A prom- 

 inence occasions vortices alternately on its two sides, and is thereby 

 developed in a symmetric way, with equal slopes and a sharp apex- 

 There is a strong tendency to produce the mole laterally into a ridge, 

 the space between ridges is definitely limited by the interference of 

 vortices, and in time there results a regular pattern of parallel ridges, 

 equally spaced. 



It has been found experimentally that by varying the amplitude of 

 the water oscillation, and also by varying its frequency, the size of the 

 resulting ripples can be controlled ; but the precise laws of control have 

 not been demonstrated. Evidently the frequency of the natural oscilla- 

 tion equals the frequenc}^ of the wind waves, and its amplitude is a func- 

 tion of the size of the waves and the depth of the water ; so that a relation 

 will ultimately be established between wave-size, wave-period, and water- 

 depth as conditions and ripple- size as a result. 



Experiment has also shown that certain combinations of amplitude 

 and frequenc}^ of water oscillation yield currents too feeble to mold sand 

 into ripples, and certain other combinations yield currents too violent. 

 When these limiting combinations have been discussed with reference 

 to the combinations occurring in nature, the formula for ripple-size ma}'' 

 be found to involve only two conditions instead of three. 



Until that general law has been worked out no ver}^ satisfactory inter- 

 pretation can be given to the giant ripples of the Medina sandstone; 

 but as its formulation may be indefinitely delaj'edk, I shall base a tenta- 

 tive interpretation on such iragmentary data as are available. Observa- 

 tions by Hunt and de Candolle show that large wind waves }n-oduce 

 larger sand-ripples than do small waves. Some observations of ni}'- own 

 on the bed of lake Ontario show that for moderate depths the size of 

 ripples is not very sensitive to variation of water depth. The investiga- 

 tions of J. Scott Russell and others indicate that the amplitude of the 

 oscillation of the Avater near the bottom is never greater than the height 

 of the corresponding surface waves. In certain experiments Darwin 

 found the width of sand-ripple about half as great as the amplitude of 

 the simultaneous water oscillation. If these facts and inferences ma)'' 

 ])roperly be put together, they give a chain connecting the height of 

 wind waves with the width of the ripple-marks they ma}^ produce, and 

 indicate that at the most the ripple-marks are only half as broad as the 

 waves rolling above them are high. 



Should this tentative law be substantiated by future research the geol- 

 ogist may infer from the structure. of the Medina sandstones that the 



