130 



MOVEMENT OF CILIA AND FLAGELLA 



The movements of the sea urchin sperm have been shown by 

 Gray and Hancock (1955) to approach closely to the ideal theoretical 

 pattern. They derived an equation expressing the rate of forw^ard 

 movement of sea urchin sperm in terms of the ampHtude and 

 wavelength of the bending waves, the number of waves in the 

 tail length, the frequency of waves, the radius of the tail and the 

 radius of the head. Substitution of measured values of these 

 parameters in the equation gave a calculated speed of movement 

 of 191 /x sec, while the average observed speed was 191 '4 /u,/sec. 



The simpHcity of the pure sine wave pattern, even in sea urchin 

 tails with a symmetrical beat, is usually complicated by an 

 increase in both wavelength and amplitude as the bend passes 



L~ 



Fig. 32. Diagram of a sperm to show the three axes mentioned 

 in the text. The oscillations of the tail take place in plane 

 T-T\ the axis P-P is at right angles to both T-T and the 



longitudinal axis L-L. 



down the tail. The beat is further complicated in the majority 

 of sperm tails by an inequality of bending on the two sides, so 

 that the wave pattern is asymmetrical, one side showing a larger 

 amplitude and longer half -wave than the other as in Fig. 31. 

 Such an asymmetry of bending will have important effects on 

 the movement of the sperm. 



Three axes of the sperm may be defined as in Fig. 32 by L-L, 

 T-T and P-Py the last being perpendicular to both the transverse 

 and longitudinal axes of the sperm (the waves of bending are 

 here assumed to be in the transverse plane). Movements about 

 these three axes are designated as follows: movements about L-L 

 constitute a roll, about T-T 2^ pitch, and about P-P a yaw. Where 

 bending of the sperm tail is asymmetrical, the sperm will 

 persistently yaw towards one side or the other because the 

 transverse forces acting on the tail will not balance about its 



