Problems of Denudation. 



189 



below, the denudation in AB is less than that in CD, for Z\ 

 is less in CD. Thus the denudation in AC is less than that 

 in BD, and therefore the ridges are more denuded than the 

 hollows and the system is stable for corrugations along 

 the slope. 



Consider next the case of ridges running down the slope. 

 The line of greatest slope starting at any point will ascend 

 rapidly towards the nearest ridge and gradually turn round 

 till at a great enough height it is almost parallel with it and 

 near the top of it. Thus lines of greatest slope equally spaced 

 at the top of the general slope will tend to rearrange them- 

 selves lower down, so as to be more densely packed in the 

 hollows and less densely on the ridges. Now water cannot cross 

 a line of greatest slope, and as it is supplied uniformly all over 

 it must tend to congregate in the hollows. Thus denudation 

 is greatest in the hollows, since the slope there does not 

 differ appreciably from that on the ridges, and therefore the 

 peneplain is essenlially unstable for distortions consisting of 

 corrugations running down the slope. Again, a is inde- 

 pendent of y to the first order, and therefore the difference 

 in f 3 between ridges and hollows can only arise through the 

 term in ~d 2 <j)fdi/ 2 in A 2 . This, other things being equal, is 

 evidently proportional to a/A, 2 , where a is the average extent 

 of the elevations above the peneplain and X the distance 

 between consecutive ridges. So long as this is small, the 

 difference between the rates of denudation in the ridges and 

 hollows is proportional to a/\ 2 , and thus the relative rate of 

 increase of any disturbance is proportional to 1/X 2 . The 

 shorter the distance between consecutive crests, then, the 

 more rapidly the disturbance will increase. As any type of 

 disturbance is initially possible, it follows that surface-water 

 alone is capable of cutting up a uniform surface into an 

 indefinitely complicated pattern if no other agency exists 

 that can counteract the instability. 



This result does not agree with the observed frequency of re- 

 markably uniform peneplains, and some stabilising cause must 

 therefore exist. One possible cause is the friability of toils, 

 which would soon cause local irregularities of considerable 

 steepness to break up and spread themselves out again under 

 the action of gravity. Sand spreads itself out when wet in 

 a similar way. On a tenacious clay soil such irregularities 

 can persist for a considerable time, and then the result is 

 well confirmed by the extremely rough and angular forms 

 developed by exposed masses of bare clay *. Clay covered 



* See, for instance, Pirsson and Sckuchert, 'Textbook of Geology,' 

 figs. 19 & 21. 



