100 YEARS AGO

“Average Number of Kinsfolk in Each Degree.” May I ask you to insert yet another brief communication on the above subject, because private correspondence shows that paradoxical opinions are not yet wholly dispelled? The clearest way of expressing statistical problems is the familiar method of black and white balls, which I will now adopt. Plunge both hands into a dark bag partly filled with black and white balls, equal in number, and well mixed. Grasp a handful in the right hand, to represent a family of boys and girls. Out of this unseen handful extract one ball, still unseen, with the left hand. There will be on the average of many similar experiments, as many white as black balls, both in the original and in the residual handful, because the extracted ball will be as often white as black. Using my previous notation, let the number of balls in the original handful be 2d. Consequently, the number in the residual handful will be 2d−1, and the average number in it either of white or of black balls will be half as many, or d−1/2. It makes no difference to the average result whether the hitherto unseen ball in the left hand proves to be white or black. In other words, it makes no difference in the estimate of the average number of sisters or of brothers whether the individual from whom they are reckoned be a boy or a girl; it is in both cases d−1/2. The reckoning may proceed from one member of each family taken at random, or from all its members taken in turn.

Francis Galton

From Nature 12 January 1905.

50 YEARS AGO

The “Proceedings” for 1954 of the Croydon Natural History and Scientific Society contains interesting articles on deneholes... Deneholes are excavations in underlying chalk reached by vertical shafts through the overload... The age of the deneholes seems to be pre-Roman, and they are probably of the Iron Age. Many explanations have been given as to why they were made; but none is satisfactory. Underground granaries or stores have been suggested, or pits for obtaining chalk for agriculture; but, if the latter explanation be the correct one, why have they been so carefully made?... It would seem clear... that some connexion must exist between these artificial caves and the earth-houses of northern Scotland. But unfortunately we do not really know why these latter were made, either.

From Nature 15 January 1955.