MEASUREMENT OF SPERM MOTILITY 39 



arguments in support of this view are: (1) the movements of the non- 

 rotating, circular swimmers are asymmetrical; (2) rotating cells can 

 be transformed into nonrotating ones by cold shock; (3) the velocity 

 of circular swimmers is in general lower (20-100 /x/sec) than that of 

 rotating cells (40-160 /i/sec); and (4) more or less intuitive arguments 

 render illogical the concept that the healthy sperm limit itself to two 

 dimensions and restrict itself in a process like fertilization (essentially 

 a chance process of meeting) to an almost fixed position (the circular 

 orbit). 



It becomes now possible to define, in a more precise way, the 

 "motility" of a semen sample. For normal, rotating cells concentra- 

 tion, velocity distribution, and mean velocity are useful concepts, 

 which can be measured by methods involving a sampling procedure. 

 The method for measuring concentration and velocity distribution 

 as described in the next section, and that which depends on "proba- 

 bility after" effects (Rothschild, 1953a) are in fact based on the as- 

 sumption that a small "subvolume" of sample shows random fluctua- 

 tions with time. This will hold for the normal, rotating cells of a 

 semen sample because the mean free path of such a sperm can be con- 

 sidered long and its velocity rather constant. Thus, by observing over 

 a period of time a small part of a slide such as the field of view of a 

 microscopic objective, a random test is obtained of concentration 

 and velocities of the rotating cells. This is not true, however, for cells 

 swimming in circles as they are practically bound to their closed 

 orbits. The cells of this type which are present in a field of view at 

 a certain moment will remain there, and no new ones will enter. 

 Special care should thus be taken in interpretation of motility data 

 obtained from sperm samples containing a large percentage of circu- 

 larly swimming cells. 



In the past, several attempts have been made toward a theoretical 

 approach to flagellar movement, Taylor (1952) considered sinusoidal 

 waves of small amplitude traveling along infinitely long flagella; it 

 was found in this case that the flagella should have a velocity: 



where / is the frequency of the wave and A the wavelength. When the 

 wave is helical (three-dimensional) a torque g tending to rotate the 



