180 
PROFESSOR KARL PEARSON, MATHEMATICAL 
Table I.—Correlation between Stature and Long Bones. 
Pairs of organs. 
Male. 
Female. 
Stature and tibia. 
Stature and radius. 
Stature and humerus*. 
Stature and femur. 
Stature and humerus + radius . . . 
Stature and femur -f tibia .... 
•7769 ± -0378 
•6956 ± -0492 
•8091 ± -0329 
•8105 ± -0327 
•7973 ± -0347 
•8384 ± -0283 
•7963 ± -0349 
•6717 ± -0523 
•7706 ± -0387 
•8048 ± -0336 
•7547 ± -0411 
•8268 ± -0302 
The means, standard deviations, and correlations of femur, tibia, humerus, and 
radius, for Rollet’s measurements, are given in the ‘ Boy. Soc. Proc.,’ vol. 61 , 
pp. 347-350. The means and variability of the remaining organs not there recorded 
were found to be as follows ;— 
Table II. 
Mean. 
Standard deviation. 
Male. 
Female. 
Male. 
Female. 
Stature . 
Humerus + radius . . 
Femur + tibia .... 
166-260 ± -525 
57-368 ± -242 
82-028 ± -380 
154-0-20 ± -520 
51-240 ± -241 
75-024 ± -382 
5'502 ± -371 
2- 536 ± -171 
3- 979 ± -268 
5-450 ± -368 
2-526 ± -170 
4-001 ± -270 
Without reproducing the full tables of the memoir referred to, it is of value to 
form the correlation tables, which serve as the determinants from which the regres- 
sion formulm have been calculated. It is only in the case of stature in terms of the 
four long bones that the numerical work proved lengthy. 
The general formula used is (ii.) on p. 172. S, F, H, T, B stand for Stature, Femur, 
Humerus, Tibia, Radius, all measured in Bollet’s manner, which will be discussed at 
length below. 
* The somewhat low value of the correlation for female stature and humerus was tested by means of 
the formula 
_ O'- I tTy 
r — _£ 7* 4- _2 7* 
<^Z A- 
where z — x y, y, and m are organs, their standard deviations, and r a coefficient of 
correlation. Hence putting x = humerus, y — radius, and u — stature, I found the correlation between 
stature and humerus + radius indirectly; it was oSGt. The table shows that the directly-calculated 
value was ’7547, a difference well within the errors of observation. Thus the correlations as given for 
female humerus and stature and female radius and stature must be correct, i.e., the somewhat lengthy 
arithmetic involved is not at fault. 
