We prove that " the center of buoyancy of floating bodies is equal to the center of hydrostatic pressure ". This subject is an unsolved problem in physics and naval architecture, even though the buoyancy taught by Archimedes' principle can be obtained clearly by the surface integral of hydrostatic pressure. Then we thought that the reason why the vertical position of the center of pressure could not be determined was that the horizontal force would be zero due to equilibrium in the upright state.

As a breakthrough, we dared to assume the left-right asymmetric pressure field by inclining the floating bodies with heel angle. In that state, the force and moment due to hydrostatic pressure were calculated correctly with respect to the tilted coordinate system fixed to the floating body. By doing so, we succeeded in determining the center of pressure. Then, by setting the heel angle to zero in order to make it upright state, it can be proved that the center of hydrostatic pressure is equal to the well-known center of buoyancy, i.e., the centroid of the cross-sectional area under the water surface.

As noted above, we have already proved this problem for rectangular and arbitrarily shaped cross-sections, and published them here on viXra.org in English. Although the case of a semi-submerged circular cylinder and a triangular prism are also included in the proof of arbitrary shapes, we prove for each shape separately in this 2nd report, since they are two typical cross-sectional shapes along with rectangles. However, there is an essential difference in the proof between the two shapes. The reason is why the former does not change its underwater shape when inclined laterally, while the latter, like the rectangle, changes its cross-sectional shape when inclined. The present paper provides clear proofs for both shapes.