1915] 



Lawson: The Epigene Profiles of the Desert 



35 



in the foregoing discussion nor in that which follows is any assumption 

 made at to the mode of origin of the initial mountain masses of which 

 the present ranges, of the Great Basin for example, are the degraded 

 remnants. We may begin at any immature stage of the cycle which 

 culminates in the panfan, and from observed facts deduce conclusions 

 which are independent of the original configuration of the relief and 

 of the genesis of that relief. These conclusions take the form of a 

 prediction of what results will ensue if the existing conditions con- 

 tinue and a statement of what has happened during the persistence 

 of those conditions in the past. For such a starting-point we may take 

 any ordinary basin range with its characteristic steep subaerial front 

 and flanking alluvial embankment. For simplicity I shall assume first 

 that the mountain front considered is the edge of a flat-topped plateau 

 or mesa of homogeneous, strong rock. As the subaerial front recedes, 

 the surface of the embankment rises parallel to itself, but at a dim- 

 inishing rate owing to (1) the increasing breadth of the alluvial slope 

 and (2) the decreasing height of the prism of material taken from 



Figure 3. — Recession of front of a mesa from OB to T. The embankment 

 is built up by smaller and smaller increments in equal times owing to the 

 diminishing height of the front and the increasing width of the embank- 

 ment. But the recession of the front is at a uniform rate; therefore the 

 rock-cut bench OPT is a hyperbolic curve convex upward. 



the front and added to the embankment. The rate of recession of the 

 subaerial front is, however, uniform and it results from this that 

 the suballuvial bench is a curved surface convex upward, defined by 

 the locus of the intersection of the fan surface and the surface of 

 the subaerial front. This relation may be expressed mathematically 

 by reference to the diagram, figure 3. The profile with which we 

 start is TROS, of which TR is the level plateau summit, RO is the 

 subaerial front and OS is the surface of the alluvial fan. RJ? is a 

 second stage of the subaerial front and PS 1 is the fan surface at the 

 same stage. A is the angle which the subaerial front makes with the 

 horizon and B is the angle of the alluvial fan. OP is the suballuvial 

 bench cut in the transition from the first stage to the second. Let 

 .( end y be the oblique coordinates of the curve OPT, tin 1 origin of 



r 



R 



Js 



