The straightening of the channel is often accomplished in another way. Even before the meanders reach the stage represented by Fig. 1, Plate XVI, the position of the channel becomes unstable. In time of flood, the whole flat is covered with flowing water. The greater depth of water in the channel tends to give it a velocity greater than that of the water on the flat outside. But the distance from _a_ to _c via b_ (Fig. 181) is much greater than that in a direct line. It follows that the slope from _a_ to _c_ direct is greater than that by way of _b_. If the current between _a_ and _c_ in time of flood be strong enough to erode, it may deepen its bed, and thereby increase the volume of water following this course. The increased volume gives increased velocity, and the result may be the opening of a channel between _a_ and _c_ direct. The channel may be worn so deep that when the flood subsides, the stream will follow it. So long as the abandoned channel-curve remains unfilled with sediment, it is often called a _cut-off_. If it contains standing water and has the proper form, it is called an _ox-bow lake_ (Fig. 182), or sometimes a _bayou_. The water-filled portions are not always bows (Fig. 183, Osage River, near Butler, Mo.). Cut-offs, with or without standing water, are of common occurrence along most rivers with wide plains. Meandering is not confined to streams which are near sea-level. Even small creeks at high altitudes may meander, if so situated as to have slight velocity. Trout Creek in the Yellowstone Park (Fig. 184) is an example. [Illustration: +Fig.+ 181.—Diagram illustrating later stages in the development of meanders.] [Illustration: +Fig.+ 182.—Meanders and cut-offs (ox-bow lakes) in the Mississippi Valley a little below Vicksburg. The figure also shows the migration of meanders down-stream, and their tendency to increase themselves. (From charts Nos. 18 and 19, Mississippi River Commission.)] [Illustration: +Fig.+ 183.—Bayou Lakes, Osage River, near Butler, Mo.] There seems to be some relation between the width of the belt within which a stream meanders, and the width of the stream itself. Recently it has been estimated that the ratio between them is 18 : 1.[72] During the development of the meanders it is to be noted that lateral planation on the one side of a stream is accompanied by deposition on the other. This is _cut-and-fill_. The sediment eroded from the curve which is concave toward the stream is shifted down-stream, while that deposited in the curve which is convex toward the stream is brought down from above. Thus even in the development of meanders, the material which is dislodged is shifted down-stream. Since the current directed against the down-stream side of a growing meander is on the average stronger than that directed against the opposite side, the meander itself has a tendency to migrate down-stream (Fig. 182).