THE LAW OF ANCESTRAL HEREDITY 167 



or the characters so few that all individuals are practically iden- 

 tical. This could not be in a race so rich in characters as man 

 or even the common domesticated animals, which differ so de- 

 cidedly in form, color, activity, and mental qualities, besides 

 many internal activities that cannot be readily detected. 



We should however expect that the offspring would resemble 

 the immediate parents more closely than any other ancestors on 

 the score of relative intensities and nearness of blood, and this 

 expectation is fulfilled. 



Galton and Pearson have given much study to this question, 

 and, arriving at results from independent standpoints and by 

 methods quite distinct, agree on the following formula as ex- 

 pressing what, on the average, is the degree of resemblance to 

 be expected between the offspring and the several generations 

 of ancestors backward : ^, J, \^ -^q, ^V» etc., to infinity. 



It will be noticed that each fraction of this series is exactly 

 half of the preceding fraction ; also that if the series be carried 

 to infinity, the fractions would add up to i, thus accounting for 

 the total inheritance. This means, substantially, that in general 

 and on the average the offspring will resemble, to the extent of 

 half his personality, the two immediate parents, and of course 

 will divide that resemblance between them equally.^ To the ex- 

 tent of one fourth of his appearance he would resemble his 

 grandparents, the resemblance being distributed between the 

 four. One eighth of his visible characters may be credited to 

 the next generation (great-grandparents), one sixteenth to the 

 next, etc., indefinitely backward, thus accounting for all sorts of 

 remote resemblances or atavisms. 



All this is not saying that every individual will thus accurately 

 divide his resemblances, but it is saying that for large numbers 

 the resemblances will be found to follow this plan, and wherever 



^ This may seem wrong to the reader, because the offspring will resemble 

 more closely the better bred parent. That, however, as we shall see, is due to 

 the influence back of the parent. If the breeding were good enough, all the 

 ancestors would be alike. 



