610 " D. W. JOHNSON— BEACH CUSPS 



It will be noticed that in series II and III the intervals between the 

 older cusps on the npper part of the beach are never less than ten paces, 

 except in the case of one triple-pointed compound cusp, while the inter- 

 vals between those formed later, farther down the slope of the beach, 

 never exceed 10 paces. The intervals in series lY are always more than 

 double those in series Y on the same beach. In the three series, YIII, IX, 

 and X, observed on the same beach at the same time, the smallest interval 

 in YIII is larger than the largest in IX, and the smallest interval in IX 

 is larger than the largest in X. 



It is evident from the above figures that a certain degree of regularity 

 is manifested in the spacing of the cusps. In any given series the spaces 

 vary within certain limits, but seldom fall below or rise above those limits 

 unless the associated cusps have a noticeably abnormal form. ISTo theory 

 of origin is tenable which does not recognize and account for the signifi- 

 cant degree of regularity indicated by these figures. 



The length of the intercusp spaces varies with the size of the waves. 

 When the waves are about an inch in height the cusps are from 3 to 9 

 inches apart; when the waves are from one and a half to two and a half 

 feet high they are 30 to 60 feet apart, while large storm waves build 

 cusps 100 feet or more apart. These figures are only approximate, and 

 are based on rough estimates of the wave height close to the shoreline. 

 Sufiicient data have not been secured on which to base a reliable deteir- 

 mination of the precise relation of intercu.sp space to wave height, but 

 within certain limits there is a suggestion that doubling the wave height 

 doubles the length of the space. A large number of careful observations 

 would probably establish this point. In conducting such an investiga- 

 tion the observer must satisfy himself that the waves he sees are actually 

 building the cusps, for waves of any size may play about cusps formed by 

 other waves of different size, and thus mislead one who compares the 

 intercusp spaces with the height of the later waves. Fortunately waves 

 of a given size do not long leave unmolested a series of cusps formed by 

 waves of an entirely different size, and the patient observer can in time 

 determine whether or not the waves then breaking on the beach are to be 

 correlated with the cusps at the water's edge. 



This brings us to the consideration of another significant point in con- 

 nection with the spacing of beach cusps, namely, the relative ease with 

 which old cusps are remodeled by waves differing in size from those 

 which formed them. If closely spaced cusps formed by small waves are 

 attacked by larger waves, there ensues a rearrangement by which the 

 cusps become larger and farther apart. This rearrangement may be 

 gradual, and may be accompanied by the combining of some cusps and 



