Abstract: Because river slope generally decreases in a downstream direction, it is generally supposed that velocity of flow also decreases downstream. Analysis of some of the large number of velocity measurements made at stream-gaging stations demonstrates that mean velocity generally tends to increase downstream. Although there are many reaches in nearly all rivers where mean velocity decreases downstream, the general tendency for conservation or for downstream increase was found in all data studied. Originally published: American journal of science ; v. 251 (August 1953).