THEORIES OF ORIGIiST 61? 



attack, and not by the escape of water imprisoned behind the barrier. 

 There is good ground for the belief that the breaching of the seaweed 

 barrier on the Lynn Beach was the effect instead of the cause of cnsp 

 formation. 



In Jefferson's more recent accounts the question of origin is very 

 briefly referred to; but from such reference it appears that the author 

 considers a barrier of sand or gravel capable of playing the same role in 

 cusp formation as a seaweed barrier. It is further implied that other 

 cusps must have had a different but unknown origin. The objections 

 urged against the seaweed barrier theory apply, in the main, with equal 

 force against the sand or gravel barrier theory. It is true that ridges of 

 sand and gravel are more frequent on beaches than barriers of seaweed; 

 but the evidence is conclusive that cusps are formed when such ridges are 

 absent, and that even when present such ridges are breached from the 

 seaward side by direct wave attack, and not from the landward side by 

 impounded waters. 



On both natural and artificial beaches more or less distinct ridges are 

 sometimes broken through before any distinct cusps have been formed. 

 This led me to entertain the hypothesis that direct wave attack on a 

 fairly uniform ridge would develop breaches in the ridge at intervals 

 proportional to the size of the waves. It seems probable, however, that 

 faint undulations in the beach, on the seaward side of the ridge, may 

 help to determine the points of breaking, just as the more evident cusps 

 and intercusp spaces do in other cases, and that the breached ridges are 

 therefore but one phase, and not an essential one, of the process of cusp 

 formation, as explained on a later page. 



BRANNER'S THEORY 



Branner's theory, while very suggestive, seems to present insuperable 

 obstacles, as will be apparent on the inspection of the accompanying 

 diagrams (figures 1 and 2). The hypothetical wave lines are evenly 

 spaced, and the wave length in both sets is the same. This is a condition 

 which probably never obtains in nature, and yet such an improbable con- 

 dition is an essential element of the theory. If the two sets of waves 

 are given different wave lengths, or if one set of waves has a velocity 

 differing from that of the other, or if either set of waves is irregularly 

 spaced, then the points of wave interference will not reach the beach at 

 the same place twice in succession. If we endeavor to approximate nat- 

 ural conditions by introducing any one of the three types of irregularities 

 mentioned (and probably all three exist in every case of intersecting 

 waves), we must correct the diagrams by making the dotted lines meet 



