Do cyanobacteria swim using traveling surface waves?

Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 mu m/s are expected for a spherical cell propagating longitudinal waves of 0.2 mu m length, 0.02 mu m amplitude, and 160 mu m/s speed. This problem was solved earlier by mathematicians who were interest ed in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested.