40 
Notes on the History of Correlation 
realises (1) that r is the same when obtained from either variate as 'relative,' 
(2) that r is always less than ixnity, (3) that r measures the closeness of co-relation, 
and (4) provides the regression line (p. 145). 
On p. 144 the term "partial co-relation" is used but hardly in our modern 
sense although Galton is feeling his way towards multiple correlation. One problem 
he gives on p. 144 perhaps deserves mention, namely, if the n variates be expressed 
in terms of their quartiles then the quartile variability of their sum is if they 
are independent and n if they be " rigidly and perfectly co-related." " The actual 
value would be almost always somewhere intermediate between these extremes, and 
would give the information that is wanted." 
What Galton needs is the " multiple correlation coefficient," i.e. 
but he is not yet on the right ti'ack for it. 
In 1889 appeared Galton 's book Natural Inheritance embodying most of the 
work we have discussed in' the earlier memoirs of 1877 to 1888. Beyond this 
Galton did not carry the subject of correlation. He, in my opinion to-day, created 
it ; there is nothing in the memoirs of Gauss or Bravais that really antedates his 
discoveries. They were dealing with the relatively narrow problem of determining 
the probable errors of indirectly observed quantities deduced from independent or 
uncorrelated directly observed quantities. The product-terms that arise in their 
investigations were expressed in terms of differential coefficients ; they were not 
treated as a means of determining organic relationships between directly measured 
variates. Galton, starting from the organic relationship between parent and off- 
spring, passed to the idea of a coefficient measuring the correlation of all pairs of 
organs, and thence to the ' organic ' relationship of all sorts of factors. If you 
think Galton did not appreciate the width of his new methods you must turn to 
the last paragraph of his Ivtrodaction to the Natural Inheritance. 
" The conclusions cannot, however, be intelligently presented in an introductory 
chapter. They depend on ideas that must first be well comprehended, and which 
are now novel to the large majority of readers and unfamiliar to all. But those 
who care to brace themselves to a sustained effort, need not feel much regret that 
the road to be travelled over is indirect, and does not admit of being mapped 
beforehand in a way they can clearly understand. It is full of interest of its own. 
It familiarizes us with the measurement of variability, and with curious laws of 
chance that apply to a vast diversitij of social subjects. This part of the inquiry 
may be said to run along a road on a high level that affords wide views in un- 
expected directions, and from which easy descents may be made to totally different 
goals to those we have now to reach. I have a great subject to write upon..." (p. 2). 
Galton realised as fully as any of us now the width of application that would 
open up to the new calculus of correlation, and what easy descents there would be 
from the " high level road " to strange goals. His notebooks of this period show 
