THE FORM OF BEAT OF FLAGELLA 



129 



angle to the axis of progression, e.g. at points X and Y in Fig. 30. 

 It will be seen from this simplified diagram that the longitudinal 

 forces on all elements of the tail tend to move the body forwards, 

 while transverse forces oppose one another, and, provided the 

 tail is as long as or longer than the length required to form one 

 complete wave, the resultant transverse force will be somewhere 

 near zero and will balance approximately about the mid-point 



Asymmetrical wave 

 A 



) ^^ I 



Fig. 31. The movement of sea urchin sperm tails. A, Two 

 cycles of bending of a sperm tail with an asymmetrical beat, 

 and B, one cycle of bending of a sperm tail with a symmetrical 



beat (from Gray, 1955). 



of the tail. The longitudinal thrust on the body tending to 

 produce forward movement is opposed by a backward drag which 

 is mainly due to viscous forces, for at this order of magnitude 

 and in this type of medium, inertia of the body has a negligible 

 effect in comparison with the viscous resistance of the medium 

 (Bidder, 1923; Taylor, 1951). 



