Page:Popular Science Monthly Volume 28.djvu/389

Rh men ten years suitably to catalogue and index thirty-five thousand of them so that they could be available for use, while the others have been gradually added. Mr. Bancroft has spent twenty-live of his best years in his work, and is spending and expects to spend other years upon it; while the pecuniary cost to him is underestimated at a million dollars.

The author has not produced, nor has he aimed to produce, a critical history nor a philosophical history, but simply to collect and preserve what existed, but was in danger of being lost. For doing that he deserves the thanks of his countrymen.



HE number of a man's ancestors doubles in every generation as his descent is traced upward. In the first generation he reckons only two ancestors, his father and mother. In the second generation the two are converted into four, since he had two grandfathers and two grandmothers. But each of these four had two parents, and thus in the third generation there are found to be eight ancestors—that is, eight great-grandparents. In the fourth generation the number of ancestors is sixteen; in the fifth, thirty-two; in the sixth, sixty-four; in the seventh, 128. In the tenth it has risen to 1,024; in the twentieth it becomes 1,048,570; in the thirtieth no fewer than 1,073,741,834. To ascend no higher than the twenty-fourth generation we reach the sum of 16,777,216, which is a great deal more than all the inhabitants of Great Britain when that generation was in existence. For, if we reckon a generation at thirty-three years, twenty-four of such will carry us back 792 years, or to 1093, when William the Conqueror had been sleeping in his grave at Caen only six years, and his son William II, surnamed Rufus, was reigning over the land. At that time the total number of the inhabitants of England could have been little more than two millions, the amount at which it is estimated during the reign of the Conqueror. It was only one eighth of a nineteenth-century man's ancestors if the normal ratio of progression, as just shown by a simple process of arithmetic, had received no check, and if it had not been bounded by the limits of the population of the country. Since the result of the law of progression, had there been room for its expansion, would have been eight times the actual population, by so much the more is it certain that the lines of every Englishman's ancestry run up to every man and every woman in the reign of William I from the king and queen downward, who left descendants in the island, and whose progeny has not died out there.