VALLEYS IN LOW LATITUDES 123 



ences of rock resistance usually overshadow it and the joint result has 

 an abnormal expression. Erosion is markedly greatest at the foot of 

 the falls where deep excavation and undercutting are pronounced. 

 A better case for the present comparison is the development of 

 rapids and cascades into vertical falls by the greater erosion at 

 the base of the plunge, even in cases where the rock is essentially 

 homogeneous. 



In all these cases the superior erosion due to superior velocity 

 or volume or both is carried only to a certain extent because it meets 

 restraint in the supporting effects of the neighboring rock, and this 

 is probably -the key to the solution of that balance of effects seen at the 

 foot-slopes of valleys. While the floods from the slope increase in 

 volume and velocity all the way down the steeper part of the slope, 

 and considered by themselves alone should increase the slope even to 

 verticality, the flat-lying rocks of the valley bottom lend support to 

 the foot of the slope by giving a less proportion of exposure and a 

 higher ratio of adhesion to its surface parts and thus render their 

 removal less easy than they would be in the absence of such support. 

 If this is not quite obvious it may perhaps become clear on picturing 

 a vertical wall formed of spherical granules meeting a horizontal sur- 

 face of like kind at right angles and noting the individual conditions of 

 the granules. If A represents a granule at the angle, BB'B", etc., the 

 successive granules above it in the face of the vertical wall and CC'C", 

 etc., the successive granules in the horizontal face, it is clear that A 

 will be least easily removed because only 90° of its circumference is ex- 

 posed while 270° is both protected and attached, whereas 180° of the 

 circumference of the B and C granules is exposed and only 180° pro- 

 tected. With equal wear the B and C granules must suffer most and 

 the angle gradually pass into a curve. In a similar way it may be seen 

 that the granules that form a short concave curve are less exposed 

 and have more attachment than the granules of a more open concave 

 curve, or of a plane or convex curve. Each portion of the slope is 

 thus dependent, in a measure, on the support of the other portions and 

 the flat portion of the valley bottom may be said to support the rock 

 at, and near, the angle and cause the development of a curve which 

 represents the working balance between the agencies of erosion and 

 of resistance. By this curve the increasing flood from the slope is 



