Mr. Darwin then proceeded by a purely genealogical method. He found that out of 9,549 marriages recorded in "Burke's _Landed Gentry_," 144 or 1.5 per cent were between persons of the same surname, and exactly half of these were first cousins. In the "_English and Irish Peerage_" out of 1,989 marriages, 18 or .91 per cent were same-name first cousin marriages. He then sent out about 800 circulars to members of the upper middle class, asking for records of first cousin marriage among the near relatives of the person addressed, and obtained the following result:
----------------------------------------------- Same-name first cousin marriages | 66 Different-name first cousin marriages | 182 Same-name not first cousin marriages | 29 -----------------------------------------------
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
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.