NATURAL HEIRSHIP : OR, ALL THE WORLD AKIN. 377 



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-five 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 de- 

 serves the thanks of his countrymen. 



NATURAL HEIRSHIP: OR, ALL THE WORLD AKIN. 



"5 



Bt Eev. henry KENDALL. 



THE 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 twen- 

 tieth it becomes 1,048,576 ; in the thirtieth no fewer than 1,073,741,- 

 834. To ascend no higher than the twenty-fourth generation we 

 reach the sum of 10,777,216, 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 a. d. 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 nine- 

 teenth-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 de- 

 scendants in the island, and whose progeny has not died out there. 



