620 D. W. JOHNSON BEACH CUSPS 



Iwpothesis does not lack support so far as the plienomena of beach cusps 

 are concerned^ but it is based on an assumption which does lack support. 

 I have questioned a number of engineers and physicists in regard to the 

 matter, but could learn nothing favorable to the assumption. 



The hypothesis which best accords with all of the available evidence 

 may now be set forth. Concisely stated, it is that selective erosion by the 

 swash develops from initial irregular depressions in the beach shallow 

 troughs of approximately uniform breadth, whose ultimate size is propor- 

 tional to the size of the waves, and determines the relatively uniform 

 spacing of the cusps which develop on the intertrough elevations. This 

 theory differs essentially from those proposed by Branner and Wilson in 

 that neither intersecting nor oblique waves are appealed to and the spac- 

 ing of the waves is disregarded; from those proposed by Jefferson and 

 Cornish in that the cusps are not regarded as mere erosion remnants of a 

 once continuous ridge, while uniformity of spacing depending on wave 

 size is considered of vital importance; from the theory proposed by 

 Shaler in that no importance is attached to the irregular front of the 

 swash, the ability of the thin edge of the swash to develop the intercusp 

 bays is not admitted, while the size of the wave is correlated with the 

 width of intercusp spaces. Other points of difference will appear in the 

 explanation which follows. 



Every beach contains numerous inequalities which tend to prevent a 

 uniform flow of water up and down the beach during wave action. 

 These inequalities have a variety of causes. Surface run-off after rains 

 may develop channels on the beach; the water draining out of the sand 

 at the upper part of the beach after high tides or after high waves may 

 produce the same result. Pebbles lying on a sandy beach interfere with 

 the "swash^^ of water up and down the beach, and cause some channeling. 

 The waves are never even crested, and may be very irregular if oblique 

 waves are superposed on them ; the irregularity of the "swash line," men- 

 tioned by Shaler, may initiate irregularities on the beach. Eemnants of 

 old beach cusps, not wholly obliterated, form another source of irregu- 

 larity; and still other sources might be mentioned. 



The continual swashing of the water up and down the beach tends to 

 enlarge the irregular depressions over which the water passes. Larger 

 channels are better adapted to the movements of the large volumes of 

 wave-supplied water. It is inevitable that in the enlarging of some de- 

 pressions others will be obliterated, just as in the case of growing drain- 

 age basins many small basins disappear as independent features, while 

 the few increase in size. Those depressions on the beach which develop 

 to larger proportions will be the ones which have some initial accidental 



