=Transporting power and velocity.=—The transporting power of running water depends on its velocity. The formula expressing the relations between them is as follows: Transporting power, _t_, varies as the sixth power of velocity, _v_, (_tαv⁶_); that is, doubling the velocity of the stream increases its transporting power 64-fold. Strictly speaking, this means that if a stream of given velocity is just able to move a stone of a given size, a stream with double that velocity will be just able to move a stone of the same shape 64 times as large as the first. This may be graphically illustrated as follows: Let a current be supposed just able to move the cube _a_ (Fig. 97). If the current be doubled, twice as much water will strike the same surface with twice the force in the same time; that is, the force exerted on the cube _a_ will be quadrupled. It will, therefore, be able not only to move the one cube, but it will be able to move three other cubes (_b_, _c_, and _d_) besides (Fig. 98). The same current against any other equal surface would also be able to move four small cubes, and there are sixteen such surfaces on the face of the large cube (Fig. 99). It follows that the dimension of the cube which the stream with the doubled velocity can move is four times as great as that of the cube which the original current could move, and the cubical contents of such a cube is 64 times as great as that of the first (64 = 2⁶) (Fig. 99). Swift streams, therefore, have enormously greater power of transportation than sluggish ones. It does not necessarily follow that transportation keeps pace with transporting power; that depends on the accessibility of materials suitable for transportation. A stream of great transporting power, like the Niagara at its rapids, may carry little sediment, because there is little to be had.