186 Dr. H. Jeffreys on 



other factors must be taken into account which can be safely 

 neglected in the present problem. 



All peneplains with parallel contours produced by surface 

 water must be geometrically similar, for the only arbitrary 

 quantities involved in the equations obtained are oo Q and z , 

 determining the position, and B, determining the scale. 



In the actual character of the motion produced in the soil- 

 particles this viscous flow would be expected to differ con- 

 siderably from the ordinary turbulent flow of a stream. The 

 latter involves great vertical agitation, and particles are lifted 

 up and down by the vertical -movements, travelling con- 

 siderable horizontal distances during each jump. In viscous 

 motion there is little or no turbulence, and little chance 

 therefore of particles being removed from contact with the 

 surface of the soil. The effect of the tangential forces will 

 be merely to roll the particles along rather than to carry 

 them. The actual rate of denudation will depend on the 

 frequency in the soil of particles of different sizes, and 

 accordingly while it will be a function of the f rietional force 

 its form cannot be predicted without a knowledge of the 

 soil-composition. So far it has only been assumed uniform, 

 requiring the rate of shearing at the bottom to be constant, 

 so that the question of the effect of variations in the soil- 

 composition has not arisen. When changes of the topography 

 are considered, on the other hand, precise information on 

 the relation between the rate of denudation and the rate of 

 shearing at the surface will be needed. 



When the denudation has proceeded a considerable time 

 the lowest parts may reach sea-level They w ill then cease 

 to be denuded, while the inland parts will continue to sink. 

 This will proceed till the whole is reduced to so low a level 

 that surface-water can no longer attain sufficient velocities to 

 carry debris with it. This corresponds to the "base-level" 

 of geologists. Its form will naturally depend on the size of 

 the particles of the soil. The length f tan a. is somewhat less 

 than a on account of the factor X: we have, in fact, 



B 



=o (?> 



Thus B increases rapidly with a. In other words, since at a 

 given horizontal distance from the ridge « is proportional to 

 B% we see that the larger the particles the greater is the 

 slope needed to transport them when the water supply is 

 the same. The variations in height would therefore be 

 expected to be greater on a coarse soil than on a fine one ; 

 at the same time we see that a heavy rainfall will act in the 



