MEASUREMENT OF SPERM MOTILITY 53 



approximation is made to assign to a sperm cell a volume where an- 

 other cell has no "access," this represents, in effect, a repulsive inter- 

 action. The spatial distribution in that case would be (de Yries, 1953) 



a(n) = [n(l - 8A-)] 1 '" (6) 



where k represents the fraction of the total volume occupied by the 

 sperm cells. If a sperm is taken roughly as a cylinder of diameter a, 

 and a length of 70 microns (the actual length of a sperm), then from 

 equation (6) it would follow that a « 8 microns. 



For the standard deviation of the distribution of time intervals, 

 a(t) was calculated, again assuming the sperm cell to be a cylinder, 



(T (t) = t (1 - 0.026a/ i ) 



From this, a value of a ^ 3.5 microns is obtained. In view of the ap- 

 proximate nature of these calculations, the difference of a factor of 2 

 in the values of a found with the two methods need not be surprising. 

 In conclusion it can be said that, in dilute suspensions of sperm, 

 a weak repulsive interaction is present which prevents effects due to 

 interactions as considered by Taylor (1952). 



Acknowledgments. This work was begun at the Research Institute 

 for Animal Husbandry, Utrecht, Holland. My thanks are due to Dr. G. 

 Van Herpen and P. Eijkhout, who cooperated closely in the experiments 

 reported. I gladly acknowledge C. van Duijn, Jr., for permission to men- 

 tion the pH measurements. 



The inspiring interest of Professors H. C. Burger and Britton Chance 

 in this work is greatly appreciated. 



REFERENCES 



Berkson, J., T. B. Magath, and M. Hurn. 1940. The error of estimate of 

 the blood cell count as made with the hemocytometer. Am. J. Physiol., 

 128, 309-323. 



Bishop, D. W. 1962. Sperm motility. Physiol. Revs. 42, 1-59. 



Bosselaar, C. A., and N. Spronk. 1952. A physical method for determina- 

 tion of the motility and concentration of spermatozoa. Nature, 169, 

 18. 



Bosselaar, C. A., N. Spronk, and C. G. Van Dam. 1955. An apparatus for 

 measuring the motility of sperm cells. ]. Agr. Sci. 46, 417-419. 



de Vries, H. 1953. On the subnormal variance in the counts of randomly 

 distributed particles. I. Approximate treatment of the three-dimen- 

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