50 Life and Letters of Francis Gallon 



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 variability, first occurred to Galton 

 while he was taking a walk in the grounds of Naworth Castle in the year 1888 

 (see p. 393 of Vol. n). 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 Dataf ." 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 con- 

 sidering correlation, and indicate that in 1888 even the spelling of the word 

 had not been fixed J : 



"'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 T 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. 

 \ Ibid. Vol. xlv, pp. 135-145. 



X 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 " correlation " was not given. 



