THE WORK OF RUNNING WATER. 59 



without let or hindrance. In both cases the wear of the waves will 

 be neglected. 



1. In the first case the water flowing off over the surface (the run-off) 

 will descend equally in all directions. It will constitute a continuous 

 sheet of surface-water, and both its volume and its velocity will be 

 the same at all points equally distant from the summit. Erosion 

 accomplished by sheets of running water, as distinct from streams, 

 is sheet (or sheet-flood) erosion} Since the material of the surface is 

 homogeneous, the wear effected by the water will be equal at all points 

 where its velocity and volume are equal. For obvious reasons the 

 depth of the run-off will increase from summit to base. The gra- 

 dient (slope) also increases in the same direction, and the increase 

 of volume and of gradient conspire to augment the velocity of the 

 water, and therefore of the wear effected by it. If the thin sheet of 

 water starting from the top of the island with relatively low velocity 

 be able to wash off even a little fine material from the surface, the 

 thicker sheet farther down the slope, moving with greater velocity, 

 will be able to carry away more of the same sort of material, and the 

 increase will be progressive from summit to base. It follows, there- 

 fore, that the surface will be worn equally at points equally distant 

 from the summit, but unequally at points unequally distant from 

 it. The first shower which falls on the island may be conceived to 



~^>c c So" 



Fig. 37. — Diagram to illustrate the effect of rain erosion on an i«land where there is 

 no deposition or wave erosion about its borders. The uppermost curve represents 

 the original surface, while aa, bb, and cc represent successive surfaces developed by 

 sheet erosion, on the supposition that no material is deposited along the shores. 



wash off from its surface a very thin sheet of material, but a sheet 

 which increases in thickness from top to bottom. The run-off will 

 not be stopped immediately on reaching the sea, but will displace the 

 sea-water to some slight depth, and wear the surface some trivial dis- 

 tance below the normal level of the sea. The result of successive showers 

 working in the same way through a long period of time will be to di- 

 minish the area of the island and to steepen its slopes. The results 

 of a considerable period of erosion under these conditions are shown 



* McGee. Bull. Geol. Soc. Am., Vol. VIII, pp. 87-112. 



