  A long cylindrical body of circular cross-section and homogeneous density may
float in all orientations around the cylinder axis. It is shown that there are
also bodies of non-circular cross-sections which may float in any direction.
Apart from those found by Auerbach for rho=1/2 there are one-parameter families
of cross-sections for rho not= 1/2 which have a p-fold rotation axis. For given
p they exist for p-2 densities rho. There are strong indications, that for all
p-2 densities one has the same family of cross-sections. (Proven in
physics/0205059)
