unimpeded ratio at which ancestors multiply, they would amount in the thirty-second generation to 4,294,707,290; and, reckoning for all the checks to this ratio through the blending of lines of ancestry, they must be reasonably estimated at the entire population of the globe—as high, in fact, as they can possibly go. The Caffre and the Hottentot, the Japanese and the Chinese, are doubtless all of them the reader's thirty-second cousins, or nearer.
There is a tendency from many causes for ancestry to diverge and spread itself over an ever-widening area; there is a struggle of the lines to part until universality has been reached, and every human being has come into the succession. Even where a tribal or religious custom mostly confines the marriages of the men in a community to the women of the same community, there are sure to be many exceptions. Jews sometimes marry Gentiles, and set the barrier that interposed between them at defiance. Boaz married Ruth, and she brought into Judah blood mingled of all Moab. When the Quakers made it a rigorous rule that members of the society should marry only with members, gates were hung in the hedge, and the fence itself was often broken through. Proselytes were brought in from the outside; members married non-members at the cost of excommunication. The law itself had eventually to be abrogated.
The tendency to avoid kinship in marriage has helped to increase the divergence of ancestral lines. While a large proportion of the marriages consummated are between persons living in the same district, the population of the district itself is continually undergoing modification—one stream flowing in, another flowing out. No use has been made in this argument of the existence of illegitimacy, and the boundless license of many periods of our national history. Yet doubtless moral transgression has greatly widened the area of relationship, and mingled in an indistinguishable mass the offspring of the rich and poor.
Hitherto we have been looking backward at the historical multiplication of the ancestors of persons now living. If we reverse the process, and apply the law of multiplication to the future, the result is equally startling. The average number of children may be reckoned on a moderate computation at two for every household. According to this average, a man who leaves permanent posterity behind him has the number of his descendants doubled every generation. The two children are followed by four grandchildren; the four grandchildren by eight great-grandchildren. At the twenty-sixth generation the number has swelled to 67,000,024. A few more generations would render them equal to the total number of the inhabitants of the globe. So that, if one could rise from the grave at a period no further removed from us in the future than the Conquest in the past, every person he met in the land, man, woman, or child, if not a mere visitor or recent immigrant, would be one of his descendants. Every
