The application of the facts in the above paragraph is clearly seen when we refer to Fig. 197. The curve of snow motion of Fig. 195 is applied to an unglaciated mountain valley. Taking a normal snow surface and filling the valley head it is seen that the excess of snow depth over the amount required to give motion is a measure at various points in the valley head and at different gradients of the erosive force of the snow. It is strikingly concentrated on the 15°-20° gradient which is precisely where the so-called process of basal sapping is most marked. If long continued the process will lead to the developing of a typical cirque for it is a process that is self-stimulating. The more the valley is changed in form the more it tends to change still further in form because of deepening snowfields until cliffed pinnacles and matterhorns result.
By further reference to the figure it is clear that a schrund 350 feet deep could not exist on a cirque wall with a declivity of even 20° without being closed by flow, unless we grant _more rapid flow_ below the crevasse. In the case of a glacier flowing over a nearly flat bed away from the cirque it is difficult to conceive of a rate of flow greater than that of snow and névé on the steep lower portion of the cirque wall, when movement on that gradient _begins_ with snow but 20 feet thick.
In contrast to this is the view that the schrund line should lie well up the cirque wall where the snow is comparatively thin and where there is an approach to the lower limits of movement. The schrund would appear to open where the bottom material changes its form, i.e., where it first has its motion accelerated by transformation into névé. In this view the schrund opens not at the foot of the cirque wall but well above it as in Fig. 198, in which _C_ represents snow from top to bottom; _B_, névé; and _A_, ice. The required conditions are then (1) that the steepening of the cirque wall from _x_ to _y_ should be effected by sapping originated at _y_ through the agencies outlined by Johnson; (2) that the steepening from _x_ to _y_ should be effected by sapping originated at _x_ through the change of the agent from névé to ice with a sudden change of function; (3) and that the essential unity of the wall _x-y-z_ be maintained through the erosive power of the névé, which would tend to offset the formation of a shelf along a horizontal plane passed through _y_. The last-named process not only appears entirely reasonable from the conditions of gradient and depth outlined on pp. 296 to 298, but also meets the actual field conditions in all the cases examined in the Peruvian Andes. This brings up the second and third of our main considerations, that the bergschrund does not always or even in many cases reach the foot of the cirque wall, and that cirques exist in many cases where bergschrunds are totally absent.