It is well established by observation that in the ordinary flow of a stream there is a slow transverse flow outwards from the middle near the bottom, and inwards near the top; and such a circulation seems to be required to explain the fact that the filament of maximum onward velocity is depressed some distance below the centre of the free surface. Qualitative explanations of the phenomenon have been offered, depending on the extra friction near the sides, but it seems that the true explanation must depend on something more fundamental. For any explanation to be satisfactory it must show uniform linear flow to be impossible; and actually it can at least be rendered highly probable that such flow can exist over a very wide range of conditions.