50 Life and Letters of Francis Galton
expressed it ten years later : " No statistical results of any consistence or value could be obtained from them*." Thus ended what had at first sight appeared to be a hopeful series of experiments, experiments upon which much thought and labour had been expended.
H. Correlations and their Measurement. As I have already pointed out the conception that the regression coefficient for inheritance could be applied to a measure of the relationship of associated variates, provided each was measured in terms of its own scale of variab ihty; first occurred to Galton while he was taking a walk in the grounds of NaiKorth Castle in the year 1888 (see p. 393 of Vol. ii). On December 5, 1888, Galton sent to the Royal Society a paper read fifteen days later and entitled : "Co-relations and their Measurement, chiefly from Anthropometric Data'." The twentieth of December is therefore the birthday of the conception of correlation in biometric data as apart from the idea of regression in heredity which Galton had reached some years earlier, without perceiving at once its capacity for wide generalisation in the treatment of associated variates in all living forms.
Like so much of Galton's work the present paper reaches results of singular importance by very simple methods; his methods are indeed so simple that we might almost believe they must lead to a fallacy had not Galton deduced thereby the correct answer. It is the old experience that a rude instrument in the hand of a master craftsman will achieve more than the finest tool wielded by the uninspired journeyman.
The first three paragraphs of this memoir define Galton's method of considering correlation, and indicate that in 1888 even the spelling of the word had not been fixed T
"`Co-relation or correlation of structure' is a phrase much used in biology, and not least in that branch of it which refers to heredity, and the idea is even more frequently present than the phrase; but I am not aware of any previous attempt to define it clearly, to trace its mode of action in detail, or to show how to measure its degree.
" Two variable organs are said to be co-related when the variation of the one is accompanied on the average by more or less variation of the other, and in the same direction. Thus the length of the arm is said to be co-related with that of the leg, because a person with a long arm has usually a long leg, and conversely. If the co-relation be close then a person with a very long arm would usually have a very long leg ; if it be moderately close then the length of his leg would only be long, not very long ; and if there were no co-relation at all then the length of his leg would on the average be mediocre. It is easy to see that co-relation must be the consequence of the variations of the two organs being partly due to common causes. If they were wholly due to common causes, the co-relation would be perfect, as is approximately the case with the symmetrically disposed parts of the body. If they were in no respect due to common causes, the co-relation would be nil. Between these two extremes are an endless number of intermediate cases, and it will be shown how the closeness of co-relation in any particular case admits of being expressed by a simple number.
"To avoid the possibility of misconception it is well to point out that the subject in hand has nothing whatever to do with the average proportions between the various limbs in different
* Roy. Soc. Proc. Vol. Lxi, p. 402.
t Ibid. Vol, xLV, pp. 135-145.
+ Five years later in 1893 when the volume containing the letter C of the Oxford English Dictionary was issued, the Galtonian or biometric sense of 11 correlation "was not given.