338 APPENDIX 



and a; in the second and third, on the other hand, there again 

 results a union of the two differentiating characters of the stocks, 

 consequently the forms resulting from these fertilisations are 

 identical with those of the hybrid from which they sprang. There 

 occurs accordingly a repeated hyhridisaiion. This explains the strik- 

 ing fact that the hybrids are able to produce, besides the two 



A a 



parental forms, offspring which are like themselves; — and — 



a A 



both give the same union Aa, since, as already remarked above, 

 it makes no difference in the result of fertilisation to which of the 

 two characters the pollen or egg cells belong. We may write then 



-- + - + -4-- = ^ + 2^a + a. 

 A a A a 



This represents the average result of the self -fertilisation of the 

 hybrids when two differentiating characters are united in them. 

 In individual flowers and in individual plants, however, the ratios 

 in which the forms of the series are produced may suffer not in- 

 considerable fluctuations.^ Apart from the fact that the numbers 

 in which both sorts of egg cells occur in the seed vessels can only be 

 regarded as equal on the average, it remains purely a matter of 

 chance which of the two sorts of pollen may fertilise each separate 

 eg,g cell. For this reason the separate values must necessarily be 

 subject to fluctuations, and there are even extreme cases possible, 

 as were described earlier in connection with the experiments on the 

 form of the seed and the colour of the albumen. The true ratios 

 of the numbers can only be ascertained by an average deduced 

 from the sum of as many single values as possible ; the greater the 

 number, the more are merely chance effects eliminated. 



The developmental series for hybrids in which two kinds of 

 differentiating characters are united contains, among sixteen 

 individuals, nine different forms, viz., 



AB-]-Ah^ aB + ah-\- 2ABb + ^aBb -f 2AaB + Mah + 4AaBb. 



Between the differentiating characters of the original stocks, Aa 

 and Bby four constant combinations are possible, and consequently 

 the hybrids produce the corresponding four forms of egg and pollen 

 cells ABy Aby aB, ab, and each of these will on the average figure 



^ [Whether segregation by such units is more than purely fortuitous may perhaps 

 be determined by seriation.] 



