PARENTAL ALCOHOLISM AND THE PROGENY 287 



philosophical breeder of animals nothing seems more certainly 

 established than that this process of selection is constantly going 

 on and is of very special importance among the germ cells. 

 Direct and convincing observational and experimental proof of 

 it has been given for ova by von Hansemann (9). The double 

 mating experiments which Cole and Davis and Cole and Bach- 

 huber have carried out, prove the same point. 



We may represent the general facts about variation in the 

 natality or vigor or survival value of germ cells with considerable 

 probability by a diagram like figure 4. This diagram represents 

 the whole population X of germ cells (ova and spermatozoa). 

 On the base the degrees of physiological vigor or survival value 

 are laid off in 10 equal intervals. 1 denotes a weak, poor sperm 

 (or ovum) unlikely to survive or take part in the formation of a 

 zygote. 9 denotes a strong highly vigorous sperm, practically 

 sure to survive and enter upon zygote formation, except under 

 the most adverse circumstances. The curve, which is the normal 

 or Gaussian curve of errors, denotes the probable frequency of 

 the different degrees of physiological vigor among the germ 

 cells. 



Now to return for a moment to our fundamental gametic 

 equation, 



X = A + a, 



it is obvious that both of the groups A and a may include germ 

 cells of varying degrees by physiological vigor, a fact which we 

 may express symbolically in this way : 



A = ^1 +.42 +^3 



a = ai + ao -\- a^ ^ 



* The degree of variation within the subgroups A and a will be given, as usual, 

 by the standard deviation of those subgroups, and these standard deviations 

 we may indicate in the usual way as <ta and aa. The quantity 



S' - -^ 



is theoretically a very important one. It measures the relation between the 

 variabilities of the parts of the total germ cell population which do and which 

 do not produce zygotes. Ordinarily we may suppose that S will be less than 1, 

 but there is no a priori reason why it should not be ^ L 



