494 



THE GRAMMAR OF SCIENCE 



to a long series of ancestry. Allowing for some degree 

 of prepotency within the individual marriage, and pos- 

 sibly for some homogamy, exclusive inheritance without 

 reversion fits best the eye-colour results of the table on 

 p. 491. 



Mr. Galton has supposed that half the offspring revert, 

 and that half of each reverting remainder is dropped at 

 each stage of the ancestry as we go backwards. Thus we 

 reach this result :— 



25 per cent of the offspring would exhibit the full 

 character of either parent. 



^£ per cent of the offspring would exhibit the full 

 character of each of the four grandparents. 



^ per cent of the offspring would exhibit the full 

 character of each of the eight great-grandparents, and so 

 on. 



Summing, we have for the total offspring :— 



25x2 + ^x4+f^x8 + tix 16 + 



= 2 5 ; 2 + I + i + 



i + 



I _ 



100 per cent. 



If this law were true, ^ the offspring would follow the 

 parents exclusively, ^ revert to the grandparents, i to the 

 great-grandparents, ^j. to the great-great-grandparents, and 

 so on. These numbers, which here give quotas of inherit- 

 ance among the total offspring, are precisely identical with 

 those we have obtained for quotas of inheritance contributed 

 by the ancestry to the type of offspring in the case of 

 blended inheritance. The two cases, however, must be kept 

 absolutely distinct. In the case of blended inheritance 

 we construct the type of offspring by taking certain 

 proportions from each of the ancestry, and the dominant 

 feature is regression ; in the case of exclusive inheritance 

 we construct the distribution of ancestral characters 

 among the whole group of offspring, and the dominant 

 feature is reversion. In both cases we may speak of a 

 law of ancestral heredity, but the first predicts the probable 

 character of the individual produced by a given ancestry, 

 while the second tells us the percentages of the total off- 

 spring which, on the average, revert to each ancestral type. 



