2.9.  Individuality an interlude.

I would like in a parenthetical section to expand and render rather more concrete this idea of the species as one divaricating flow of blood, by an appeal to its arithmetical aspect.  I do not know if it has ever occurred to the reader to compute the number of his living ancestors at some definite date, at, let us say, the year one of the Christian era.  Everyone has two parents and four grandparents, most people have eight great-grandparents, and if we ignore the possibility of intermarriage we shall go on to a fresh power of two with every generation, thus:—­

Column 1:  Number of generations.

Column 2:  Number of ancestors.

     3 :  8
     4 :  16
     5 :  32
     7 :  128
    10 :  1,024
    20 :  126,976
    30 :  15,745,024
    40 :  1,956,282,976

I do not know whether the average age of the parent at the birth of a child under modern conditions can be determined from existing figures.  There is, I should think, a strong presumption that it has been a rising age.  There may have been a time in the past when most women were mothers in their early teens and bore most or all of their children before thirty, and when men had done the greater part of their procreation before thirty-five; this is still the case in many tropical climates, and I do not think I favour my case unduly by assuming that the average parent must be about, or even less than, five and twenty.  This gives four generations to a century.  At that rate and disregarding intermarriage of relations the ancestors living a thousand years ago needed to account for a living person would be double the estimated population of the world.  But it is obvious that if a person sprang from a marriage of first cousins, the eight ancestors of the third generation are cut down to six; if of cousins at the next stage, to fourteen in the fourth.  And every time that a common pair of ancestors appears in any generation, the number of ancestors in that generation must be reduced by two from our original figures, or if it is only one common ancestor, by one, and as we go back that reduction will have to be doubled, quadrupled and so on.  I daresay that by the time anyone gets to the 8916 names of his Elizabethan ancestors he will find quite a large number repeated over and over again in the list and that he is cut down to perhaps two or three thousand separate persons.  But this does not effectually invalidate my assumption that if we go back only to the closing years of the Roman Republic, we go back to an age in which nearly every person living within the confines of what was then the Roman Empire who left living offspring must have been ancestral to every person living within that area to-day.  No doubt they were so in very variable measure.  There must be for everyone some