1888.] Co-relations and their Measurement. 135 



Observations, &c. (continued). 



Order. 1884. 4to. LondonlSSS-, Daily Weather Reports. 1888. 



January to June. 4to. London. The Office. 



Nautical Almanac Office. The Nautical Almanac for 1892. 



8vo. London 1888. The Office. 



Madrid : Observatorio. Observaciones Meteorologicas. 1883-85. 



8vo. Madrid 1887-88. The Observatory. 



December 20, 1888. 



Professor G. G. STOKES, D.C.L., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : 



I. " Co-relations and their Measurement, chiefly from Anthropo- 

 metric Data." By FRANCIS GALTON, F.R.S. Received 

 December 5, 1888. 



" 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 

 usually be only 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 I // 

 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 



