| Same-name first cousin marriages All same-name marriages | = | 142 249 | = | .57 |
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_ Different-name first cousin marriages | = | _1_ 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 All first cousin marriages | = | _1_ 5 |
The completed formula then becomes:
| All same-name marriages All first cousin marriages | = | 100 57 | X | _1_ 5 | = | .35 (nearly) |
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 1/532, 1/1922, 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.