Effective mean annual precipitation is related to sediment yield from drainage basins throughout the climatic regions of the United States. Sediment yield is a maximum at about 10 to 14 inches of precipitation, decreasing sharply on both sides of this maximum in one case owing to a deficiency of runoff and in the other to increased density of vegetation. Data are presented illustrating the increase in bulk density of vegetation with increased annual precipitation and the relation of relative erosion to vegetative density. It is suggested that the effect of a climatic change on sediment yield depends not only upon direction of climate change, but also on the climate before the change. Sediment concentration in runoff is shown to increase with decreased annual precipitation, suggesting further that a decrease in precipitation will cause stream channel aggradation.

The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable t o those observed in the field. The most probable river profiles approach

Flood data are ordinarily listed either in annual‐flood series or in a partial‐duration series. If the expectancy of a flood in the duration series ϵ is known, then the probability of that flood being an annual flood is shown to be e−ϵ. From this relationship it is possible to transform recurrence intervals in the partial duration series to those in the annual‐flood series. It is shown that for equivalent floods, the recurrence intervals in the partial‐duration series are smaller than in the annual‐flood series, but that the difference becomes inconsequential for floods greater than about five‐year recurrence interval.

ARSTRACT. Ohser\ed foim ol stream clianriel\ of given &e and pattern varies, but the inem foim hay 1,ec.n deumhr i n the liteiatuic by what has heen called the hydraulic geonirtiy. Tliiq cmpiiically de 1 ihcd i n r m 11~15 heen assumed to he the quasi-equilibrium Eoiin. It i i heic shown, wit110 mathematical detalls, that the ohseived form can be de-ri\ed theoretically; the obsericd foiin IS Li quail eqnilibrium state which must, of course, fiilhll the usiial hydiaulir laws, hut in addition, it repiesents the most prohahle state bet \ i r e n two opposing tendenrirs. (a , toward miiiiinuni total rate of work in the whole fluvial system, and (I)) toi\ ai d unifoim disti h i i t ion of eiieigy expenditiiie throughout the system. 'Their tciideiiries ale pi omotrd hy \teell-known pioc~s\es of qroui and deposition oi related internal adjustments of enrigy utiliscition. Aspects of scveral types of fluvial systems can be

Path of greatest probability between two points._._ 2 The sine-generated curve_____________________.__ 3 Analysis of some field examples__-_-_____-__-_-4 Comparison of variances of different meander curves. 4 Meander length, sinuosity, and bend radius..______ 5