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Dally^[23] is very skeptical about the accuracy of the French figures, but says that in Paris the records are well kept. He found that in the years 1853-62 there were 10,765 marriages in the 8me arrondissement of Paris, and of these he finds:

This is rather higher than the average for urban districts, according to official figures, but Dally seems to consider it as typical. He gives examples of the carelessness and incompetency of the rural record keepers, and insists that the percentage is really much higher than the official figures would indicate. He estimates the consanguineous marriages in France not including second cousins, at from four to five per cent.

A very ingenious method of determining the approximate number of first-cousin marriages was devised by Mr. George H. Darwin.^[24] Noticing that in marriage announcements, some were between persons of the same surname, it occurred to him that there might be a constant ratio between same-name marriages and first cousin marriages. Some same-name marriages would of course be purely adventitious; so, to eliminate this element of chance, he obtained from the Registrar General's Report the frequency of occurrence of the various surnames in England. The fifty commonest names embraced 18 per cent of the population. One person in every 73 was a Smith, one in every 76 a Jones and so on. Then the probability of a Smith-Smith marriage due to mere chance would be 1/73² and of a Jones-Jones marriage 1/76². The sum of fifty such fractions he found to be .0009207 or .9207 per thousand. After the fiftieth name the fractions were so small as to have comparatively little effect upon the total. He therefore concluded that about one marriage in a thousand takes place, in which the parties have the same surname and have been uninfluenced by any relationship between them bringing them together.

The next step was to count the marriages announced in the "Pall Mall Gazette" for the years 1869-72 and a part of 1873. Of the 18,528 marriages there found, 232 or 1.25 per cent were between persons of the same surname. Deducting the percentage of chance marriages at least 1.15 per cent were probably influenced directly or indirectly by consanguinity.

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:

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:

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:

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:

The completed formula then becomes:

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

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.

Of 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