l^HEOftlES OF ORIGIN 6l9 



posed to their attack, and the remains of the cusps then have the asym- 

 metrical form described by this author. 



ADDITIONAL THEORIES 



In attempting to explain the formation of beach cusps I have tested 

 and rejected several working hypotheses in addition to those mentioned 

 above. For example, there was considered the possibility that the waves 

 breaking parallel with the shore had superposed obliquely upon them 

 smaller waves, and that the portions of the main waves thus increased in 

 height excavated the intercusp spaces. One bit of evidence which ap- 

 peared to harmonize with this theory was reported by Mr. Read, who 

 noted that on Virginia Beach the incoming waves showed the first tend- 

 ency to break at regularly spaced intervals which corresponded with the 

 intervals between cusps. The hypothesis was rejected because the cause 

 was irregular, while the effect was regular, because of an almost com- 

 plete lack of direct evidence pointing to a relation between superposed 

 waves and cups, and because the experiments seemed to point conclu- 

 sively to some other origin. 



Another hypothesis was based on the assumption that an extended 

 sheet of water descending an inclined plane may not move with the same 

 velocity throughout, but may tend to develop lines of swifter flow, or 

 currents, at certain intervals. I was tempted to make this assumption 

 because of the fact that water descending a flat-bottomed inclined trough, 

 or conduit, does not flow uniformly, but is successively retarded in such 

 a manner as to produce a succession of waves. Admirable illustrations 

 of this phenomenon have recently been published by Yaughan Cornish 

 in a paper on "Progressive Waves in Rivers^^ (1907). It occurred to me 

 that if a broader sheet of fluid were retarded by friction while descending 

 an inclined plane, the resistance might be overcome first, or more rapidly, 

 at certain points, and that the slightly increased rate of advance at these 

 points would disturb the equilibrium in such manner as to create zones 

 or currents of accelerated flow wherever these slight initial advantages 

 had been gained. If the sheet of water were shallow, there would be a 

 tendency for the currents to be smaller and more closely spaced than if 

 the sheet of water were of greater depth. This hypothesis was especially 

 tempting, inasmuch as granting the basal assumption all the phenomena 

 of beach cusps find a ready explanation. Small waves advancing and 

 retreating on the beach would give small currents closely spaced, which 

 would in turn scour small intercusp spaces leaving closely spaced cusps. 

 Any change in the size of waves resulting in a change in the size and 

 spacing of the currents would necessitate a respacing of the cusps. The 



