When a polished thin straight wire turns on a fixed point in space, the point at which light coming from a fixed source is reflected, moves in a curved surface. In this paper the motion of the wire was supposed to be restricted to the plane passing through the eye and the source of light. The curve was shown to be of the third order, having a straight line as a symptote both ways, and to depend for its form upon a characterising angle. The interest of the subject lay chiefly in the remarkable transformations of the curve.