introduction: flagellar propulsion 3 



inert head, the calculated and observed speeds of progression of the 

 sperm of a sea urchin (Psammechinus) were found to be almost iden- 

 tical (Gray and Hancock, 1955). 



So far, so good; but it is necessary to look rather carefully at the 

 assumptions which underlie the theory and decide how far they can 

 be justified by observation. These assumptions are at least four in 

 number. (1) The transverse movement is identically the same for 

 all elements; in other words, the wave does not change its wave- 

 length or amplitude as it moves along. (2) All elements execute their 

 movements in one and the same plane; there must be no tendency 

 for the filament to rotate about the axis of the wave. (3) All transverse 

 forces acting on the filament in directions normal to the axis of pro- 

 gression summate to zero throughout each complete cycle; in other 

 words, the wave is symmetrical about its longitudinal axis, and there 

 is no tendency for the filament to yaw in the plane of motion of its 

 constituent elements. (4) The length of the filament is much greater 

 than the length of a single wave and is such as to constitute an in- 

 tegral number of waves. So far as is known, no living system con- 

 forms strictly with these requirements. All we can safely say in the 

 case of Psammechinus sperm is either that discrepancies due to each 

 of these factors are relatively small or that collectively they cancel 

 each other out. 



observational data 



If the transverse displacements of all elements of a flagellum were 

 identically the same and occurred in one and the same plane, the 

 "envelope" seen under dark-ground illumination would be that 

 of a rectangular lamina when viewed in a direction normal to the 

 plane of this movement. In practice the transverse amplitude of ele- 

 ments near the head of the sperm is always less than those near the 

 tip of the tail (Gray, 1955, 1958). Further, a tendency to roll is one 

 of the most characteristic features of an active spermatozoon, and 

 this is, in itself, very strong presumptive evidence that all transverse 

 movements are not taking place in one and the same plane. If for 

 any reason a spermatozoon of a sea urchin is prevented from rolling, 

 it characteristically swims along a curved path (Gray, 1955); a simi- 

 lar phenomenon has recently been reported by Blokhuis (1961) in 

 bull sperm. The ability of such systems to progress along a straight 



