  Swimming velocity and rate of dissipation of a sphere with surface
distortions are discussed on the basis of the Stokes equations of low Reynolds
number hydrodynamics. At first the surface distortions are assumed to cause an
irrotational axisymmetric flow pattern. The efficiency of swimming is optimized
within this class of flows. Subsequently more general axisymmetric polar flows
with vorticity are considered. This leads to a considerably higher maximum
efficiency. An additional measure of swimming performance is proposed based on
the energy consumption for given amplitude of stroke.
