Rational equation of river‐bed profile

River engineering has been faced for many years with the dilemma that, on the one hand, its accumulated experience is sometimes inadequate for reliable prediction of river behavior, while, on the other hand, there has been little attempt at systematic quantitative evaluations to “discover identity in difference”—all the above referring particularly to the form of river-channels, in cross-section, plan, and profile. The purpose of this paper is to review certain principles which afford a rational derivation of the profile of river-beds and to test the results on several American rivers.