HEREDITY 303

this? My brother-in-law, J. Hamilton Dickson of Peterhouse, ,loves problems and wants new ones. Send it to him." I did so, under the form of a problem in mechanics, and he most cordially helped me by working it out, as proposed, on the basis of the usually accepted and generally justifiable Gaussian Law of Error. So I begged him to allow his solution to be given as an appendix to my paper [9 i ], where it will be found.

It had appeared from observation, and it was fully confirmed by this theory, that such a thing existed as an " Index of Correlation " ; that is to say, a fraction, now commonly written r, that connects with close approximation every value of deviation on the part of the subject, with the average of all the associated deviations of the Relative as already described. Therefore the closeness of any specified kinship admits of being found and expressed by a single term. If a particular individual deviates so much, the average of the deviations of all his brothers will be a definite fraction of that amount ; similarly as to sons, parents, first cousins, etc. Where there is no relationship at all, r becomes equal to o ; when it is so close that Subject and Relative are identical in value, then r= i. Therefore the value of r lies in every case somewhere between the extreme limits of o and i. Much more could be added, but not without using technical, language, which would be inappropriate here.

The problem as described above is by no means difficult to a fair mathematician. Mr. J. H. Dickson set it to a class of his higher students, most of whom answered it. It has since been remarked that this