8 JAMES GRAY 



bor by torsional rotation. This may not be true. If the bending of 

 each element occurs in the same plane throughout its whole cycle, 

 while successive elements are twisted relative to their neighbors, the 

 envelope of the whole filament would form part of a screw surface 

 and the system would roll as it moved forward (see Gray, 1955). The 

 concept of a filament actively propagating torsional waves by internal 

 effort may be somewhat hypothetical, but it is relevant to a question 

 asked by Rothschild (1961) "Can a spermatozoon roll about its lon- 

 gitudinal axis when its tail exhibits no bending waves?" A cat dropped 

 upside down rights itself in the air by appropriate torsional move- 

 ment of different parts of its body. It would be interesting if the 

 physicists could tell us whether a similar acrobatic feat could be 

 performed in systems with negligible inertia. 



Perhaps the moral to be drawn from all this is the need for more 

 precise information about the actual changes in form executed by 

 a moving flagellum by simultaneous microscopic observation in more 

 than one plane. Until such a technique is available, it is unwise to 

 overstress the significance of theoretical estimates of propulsive speed 

 which are based on relatively simplified systems. It would be most 

 valuable if mathematicians could extend their analysis to (1) waves 

 of changing amplitude and length, and (2) systems in which the path 

 of displacement of each element is elliptical and the whole system 

 rolls about its longitudinal axis at a known frequency. They might 

 well say, "Yes, if biologists will give us adequate quantitative data 

 on which to base the calculations." 



MECHANISM OF BENDING 



When subjected to two equal but opposite bending couples, an 

 elastic rod bends in the plane of the applied couples; one side of the 

 rod is stretched and the other is compressed, energy being stored in 

 both regions. In a flagellum the couples are generated by internal 

 effort, but neither the structures concerned with the development of 

 tension or those which resist compression can be identified with any 

 certainty. On the analogy of muscle, it seems reasonable to regard 

 the radially arranged ultramicroscopic fibrils as actively contractile, 

 relegating compression to the action of hydrostatic pressure or to 

 structures thus far unidentified. The situation would be clearer if 

 it were possible to isolate a single fiber and see whether it changed 



