The first complete solution of the problem of the tidal waves in a rotating rectangular basin of uniform depth was given by G. I. Taylor. In the course of the investigation he deduced certain general conclusions regarding the wave motion in such a basin. Two of these conclusions are :— (1) There is only a single infinity of modes of oscillation; and (2) All modes consist of waves moving round the basin in the same direction, namely the direction of rotation of the basin. These conclusions were criticised by Jeffreys, pointed out that a double infinity of modes was really implied in Taylor’s solution and that the second of the above conclusions was not completely proved.