The development of aerodynamical research into the usefulness of wing profiles of various types for aerofoils of high aspect ratio lends special interest to new results in two-dimensional hydrodynamics relating to the motion of a perfect fluid in the presence of a cylindrical body, especially in the case when the curve of cross-section of the body possesses only a smali amount of camber and is cusped at one end and rounded at the other.The possibility of formulating a theory which represents with reasonable accuracy the actual motions of aerofoils of high aspect ratio in a stream of air, when the air it taken to be inviscid, depends, of course, essentially in the first place on finding motions in which there is a force on the body at right angles to the direction of streaming. No theory which omits to produce this lifting force can give an account of the actual motions of aerofoils which is even approximately satisfactory.