4 W. M. DAVIS 



without marked deformation is assumed : it may be taken to have 

 the form of a very broad dome. In the first ideal cycle, a gradual 

 and long enduring upheaval is postulated. During an early stage, 

 the initially flat interstream upland spaces will suffer httle erosion 

 and will consequently for a time gain in altitude about as much 

 as they are upheaved. At the same time the depth of the young 

 valleys, which the streams are rapidly incising beneath the flat 

 uplands, must be less than the measure of upheaval. Hence at 

 this stage both the absolute altitude and the local relief of the 

 region are increasing. But as upheaval continues, and as the 

 deepening valleys are opened by weathering, so that their side 

 slopes wiU have a fairly uniform declivity, a stage must be reached 

 when the flat uplands will be narrowed to sharp ridge crests 

 (Schneiden), and on the attainment of this stage the altitude of 

 the ridges will be as nearly constant as the valleys are evenly 

 spaced. (This deduction depends on a general principle, according 

 to which the height of a ridge crest above the neighboring valley 

 bottoms will be a simple fraction — about a quarter, according to 

 Penck — of the distance between the valleys, provided that the 

 cliffs and ledges on the ridge sides are obliterated by the upward 

 or retrogressive extension of graded slopes of fairly uniform declivity, 

 from the banks of the streams at the valley bottoms all the way up 

 to the ridge crests. Previous to the attainment of this graded 

 stage, the occurrence of ungraded cHffs and ledges in the ridge 

 sides would allow the ridge crests to have heights independent of 

 the spacing of the valleys. Evidently, therefore, the less perfect 

 the grading of the ridge sides from the streams up to the crests, 

 the less perfect the control of crest height by valley spacing.) 



During the continuance of this stage the deepening of the 

 valleys in the rising mass will go on, but not yet fast enough to 

 counterbalance the upheaval which is still in progress. The sharp 

 ridge crests will no longer gain in altitude by the measure of 

 upheaval, but only by that measure minus the rate of valley 

 deepening; hence while crest altitude is now slowly increasing, 

 local relief will remain constant. (In view of the fact that large 

 streams grade their courses sooner than the side slopes of their 

 valleys are graded, it seems necessary to assume that when the 



