these 10,198 marriages, 211, or 2.07 per cent were between persons
bearing the same surname. Applying Darwin's formula we would have 5.9
as the percentage of first cousin marriages in colonial New York.
This figure is evidently much too high, so in the hope of finding the
fallacy, I worked out the formula entirely from American data. To
avoid the personal equation which would tend to increase the number of
same-name first cousin marriages at the expense of the same-name not
first cousin marriages, I took only those marriages obtained from
genealogies, which would be absolutely unbiassed in this respect. Out
of 242 marriages between persons of the same name, 70 were between
first cousins, giving the proportion:

Same-name first cousin marriages 70
-------------------------------- = --- = .285
All same-name marriages 242

as compared with Darwin's .57. So that we may be fairly safe in
assuming that not more than 1/3 of all same-name marriages are first
cousin marriages. Taking data from the same sources and eliminating as
far as possible those genealogies in which only the male line is
traced, we have it:

Same-name first cousin marriages 24 1 1
------------------------------------- = -- = -------- = -------
Different-name first cousin marriages 62 (2-7/12) 2.583

This is near the ratio which Darwin obtained from his data, and which
he finally changed to 1/4. I am inclined to think that his first ratio
was nearer the truth, for since we have found that the coefficient of
attraction between cousins would be so much greater than between
non-relatives, why should we not assume that the attraction between
cousins of the same surname should exceed that between cousins of
different surnames? For among a large number of cousins a person is
likely to be thrown into closer contact, and to feel better acquainted
with those who bear the same surname with himself. But since the
theoretical ratio would be about 1/4 it would hardly be safe to put
the probable ratio higher than 1/3, or in other words four first
cousin marriages to every same-name first cousin marriage. Our
revised formula then is:

All same-name marriages 3 1
--------------------------- = --- X --- = .75
All first cousin marriages 1 4

Instead of Mr. Darwin's .35.

Taking then the 10,198 marriages, with their 2.07 per dent of
same-name marriages, and dividing by .75 we have 2.76 per cent, or 281
f