1784] Essays )
But the absurdity of descending honors is not a
mere matter of philosophical opinion; it is capable
of mathematical demonstration. A man’s son, for
instance, is but half of his family, the other half belonging
 to the family of his wife. His son, too,
marrying into another family, his share in the grandson
 is but a fourth; in the great-grandson, by the
same process, it is but an eighth; in the next generation
 a sixteenth; the next a thirty-second ; the next
a sixty-fourth; the next an hundred and twentyeighth;
 the next a two hundred and fifty-sixth; and
the next a five hundred and twelfth. Thus in nine
generations, which will not require more than three
hundred years (no very great antiquity for a family),
 our present Chevalier of the Order of Cincinnatus’
 share in the then existing knight will be but a
five hundred and twelfth part, which, allowing the
present certain fidelity of American wives to be insured
 down through all those nine generations, is
so small a consideration that methinks no reasonable
man would hazard for the sake of it the disagreeable
consequences of the jealousy, envy, and ill-will of
his countrymen.
Let us go back with our calculation from this
young noble, the five hundred and twelfth part of
the present knight, through his nine generations,
till we return to the year of the institution. He
must have had a father and a mother, they are two;
each of them had a father and a mother, they are
four. Those of the next preceding generation will
be eight, the next sixteen, the next thirty-two, the

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