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 few individuals in that period who have so to speak intermarried with themselves again and again and again down the genealogical series, and others who are represented by just one touch of their blood. The blood of the Jews, for example, has turned in upon itself again and again; but for all we know one Italian proselyte in the first year of the Christian era may have made by this time every Jew alive a descendant of some unrecorded bastard of Julius Caesar. The exclusive breeding of the Jews is in fact the most effectual guarantee that whatever does get into the charmed circle through either proselytism, the violence of enemies, or feminine unchastity, must ultimately pervade it universally.

It may be argued that as a matter of fact humanity has until recently been segregated in pools; that in the great civilization of China, for example, humanity has pursued its own interlacing system of inheritances without admixture from other streams of blood. But such considerations only defer the conclusion; they do not stave it off indefinitely. It needs only that one philoprogenitive Chinaman should have wandered into those regions that are now Russia, about the time of Pericles, to link east and west in that matter; one Tartar chieftain in the Steppes may have given a daughter to a Roman soldier and sent his grandsons east and west to interlace the branches of every family tree in the world. If any race stands apart it is such an isolated group as that of the now extinct Tasmanian primitives or the Australian black. But even here, in the remote dawn of navigation, may have come some shipwrecked Malays, or some half-breed woman kidnapped by wandering Phoenicians h............