5()'i THE PKOBLEMS OF HEKEDITY AND THEIR SOLUTION. 



and on the tran.siiiisfsion of colors in Basset hounds. In racli of these 

 cases he has shown that the expectation of inheritance is such that a 

 simple arithmetical rule is approximatel}' followed. The rule thus 

 arrived at is that of the Avhole heritage of the ofi'sprino- the twx) parents 

 tot^ether, on an avei'a^-e, contribute one-half, the four tiiand parents 

 one-fourth, the eight great grand parents one-eighth, and so on, the 

 remainder l)eing eontri})uted 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 

 particidar character W'hich it is desired to tix, on the assumption that 

 successive self-fertilizations are possible, according to Galton's law 

 the expectation of purity should be in the first generation of self- 

 fertilization 1 in "2, in the second generation ?> in 4. in th(> third 7 in 8, 

 and so on." 



But already many cases are known to which the rule in any simple 

 form will not apply, (lalton 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 tirst crossbred generation. Examples 

 of these will be familiar to those who have experience in such matters. 

 The oti'spring of the Polled Angus cow and the Shorthorn bull is 

 almost invarial)ly polled or with very small loose "scurs.'"' Seedlings 

 raised by crossing Airopa Ix^lhuJonua with the 3'ellow-fruited variety 

 have without exception th(» blackish-purple fruits of th(» type. In 

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

 the tirst crossbred generation is altogether hairy.''' 



Still more numerous are examples in which th(> characters of one 

 variety very largely, though not exclusiAely. predominate in the 

 offspj-ing. 



These large classes of exceptions — to go no further — indicate that, 

 as we might in any case expect, the principle is not of unixcrsal ai)pli- 

 cation, and will need various modihcations if it is to be extended to 

 more complex cases of inheritance of varietal characters. No more 

 useful woi-k can Ix^ imagined than a systematic determination of the 

 precise ''law of luM'edity'^ in numlxM-s of particular cases. 



Until lateh' the work which (Jallon accomplished stood almost alone 

 in this lield, but ((uit(> recently r(>markable additions to our knoAvledgc 

 of these questions have been made. In the year 1900, Professor de Vries 



"See later. (Jalton gave a f?iiii]>le (liatrnimmatic representation of liis law in 

 Nature, 1898, Vol. LVII, j). 298. 



''These we now recognize as exaMii)le,s of ^Nlendelian "doniinanci'."' 



