--------

These cases furnished by correspondents he calculated to be 3.41 per
cent of all marriages in the families to which circulars were sent.

From the data collected from all these sources Mr. Darwin obtains the
following proportion:

Same-name first cousin marriages 142
-------------------------------- = --- = .57
All same-name marriages 249

He is inclined to think that the ratio should be lower and perhaps .50
instead of .57. By a similar line of reasoning he obtains this
proportion:

Same-name first cousin marriages 1
------------------------------------- = ---
Different-name first cousin marriages 3

Here too, he fears that the denominator is too small, for by
theoretical calculation he obtains by one method the ratio 2/7, and
by another 1/1. He finally takes 1/4 for this factor. To express the
proportion in another form:

Same-name first cousin marriages 1
-------------------------------- = ---
All first cousin marriages 5

The completed formula then becomes:

All same-name marriages 100 1
-------------------------- = ----- X --- = .35 (nearly)
All first cousin marriages 57 5

Applying this formula to the English statistics, Mr. Darwin computes
the percentages of first cousin marriages in England with the
following results:

---------------------------------------
London | 1.5
Other urban districts | 2.
Rural districts | 2.25
Middle class and Landed Gentry | 3.5
Aristocracy | 4.5
---------------------------------------

In order to apply this formula to the American population I counted
the names in the New York Marriage License Record previous to
1784,[25] and found the number to be 20,396, representing 10,198
marriages. The fifty commonest names embraced nearly 15 per cent of
the whole (1526), or three per cent less than the number found by
Darwin.[26] Of these, one in every 53 was a Smith, one in 192 a
Lawrence, and so on. The sum of the fraction 1/53^2, 1/192^2,
etc., I found to be .000757 or .757 per thousand, showing that the
probability of a chance marriage between persons of the same name was
even less than in England, where Mr. Darwin considered it almost a
negligible quantity.

[Footnote 25: _Names of Persons for whom Marriage Licenses were issued
by the Secretary of the Province of New York_.]

[Footnote 26: _Cf. supra_, p. 21.]

Of