“The doctrine of lineal consanguinity is sufficiently plain and obvious; but it is at the first view astonishing to consider the number of lineal ancestors which every man has within no very great number of degrees:  and so many different bloods is a man said to contain in his veins, as he hath lineal ancestors.  Of these he hath two in the first ascending degree, his own parents; he hath four in the second, the parents of his father and the parents of his mother; he hath eight in the third, the parents of his two grandfathers and two grandmothers; and by the same rule of progression, he hath an hundred and twenty-eight in the seventh; a thousand and twenty-four in the tenth; and at the twentieth degree, or the distance of twenty generations, every man hath above a million of ancestors, as common arithmetic will demonstrate.

“This will seem surprising to those who are unacquainted with the increasing power of progressive numbers; but is palpably evident from the following table of a geometrical progression, in which the first term is 2, and the denominator also 2; or, to speak more intelligibly, it is evident, for that each of us has two ancestors in the first degree; the number of which is doubled at every remove, because each of our ancestors had also two ancestors of his own.

  Lineal Degrees. Number of Ancestors.

1 .. .. .. 2 2 .. .. .. 4 3 .. .. .. 8 4 .. .. .. 16 5 .. .. .. 32 6 .. .. .. 64 7 .. .. .. 128 8 .. .. .. 256 9 .. .. .. 512 10 .. .. .. 1024 11 .. .. .. 2048 12 .. .. .. 4096 13 .. .. .. 8192 14 .. .. .. 16,384 15 .. .. .. 32,768 16 .. .. .. 65,536 17 .. .. .. 131,072 18 .. .. .. 262,144 19 .. .. .. 524,288 20 .. .. .. 1,048,576

“This argument, however,” (proceeds Mr. Godwin) “from Judge Blackstone of a geometrical progression would much more naturally apply to Montesquieu’s hypothesis of the depopulation of the world, and prove that the human species is hastening fast to extinction, than to the purpose for which Mr. Malthus has employed it.  An ingenious sophism might be raised upon it, to shew that the race of mankind will ultimately terminate in unity.  Mr. Malthus, indeed, should have reflected, that it is much more certain that every man has had ancestors than that he will have posterity, and that it is still more doubtful, whether he will have posterity to twenty or to an indefinite number of generations.”—­ENQUIRY CONCERNING POPULATION, p. 100.