When a floating body performs free simple harmonic vibrations in a vertical plane it will create a field of pulsating current flow in the liquid, and the total kinetic energy of the whole moving system will correspond to that of the floating body with an enhanced mass. The total apparent mass of the body is often called the “virtual mass” and the apparent increment the “added mass,” and these terms will be used subsequently. We are concerned in this paper with finding the “added mass” of rectangular and triangular prisms floating in water. The authors' concern with this problem is related to their investigation of the natural frequency of lateral vibration of a ship's hull, and they have contributed already two papers to these Proceedings which should be associated with the present one. In their ultimate problem the body is not moving as a whole in a vertical plane but is flexing about two or more nodal points, but in the present problem the floating body is supposed rigid and all parts of it are moving vertically with the same velocity. It is believed the present investigations are applicable to the lateral vibrations of ships' hulls, but whether or not this is so the investigation is complete in itself: for example it may be used to calculate the natural frequency of a punt or pontoon which has, say, been relieved suddenly of a dead load.