'42 
Notes on the History of Correlation 
In this paper Weldon also published for the first time with due appreciation of 
their meaning negative correlation coefficients. In conclusion Weldon remarks: 
" A large series of such specific constants would give an altogether new kind of 
knowledge of the physiological connexion between the various organs of animals ; 
while a study of those relations which remain constant through large groups of 
species would give an idea, attainable at present in no other way, of the functional 
correlations between various organs which have led to the establishment of the 
great subdivisions of the animal kingdom " (p. 11). In these lines we can read the 
starting-point of biometry as applied to other types of life than man. 
I will not keep you longer over Weldon's contributions than to say that in 1893 
appeared his third statistical paper* on "Correlated Variations in Naples and 
Plymouth shore Crabs." Weldon dealt with 23 pairs of organs in both Naples and 
Plymouth races. He proposes to call r "Galton's function"f. The paper shows that 
the 23 values of ?■ at Plymouth and Naples are fairly close, but was again incon- 
clusive because the significance of the differences could not be ascertained without 
a knowledge of the probable error (if r. 
We may next turn to Edgeworth, whose fundamental paper is that on " Corre- 
lated Averages" which appearetl in the Philosupliical IMagazine of August, 1892, 
pp. 190 — 204. Edgeworth starts by referring to Galton's memoir of 1888 and 
Weldon's of 1892 on shrimps. He assumes for the probability that any particular 
values a\, x.,, ... shall occur 
where R is 
= lh (a'l - ^'i)- + P-2 {^-2 - •^■■>)- + ■■■ + "2qi-2 {^\ ~ ^i) (^t'o -x.^+ ... .. 
He does not justify this assumptiim but hopes to do so in a subsequent paper. He 
states that Galton by the happy device of measuring each deviation by the 
corresponding quartile had reduced in the case of two variates 
1 - p- i-p- 1 - p- 
to the discovery of a single constant p. This is hardly accurate ; to reduce the 
expression R to the above it would be needful to measure not in terms of the 
quartile but of S.D., which is I think sometimes termed the ' modulus|. 
Edgeworth replaces Galton's "Index of Co-relation" and Weldon's "Galton's 
Function " by the term " coefficient of correlation." He then proceeds to weaken 
down Weldon's process of finding a mean r by suggesting that it will be adequate 
to find it by taking some of the ratios of 'subject' and mean 'relative' instead of 
the whole series. I look upon this suggestion as a distinctly retrogressive step. 
* R. S. Proc. Vol. Liv. pp. 318—329. 
t " The importance of this constant in all attempts to deal with the problems of animal variation was 
first pointed out by Mr Galton. ..and I would suggest that the constant whose changes he has investigated 
and whose importance he has indicated, may fitly be known as ' Galton's function,'" p. 325. 
X Edgeworth appears to realise this on p. 194, but he did not go back and correct his statement of 
p. 190. 
