296 



THE ANDES OF SOUTHERN PERU 



schrunds, how shall we explain the topographic depressions ex- 

 cavated underneath the snow? If cirque formation can be shown 

 to take place without concentrated frost action at the foot of the 

 bergschrund, then is the bergschrund not a secondary rather than 

 a primary factor? And must we not further conclude that when 

 present it but hastens an action which is common to all snow-cov- 

 ered recesses? 



It is a pleasure to say that we may soon have a restatement of 

 the cirque problem from the father of the bergschrund idea. The 

 argument in this chapter was presented orally 

 to him after he had remarked that he was glad 

 to know that some one was finding fault with his 

 hypothesis. "For," he said, with admirable 

 spirit, " I am about to make a most violent 

 attack upon the so-called Johnson hypothesis." 

 I wish to say frankly that while he regards 

 the following argument as a valid addition to 

 the problem, he does not think that it solves 

 the problem. There are many of us who will 

 read his new explanation with the deepest 

 interest. 



We shall begin with the familiar fact that many valleys, now 

 without perpetual snow, formerly contained glaciers from 500 to 

 1,000 feet thick and that their snowfields were of wide extent and 

 great depth. At the head of a given valley where the snow is 

 crowded into a small cross-section it is compacted and suffers a re- 

 duction in its volume. At first nine times the volume of ice, the 

 gradually compacting neve approaches the volume of ice as a limit. 

 At the foot of the cirque wall we may fairly assume in the absence 

 of direct observations, a. volume reduction of one-half due to com- 

 pacting. But this is offset in the case of a well-developed cirque 

 by volume increases due to the convergence of the snow from the 

 surrounding slopes, as shown in Fig. 196. Taking a typical 

 cirque from a point above Vilcabamba pueblo I find that the 

 radius of the trough's end is to the radius of the upper wall 

 of the cirque as 1:4; and since the corresponding surfaces are 



Fig. 196— Rela- 

 tion of cirque wall to 

 trough's end at the 

 head of a glaciated 

 valley. The ratio 

 of the inner to the 

 outer radius is 1:4. 



