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, oz ‘he average, is the degree of resemblance to 
be expected between the offspring and the several generations 
of ancestors backward: }, |, 4, 35, sls, 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 1, 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 
1 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. 
