l66 D. W. JOHNSON AND W. G. REED, JR. 



graded shoreline. The process is analogous to the formation of 

 graded stream profiles by the degrading of elevations and the aggrad- 

 ing of depressions. If the waves cut back faster on one side of a head- 

 land than they do at the headland or beyond, and a strong current 

 sweeps along the shore, the formation of a sharp angle at the head- 

 land is prevented by the prograding of the shore beyond the headland 

 as rapidly as it is retrograded in the region of pronounced cutting. 

 Thus, in the case of Cape Cod, Professor Davis has shown that the 

 retrograding of the shore in the vicinity of Highland Light, due to 

 active wave erosion, has been accompanied by a prograding of the 

 shore farther north, where successive beaches have been built forward 

 to maintain the simple curvature of a maturely graded shoreline. 

 Equilibrium is reached, or the beach is maturely graded, when a 

 gently curved or straight shoreline is developed ; thereafter the head- 

 lands and beaches both retrograde gradually under the continued 

 attack of the waves. 



Inasmuch as the Nantasket problem involves a complex example 

 of island-tying, we may here consider certain principles underlying 

 the formation of connecting beaches, or tying bars as they are often 

 called. If an island faces a large expanse of open water on which 

 large waves are produced, and these waves come in general from one 

 direction, the end of the island exposed to the brunt of the wave 

 attack will be eroded, and the eroded material will be gradually 

 drifted back along the sides of the island and strung out behind as a 

 spit. In course of time the spit may reach the mainland or another 

 island, and the island-tying is complete. Variations in local condi- 

 tions may result in various forms of the tying bar; examples of several 

 forms are described by Dr. Gulliver. It is possible that in some cases 

 the bar may be built from the mainland out to the island (Gulliver, 

 p. 192). 



Backward tying is not the only form of island-tying to be observed 

 along the shores. Lateral tying is certainly strongly developed in the 

 Boston region, and we believe that many cases now regarded as 

 examples of simple backward tying will prove to be more or less 

 complicated examples of lateral tying. If wave erosion is most active 

 on the eastern end of an island which lies at the mouth of a bay, and 

 which is between two headlands situated to the north and south of 



