1915] 



Lawson: The Epigene Profiles of the Desert 



37 



accumulates. For if 08 be large, the rise of the fan surface will 

 be slow and the curvature of the bench will be flat; and if small, 

 the growth of the fan will be rapid and the curvature steeper. But 

 whether OS be large or small, it is the acceleration of the rate of 

 rise of the fan surface which determines whether the curvature shall 

 be convex or concave upward. If the acceleration be negative, it is 

 convex; if positive, concave. And this acceleration is directly due, 

 as has been stated, to the ratios between the areas ORB J 3 and OS8-J J 

 in two successive periods of equal time. 



It is also evident that if the valley at one end of a uniform 

 mountain ridge be wide and at the other end narrow, the bench will 

 vary from flat to steep, the width of the bench remaining constant. 

 If, on the other hand, we have a mountain ridge low at one end and 

 high at the other, flanked by a uniformly wide valley, there will be 

 developed a flat bench at the low end of the range and a steep bench 

 at the high end; and similarly for other relations of mountain and 

 valley. 



In the ordinary case, where the surface of the alluvial embankment 

 rises by diminishing increments and the surface of the suballuvial 

 bench is consequently convex upward, an interesting condition de- 

 velops in the late stages of the general process. In cross-section the 

 direction of the embankment slope is asymptotic to the hyperbolic 

 profile of the bench. In the late stages of the recession of the sub- 

 aerial front, when its height is relatively small, and the embankment 

 is relatively broad, the latter rises very slowly by increments that 

 are nearly equal ; and the hyperbola approaches very closely to a 

 straight line and to tangency with the surface profile of the embank- 

 ment. The profiles of both the bench and the embankment, though 

 mathematically distinct, are then practically coincident. Under these 

 conditions the horizontal extension of the embankment does not keep 

 pace with the recession of the subaerial front. Between the upper 

 edge of the embankment and the base of the front there is evolved 

 a graded rock slope. The suballuvial bench becomes at this stage a 

 subaerial bench, across which the detritus from the vanishing front 

 is swept in times of cloud-burst, to be spread over the surface of the 

 embankment below. This emergence of the bench and its persistence 

 as a subaerial feature appears to be most characteristic of granite 

 ranges which disintegrate into fragments composed chiefly of the 

 individual mineral constituents, and therefore very uniform in size. 

 The phenomena are exemplified in the group of mountains in southern 



