An explicit determination is made of the velocity potential for the small-amplitude time-periodic excitation of a bottomless, heavy, incompressible fluid which results from an internal point source, assuming that the equilibrium free surface lies in a horizontal plane and taking account of the presence within the fluid of a thin rigid plane with a vertical straight edge. The surface-wave component of the potential is expressed by means of single quadratures for any relative disposition of the source and observation points and, apart from exponential factors involving the depths of the respective points, proves to have the same functional character as the steady-state velocity potential for the acoustic (or compressional) motion which is sustained by an infinite line source parallel to the straight edge of a thin rigid half-plane.