Karl Pearson 
41 
that he was applying correlation and the regression line in a variety of ways thus 
to the relation between wing and tail length in birds, to fertility and to disease. 
His advance was chiefly hampered by the restriction of his data and the need for 
organised observers and computers. 
The publication of Natural Inheritance provided Francis Galton with at least 
three recruits for the field of correlation : Weldon, Edgeworth and myself. 
Weldon started in 1889 measuring the organs of shrimps at Plymouth and he 
was able to announce early in 1890 — the letter is now in the glass case in our library 
here — the first correlation coefficients, or as he termed them " Galton Functions," 
between organs in shrimps. This was rapidly followed by his work on crabs, and 
the attempt to show that Galton functions were the same for all local races of the 
same species. In his first paper on shrimps Weldon writes* : 
" In making this investigatitjn I have had the great privilege of being constantly 
advised and helped in every possible way by Mr Galton. My ignorance of 
statistical methods was so great tliat without Mr Galton's constant help, given by 
letter at the expenditure of a very great amount of time and trouble, this paper 
would never have been written." 
The pupil, however, was soon to outdistance the master in the width of his 
theoretical knowledge. A second paper on the shrimp followed in 1892 f, and this 
deals more closely with the correlations. Weldon now replaces medians by means 
in both marginal totals and arrays. He still uses probable erroi-s or quartiles, and 
goes through the laborious process of reducing each deviation to the probable error. 
He uses r "in accordance with Mr Galton's notation" to represent the constant 
which measures the " degree of correlation " between organs. I think, but it is not 
quite clear, that he determined his probable error from the mean error, not from 
the quartile. He then determined r from each individual array and took the mean 
value of these r's as the true r. He accordingly introduced a greatly increased 
accuracy into the computing of correlation. Ho dealt with five local races of shrimps 
and found correlations for 22 pairs of organs. His regression diagram, p. 8, is still 
an admirable sample of this type of work. The correlations between post-spinous 
portion and total carapace length may be cited as illustrations of what Weldon and 
Galton were testing : 
Plymouth (1000) r = 0-81 
Southport (800) /■ = 0-85 
Roscofif(500) r = 0-80 
Sheerness (380) r = 0-85 
Helder(300) ?• = 0-83 
The suggestion that r has the same value for all races of the same species was 
supposed to be confirmed by these results. We now realise that without a know- 
ledge of the probable error of r, such a statement is illusory. But it was this very 
series of values which led to the investigation of the probable error of r and so to 
the extension of the correlational calcubis. 
* R. S. Proc. Vol. xr.vii. p. 445, 1890. t R. S. Proc. Vol. xm. p. 2. 
