THE WORK OF RUNNING WATER. 67 



profile becomes concave (compare the profiles of Figs. 39 to 41), but 

 the extreme upper end still remains convex. Since the side slopes of 

 a valley are much shorter than its lengthwise slope, a larger propor- 

 tion remains convex. Under the conditions here discussed the change 

 from convexity above to concavity below would begin at about the 

 point where deposition begins.^ 



Fig, 47. — Diagram representing several meridional valleys developing in a circular 

 island. The valleys are all young and narrow. All are making deposits at their 

 debouchures. 



The deposition at the debouchure of the valley, and later above 

 the debouchure, will follow the same course as about the island under 

 the conditions already discussed (pp. 61, 62). 



Limits of growth. — In all cases there are limits in depth, length, 

 and width, beyond which a valley may not grow. In depth it may 

 reach base-level. At the coast, base-level is sea-level,^ but inland it rises 

 by a gentle gradient. In length, the valley will grow as long as its 

 head continues to work inland. In the case represented by Figs. 45 

 and 46 the head of the valley would not cease to advance when the cen- 

 ter of the island was reached, though beyond that point head erosion 

 would not be more rapid than lateral erosion on either side. If but a 

 single valley affected a land area the limit toward which it would tend, 



^ For a discussion of convex and concave erosion slopes see Bain, Geol. Surv. of la., 

 Vol. VI, p. 449. 



' Great rivers, like the Mississippi, cut their channels somewhat below sea-level, 

 but probably not by an amount exceeding the depth of the stream itself (see p. 79). 



