no FERTILIZATION 



probably a mosaic of sperm-receptive and non-receptive regions. 

 It can be expressed, approximately, in the form a = Zp, where p 

 is the probability of a successful sperm-egg collision. Some bio- 

 logists have felt uncomfortable about treating spermatozoa as gas 

 molecules colliding elastically with spheres. In defence of this 

 feeling, a, though more abstract, has more 'depth' than p and Z. 

 For if we only make the plausible and weak assumption that the 

 chance of an egg being fertilized in a time interval §t is propor- 

 tional to that interval of time, the proportionality constant being 

 denoted by a, Equ. (2) automatically follows. Another advantage 

 of oc over p and Z is that it does not involve such considerations as 

 the random movements of spermatozoa, chemotaxis, and the trap 

 action of egg jelly on spermatozoa. Excluding chemotaxis, these 

 factors interfere, though perhaps not to a great extent, with the 

 *sperm-gas molecule' analogy. 



Calculations based on Equ. (2) show that at sperm densities of 

 7-4 X lo'^/ml., p = 0-23 and at a density of 9-6 X lo^/ml., p = 

 o-oi. Further enquiries into the conduction time of the block to 

 polyspermy can be made by means of the following pair of experi- 

 ments, run at the same time (Rothschild & Swann, 195 1). In Exp. 

 I unfertilized eggs were mixed with spermatozoa at t = o and 

 functionally separated after 25 seconds, by killing the spermatozoa 

 but not the eggs. The same procedure was adopted in Exp. 2, 

 but, at the time when the spermatozoa were killed in Exp, i, more 

 spermatozoa were added, the sperm density being increased by a 

 factor of 100. From the experiment described immediately above 

 Equ. (2), it is known what proportion of eggs will have been fer- 

 tilized in 25 seconds (Exp. i ), at any given sperm density, and there- 

 fore what proportion of the eggs will have started their blocks to 

 polyspermy during that time. If, therefore, instead of killing the 

 spermatozoa at t = 25, the number of sperm-egg collisions is 

 greatly increased by the addition of more spermatozoa, there should 

 be a negligible incidence of polyspermy unless a considerable 

 number of successful sperm-egg collisions do occur during the block 

 to polyspermy. Table 17 shows that, in such an experiment, there 

 are three times as many polyspermic eggs in Exp. 2 as there were 

 unfertilized eggs in Exp. i . In other words, nearly half of the eggs 

 which were fertilized in 25 seconds had not finished propagating 

 their blocks to polyspermy in that time, and became polyspermic 

 because of the new lot of collisions they received after the initial 



