Floating Bodies in Neutral Equilibrium

In his paper preceding in this issue, Finn proved that if the contact angle gamma of a convex body B with a given liquid is pi/2, and if B can be made to float in "neutral equilibrium" in the liquid in any orientation, then B is a metric ball. The present work extends that result, with an independent proof, to any contact angle in the range 0 < gamma < pi. Our result is equivalent to the general geometric theorem that if for every orientation of a plane, it can be translated to meet a given strictly convex body B in a fixed angle gamma within the above range, then B is a metric ball.