6 The Problems 



great-grandparents one-eighth, and so on, the remainder 

 being contributed by the remoter ancestors. 



Such a law is obviously of practical importance. In 

 any case to which it applies we ought thus to be able to 

 predict the degree with which the purity of a strain may 

 be increased by selection in each successive generation. 



To take a perhaps impossibly crude example, if a 

 seedling show any particular character which it is desired 

 to fix, on the assumption that successive self- fertilisations 

 are possible, according to Gallon's law the expectation of 

 purity should be in the first generation of self- fertilisation 

 1 in 2, in the second generation 3 in 4, in the third 7 in 8, 

 and so on*. 



But already many cases are known to which the rule in 

 any simple form will not apply. Galton points out that 

 it takes no account of individual prepotencies. There are, 

 besides, numerous cases in which on crossing two varieties 

 the character of one variety almost always appears in each 

 member of the first cross-bred generation. Examples of 

 these will be familiar to those who have experience in such 

 matters. The offspring of the Polled Angus cow and the 

 Shorthorn bull is almost invariably polled or with very 

 small loose "scurs." Seedlings raised by crossing Atropa 

 belladonna with the yellow-fruited variety have without 

 exception the blackish-purple fruits of the type. In several 

 hairy species when a cross with a glabrous variety is made, 

 the first cross-bred generation is altogether hairy t. 



Still more numerous are examples in which the characters 

 of one variety very largely, though not exclusively, pre- 

 dominate in the offspring. 



* See later. Galton gave a simple diagrammatic representation of 

 his law in Nature, 1898, vol. LVII. p. 293. 



t These we now recognize as examples of Mendelian ' dominance.' 



