ABSTRACT
The movement of any short length of the tail of a spermatozoon of Psammechinus miliaris and the characteristic changes which it undergoes during each cycle of its displacement through the water can be described in terms of the form and speed of propagation of the bending waves which travel along the tail (Gray, 1953, 1955); the form of the wave depends on the maximum extent of bending reached by each element and on the difference in phase between adjacent elements. The object of this paper is to consider the forces exerted on the tail as it moves relative to the surrounding medium and to relate the propulsive speed of the whole spermatozoon to the form and speed of propagation of the bending waves generated by the tail. The mathematical theory of the propulsive properties of thin undulating filaments has recently been considered by Taylor (1951, 1952) and by Hancock (1953); the present study utilizes and extends their findings but approaches the problem from a somewhat different angle. resistance, and consequently the transverse displacement (Vy) elicits reactions tangential and normal to the surface of the element. The latter force (δNy) has a component(δNysinθ) acting forward along the axis (xx ′) of propulsion; it is this component which counteracts the retarding effect of all the forces acting tangentially to the surface.
* If V1V2 tan d the element has no component of motion normal to its surface ; motion of this type could only ensue if the element were exerting its effort against a rigid medium—and were equivalent to a snake gliding through a rigid close-fitting tube.
