When a stream is flowing along a wall against an adverse pressure gradient, the skin friction at the wall decreases to zero, at which point or at least very near it the flow seems to leave the surface altogether. Between the main stream and the wall there may be a slow back-flow. Upstream of separation the influence of the wall on the flow is satisfactorily explained by the boundary-layer theory, which among other things presupposes that this influence is confined to a narrow region near the wall. Such a theory is clearly inadequate downstream, however, because this layer rapidly increases in width and, further, the main stream is seriously affected, and consideration of the Navier-Stokes equations would seem to be necessary before a full theoretical explanation of separation could be given. Apart from a note by Dean (2) on the relations between the pressure and velocity at separation, there has, however, been no relevant attack on these equations.