190 Problems of Denudation. 



with vegetation is not affected in the same way, and it seems 

 likely that vegetation does have a stabilising influence. It 

 reduces the rate o£ denudation as a whole, and when the soil 

 under a grass or other plant with fibrous roots is removed 

 it is possible that the exposed roots may act as a filter, thus 

 increasing redeposition and counteracting denudational in- 

 stability. The general result that the rate of denudation is 

 a function of f tana thus ceases to hold for these distortions 

 of short wave-length, but remains true when areas large 

 compared with the size of the plants are considered. The 

 form of the peneplain deduced in Section II. will therefore 

 still hold. 



Summary, 



In Section I. it is shown that the movement of surface 

 water is controlled by gravity and friction ; hydrostatic 

 pressure and inertia are ordinarily negligible. In con- 

 sequence of this the water always moves along the lines 

 of greatest slope. In mountainous regions the friction 

 may be due to turbulence, but in ordinary cases it is due 

 to ordinary viscosity ; in either case the motion is com- 

 pletely determinable when the form of the land and the 

 distribution of rain are known. 



In Section II. it is shown that in the case of viscous flow 

 the rate of denudation with uniform soil is a function of 

 f tan a, where f is the depth of the water and a. the slope. 

 Thus, if ftana is a constant, the whole surface will sink at 

 a uniform rate : an example of this is a surface with straight 

 contours and almost parabolic dip-lines with the concavity 

 upwards and the axis horizontal, agreeing in general 

 appearance with ordinary peneplains. 



In Section III. the peneplain already described is shown 

 to be stable for corrugations running along the slope ; but 

 corrugations running down the slope tend to increase in 

 depth, and the shorter the distance between consecutive 

 crests the more rapidly will this increase occur. This 

 corresponds well with the complicated character of the 

 surface of weathered clay ; the smoother types of peneplain 

 are probably able to persist because the instability is 

 counteracted for these disturbances of short wave-length by 

 friability and vegetation. 



