Karl Pearson 
39 
He gives under the headings " Mean regression w," and " Quartile of individual 
variability " the coefficients of correlation of various pairs of relations : Midparent 
and Offspring, Brothers, Fathers and .Sons, Uncles and Nephews, Grandparents and 
Grandsons, but he dues not realise that on the theory of multiple regression there 
are certain inconsistencies in his values. I do not think that there is much 
additional contribution to theory in this paper. 
In 1888, however, Galton took a great step forward. He recognised that the 
whole statistical apparatus he had evolved for the treatment of the problem of 
heredity had a vastly wider significance. In a paper read to the Royal Society on 
December 5, 1888*, entitled "Correlations and their Measurement chiefly from 
Anthropometric Data," the term correlation first appears in our subject. Thus 
Gal ton's opening lines run : 
"Co-relation or correlation of structure" is a phrase uuicli used in biology, and not least in 
that branch of it which refers t(i heredity, and the idea is even more frequent than the phrase; 
but I am not aware of any previous attempt to detine it clearly, to trace its mode of action, or to 
show how to measure its degree. 
Two variable organs are said to be correlated when the variation of the one is accompanied on 
the average by more or less variation of the other, and in the same direction (p. 135). 
The last words seem to us now out of place, but Galton had not yet reached 
the idea of negative correlation. Also the balance is still swinging between ' co- 
relation' and 'correlation' although it has ultimately fxUen to the more weighty 
word. How clearly Galton grasped the essence of correlation may be shown by the 
following sentences which might have saved many ingenious later investigators 
thinking they had made an important discovery. " 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 ca.ses, 
and it will be shown how the closeness of co-relation in any particular case admits 
of being expre.ssed by a single number " (p. 135). This single number it is needless 
to say is our present coefficient of correlation. Galton drops now the -w of his 1886 
work and retyrns to the r of his 1877 lecture, and the symbol r has remained to 
the present day. 
Galton's process is the same as in the heredity problem. He used median and 
quartile and reduces the deviations to their respective quartiles as unit. He then 
smooths his means of arrays, draws a line to represent them and reads off its slope 
as 7\ He thus determines seven correlations which he here terms " indices of corre- 
lation f." They are between Stature and Cubit, Stature and Head Length, Stature 
and Middle Finger Length, Cubit and Middle Finger Length, Head Length and 
Head Breadth, Stature and Height of Knee, Cubit and Height of Knee. He fully 
» R. S. Proc. Vol. XLV. pp. 135—145. 
t On p. 143 ?•, the index of co-relation, is identified with the ' regression ' or ' reversion " of Galton's 
earlier papers. 
