346 G. K. GILBERT 
D and B has been carried past B. The quantity passing each point 
of the slope has been proportional to the distance of the point from 
the summit. If the depth of the creeping layer has been uniform, 
the mean velocity of creep has been proportional to the distance from 
the summit. On the other hand the impelling force, gravity, depends 
for its effectiveness on slope, being able to cause more rapid flow where 
the slope is steeper. Therefore, on a mature or adjusted profile, the 
Fic. 2.—Miniature hills, illustrating the convexity of divides and interstream 
ridges. 
slope is everywhere just sufficient to produce the proper velocity. It 
is greatest where the velocity is greatest, and therefore increases 
progressively with distance from the summit. In other words the 
normal product of degradation by creep is a profile convex outward. 
If soil creep and carriage by water are the only important processes 
of transportation operative in a region of maturely sculptured hills, 
the above analysis seems adequate. On the upper slopes, where 
water currents are weak, soil creep dominates and the profiles are 
convex. On lower slopes water flow dominates and profiles are con- 
