THEORY OF SAND-RIPPLES 137 



Another example of great size was observed in the north part of the 

 area worked over b}^ the Whitmore quarries at Lockport. A solitary 

 crest of the broad, low ty]3e (c, figui'e 2) exhibits a convex profile for 

 about 15 feet. In ripples of this type the concave portion of the profile 

 is usually as wide as the convex, and we again have an estimate of 30 

 feet as the approximate maximum width of the ripples. 



Interpretation in Terms of physical Condition 



If full}^ understood, these giant ripples should tell us something of 

 the local physical conditions at the time of their formation, and some 

 suggestions on this point are afforded by the theory of sand-rippling as 

 at present developed. Previous to 1882, ideas as to the origin of water- 

 made sand-ripples were crude and unsatisfactory. In that year an im- 

 portant paper was published by A. R. Hunt,* and two years later the 

 results of three other investigators, C. de Candolle,t F. A. Forel,;): and 

 G. H. Darwin, § appeared. While these contributions did not build up a 

 comj^lete theory, they left the subject in so satisfactory a shape that 

 there has been little subsequent discussion. 



The following summary statement outlines the present condition of 

 the theory, without attempting to distribute to individuals the credit for 

 their several shares. 



A current of water flowing over a bed of sand reacts on any prom- 

 inence of the bed. An eddy or vortex is created in the leo of the prom- 

 inence, and the return current of this vortex checks traveling particles, 

 causing a growth of the prominence on its downstream side. At the 

 same time the upstream side is eroded, and the prominence thus travels 

 downstream. It is a subaqueous dune. Its upstream slope is.long and 

 gentle; its downstream slope is short and steep. Such dunes have a 

 moderate tendency to develop laterally, and they interfere with one an- 

 other to some extent if they approach, but they do not develop a regular 

 pattern with equal interval. They are rarel}^ preserved as fossil. 



The ordinary ripple-mark of beaches and rock faces is produced by 

 the to-and-fro motion of the water occasioned by the passage of wind 

 waves. During the passage of a wave each particle of water near the 

 surface rises, moves forward, descends, and moves back, describing an 

 orbit which is approximately circular. The orbital motion is communi- 

 cated downward, with graduall}^ diminishing amplitude. Unless the 

 water is deep the orbits below the surface are ellipses, the longer axes 



* Proe. Roy. Soe. London, vol. 34, p. 1. 

 t Arch. Sei. Phys. efc Nat., Geneva, vol. 0, p. 241. 

 J Arch. Sci. Phys. et Nat., Geneva, vol. 10, p. 39. ' 

 I Proc. Roy. Soc. London, vol. 36, p. 18. 



