74 CORRELATED VARIATIONS. 



correlated with another conveys no exact meaning. 

 Such a statement must vary according to the notion of 

 the observer as to what does and what does not consti- 

 tute correlation. In order to obtain reliable and com- 

 parable data concerning the degree of correlation, it is 

 necessary to obtain a mathematical expression for it, 

 just as one was found to be necessary for indicating the 

 range of a variation. The fundamental theorems of 

 correlation were for the first time exhaustively discussed 

 by Bravais * more than half a century ago, but a more 

 convenient and improved method of obtaining an ex- 

 pression was first indicated by Galton, and he termed it 

 the correlation constant, or r. It is now more generally 

 known as " Galton's function." 



The principle on which this constant is determined is 

 best explained by a concrete instance, viz., one given by 

 Galton in the original paper in which he explained his 

 method.f Galton's data are anthropometric ones, ob- 

 tained at his own laboratory, and consist of several 

 measurements made on 350 males of 21 years and up- 

 wards. For instance, Galton found that the average 

 relation between stature and cubit, or distance between 

 the elbow of the bent arm and the tip of the middle 

 finger, was as 100 to 37. In determining the correla- 

 tion between these two measurements, however, it is 

 obvious that it is not possible to compare the absolute 

 amount of variation of the one with the absolute amount 

 of the other, or even the proportionate amounts, but 



* " Analyse mathematique sur les probabilites des erreurs de situ- 

 ation d'un point." Memoires par divers Savans, T. ix., Paris, 

 1846, p. 255. 



f Proc. Roy. Soc. , vol. xlv. p. 135, 1888. 



