CHARACTERISTICS OF RIVERS. n 



there forms a bar, which in turn directs the current toward the bank whence the trouble 

 first started. If we add to this that the current once turned aside from the original 

 straight line wanders farther and farther away by the very force of inertia, and that 

 this deviation continues until, from the very fact of its digression, the 'slope and velocity 

 of the current are reduced and come into equilibrium with the resistance of the banks, 

 we shall see how bends are slowly and gradually formed, making detours both to right 

 and left of the line of maximum slope. The elongation of bends only ceases when the 

 slope is so diminished from the increased length given to the course through which the 

 water must flow that there is no further tendency to produce scour of bottom or banks. 

 Theory and experience teach us also that velocity of current is determined not only 

 by the inclination of water-surface, but also by the form of the bed ; that is, by the form 

 of its cross-section. For any given soil and any given inclination there is but a single 

 form of flowing cross-section which will give the maximum velocity of current with 

 the least resistance. In the above assumed case of an artificial river whose curves are 

 freely developed, the form of cross-section will undoubtedly vary according as we con- 

 sider the bed at the head of a bend, at its apex, or at the point of passing from one bend 

 to another; these variations, however, will be constant at similar points, for the slope, 

 by reason of the increased length, has become almost uniform, and the other two fac- 

 tors velocity of current and nature of the bottom being likewise uniform, the depths 

 of the sections and their widths will have a constant maximum limit. But what 

 will happen if one of the banks is higher or more solid than the other, and if from this, 

 or any other special condition of the surface of the adjacent bottom land, the river can- 

 not sufficiently increase the length of one or more of its bends' It cannot maintain a 

 very steep slope ; the nature of the soil forbids that. In such a case it is evident that 

 the stream will more and more scour out its bed, and deposit the debris in those places 

 favored by the topographical features of the valley ; that is, where it is possible to build 

 up the bottom. In other words, the result will naturally be an elevation of the bed 

 of the stream, and this elevation will act as a cross-dike, damming the river like a weir; 

 it will withstand and considerably diminish the force of the current; the water will flow 

 over it in a thinner sheet, and, following the exterior slope of the bar, will fall into the 

 lower pool by a route much shorter than through a bend, and without a tendency to 

 cut away its bed ; for we know that with a given slope the velocity of bottom flow dimin- 

 ishes with the depth of the sheet of water. 



" If the discharge of our artificial river always remained the same, at the end of a 

 certain time it would finally come into equilibrium with the resistance of the soil through- 

 out its whole length. The bends and the bottom, when they had once assumed their 

 proper form, would retain it, whatever might be the consistency of the soil. But the 

 discharge of rivers often varies through wide limits. Into our artificial canal we let 

 loose a river at flood-height. If the discharge should gradually diminish, the water- 

 level would fall. At deep places the section would always be sufficient for the passage 

 of the water in spite of any diminution of the slope caused by lowering the level, and 



