40 ROBERT RIKMENSPOEL 



flagellum is exerted by the surrounding fluid: 



. f-b 2 



where rj is the viscosity of the fluid. From this it follows that under 

 these conditions the flagellum rotates with a frequency proportional 

 to the velocity. A flat tail wave would, of course, not induce any 

 torque. The main observed properties of sperm movement are indeed 

 described in this way: (1) the forward velocity is a second order ef- 

 fect, proportional to the square of the amplitude /;, and (2) the helical 

 waves give rise to rotation of the whole cell. 



Later Gray and Hancock (1955) derived for a flat sinusoidal tail 

 wave essentially the same formula as Taylor (equation 3), by using a 

 simplified model of the fluid motion around the tail which enabled 

 them to extend the theory for larger amplitudes. 



The models of both Taylor and of Gray and Hancock appear too 

 simplified to yield a quantitative description of sperm movement. 

 Actual measured data for /, b, and A of circularly swimming cells give, 

 according to equation (3), velocities which are too high (Rikmenspoel 

 et al., 1960), by a factor of 10 for the model of Taylor or a factor of 5 

 for that of Gray and Hancock. 



DETERMINATION OF STATISTICAL DATA OF SEMEN SAMPLES 



Apparatus 



For measuring mean velocity of semen samples, a photoelectric 

 device has been developed, the principle and design of which war- 

 rant some discussion. A semen sample is illuminated in dark field so 

 that the sperm appear bright on a dark background. An objective 

 focuses the sample on a diaphragm. An aperture in the diaphragm, 

 about the size of the image of the head of a sperm cell, is viewed by a 

 photomultiplier. The multiplier thus "looks" at a certain small area 

 of the sample. Whenever a sperm cell passes over this area, the mul- 

 tiplier receives a light signal, which is recorded or electronically 

 analyzed. 



The specimen of semen is again 42 ± 2 microns deep, and a low 

 power objective (XlO, NA = 0.25) is used. The aperture in the dia- 

 phragm is 100 microns in diameter, representing 10 microns in the 

 sample. 



