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ive 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. Mr. Malthus's style is correct and elegant; his tone of controversy mild and gentlemanly; and the care with which he has brought his facts and documents together, deserves the highest praise.
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