24 N. M. FENNEMAN 
everywhere the same. A current of uniformly increasing power 
requires a uniformly increasing depth, that is, a plane slope. 
The opposite is true for a current of uniformly diminishing 
power. A current whose power is augmented at an znucreasing 
vate, as, for example, in geometrical ratio, requires a descent to 
deep water on a curve which is convex upward. Increase of 
power at a diminishing rate requires concavity. Loss of power 
at increasing rates, and loss at diminishing rates, require con- 
cavity and convexity respectively. 
Uniform cutting or building.— Tf a uniform current on a level 
bottom has eroding power, the whole will be cut down at the 
same time, and the bottom will remain level while depth increases. 
In this case the load is furnished at all points equally, and is 
all carniedstorward at the same rate. (lf load be iunnished: im 
excess of carrying power, and at all points uniformly (as from 
top or sides), then the level surface of the bottom would be 
preserved while depth would decrease. 
Load derived from the shore.-—TYo make the case applicable to 
undertow, the excessive load must be supposed to be furnished 
at the end where the current enters upon the bottom in ques- 
tion. In this case deposition will first reduce the load at the 
end upon which it enters and at the same time reduce the depth 
and thus constrict the current, increasing its power. The latter 
influence will determine a higher level to which the bottom will 
be built; a level at which the power of the water is sufficient to 
carry the load which before was excessive. Filling will then 
advance forward over the bottom, the filled and unfilled portions 
both being level, the former growing while the latter diminishes, 
and the two being separated by a slope, mentioned below. It is 
evident that the depth at which this slope begins is determined 
jointly by the power of the water, the amount of the load, and 
the size of the fragments which make up the load. 
The front—The shape of the slope which intervenes between 
the area which has been filled and the bottom beyond, will be 
determined by the rate at which the power of the current 
decreases. If the loss of power were instantaneous, the slope 
