Summary.To understand the functions of the longitudinal and transverse flagella of dinoflagellates, the flagellar waveform and frequency of each flagellum were observed by high-speed video-recording. The longitudinal flagellum emerged from the anterior end of the cell and beat with a planar undulating wave whose plane was perpendicular to the valval sutural plane. The transverse flagellum curved around the anterior end of the cell and beat with a helical wave, with different alternating half pitches. The half pitch corresponding to the parts farther from the cellular antero-posterior axis was shorter than that of the parts closer to the axis. This pattern is described by the ratio of the outer-parts half pitch to the pitch of the whole period of the helix and seems to be characteristic of the dinoflagellates' transverse flagellum.

Equations describing the motion of the dinoflagellate Prorocentrum minimum, which has both a longitudinal and a transverse flagellum, were formulated and examined using numerical calculations based on hydrodynamic resistive force theory. The calculations revealed that each flagellum has its own function in cell locomotion. The transverse flagellum works as a propelling device that provides the main driving force or thrust to move the cell along the longitudinal axis of its helical swimming path. The longitudinal flagellum works as a rudder, giving a lateral force to the cell in a direction perpendicular to the longitudinal axis of the helix. Combining these functions results a helical swimming motion similar to the observed motion. Flagellar hairs present on the transverse flagellum are necessary to make the calculated cell motion agree with the observed cell motion.