introduction: flagellar propulsion 



Ncos0 + l_sin0(=T) 



L 



Fig. 1. In a regular helical system all the forces (normal and tangential) 

 exerted on a wave act tangentially to the surface of a cylinder. For any one 

 element the normal force N has a forward component N sin 9 and a trans- 

 verse component N cos 9; the tangential drag L has a backward compo- 

 nent L cos 9 and a transverse component L sin 9- For an element situated 

 one-half of a wavelength from the first, the total transverse force will, with 

 that of the first element, yield a couple turning the elements and the body 

 as a whole about the axis of the cylinder in a direction opposite to that in 

 which the elements are moving round the cylinder. During steady motion 

 AT sin 9 = L cos 9, while the "spinning" couple is d-L cosec 9, where d is the 

 diameter of the helix. 



ing over the filament, there is no translatory displacement of any 

 part of the filament relative to the water; each element is then simply 

 spinning about its own longitudinal axis; there is no movement of 

 the wave relative to the ground and no propulsion can occur. If, 

 therefore, a spermatozoon rolls with the same frequency as it gen- 



