K. Pearson 
145 
Now from such a division the mathematician can deduce* the slope of the 
regression line on the assumption of normal distribution. Here, to give us 
confidence, are the results for head breadth and height in boys, which were 
worked out both ways : — 
Resemblance of Brothen 
Long table 
Fourfold division 
Head Breadth 
Auricular Height 
•59 
•58 
•56 
For practical purposes these results are identical. 
Accordingly let us assume this fourfold division will work, and investigate by 
means of it a non-quantitatively measurable physical character in man. I choose 
Health as an example. In Table A (i), Appendix III., we have the distribution of 
health in a population of 1918 school boys, and in Diagram IX., we have the 
arrangement of the same material, supposing it to follow a normal curve. My five 
classes were (i) Very Strong; (ii) Strong, being here used not in the sense of 
physically strong, but of Robust; (iii) Normally Healthy; (iv) Rather Delicate; and 
(v) Very Delicate. You will see that the "modal" boy is somewhat on the normally 
healthy side of robust, but that the Very Robusts are more numerous than the Very 
Delicates and the Robusts than the Delicates. I think the scale is not without 
suggestiveness even as a general health distribution for the population at large. 
It gives us for the first time an exact measure of the ranges of delicacy and 
robustness in terms of normal health. 
Now I applied this scale to the relation between brothers in health character. 
I plotted up at the mean of robust boys, a length on this scale equal to the mean 
on the same scale of the array of brothers of these robust boys; there was naturally 
a regression towards normal health. I did this for all the possible five arrays-f-, and 
I thus obtained the five points given in Diagram X. You will see at once that 
our five points lie quite nicely distributed about the regression liae as found by 
the fourfold division method discussed above. In other words, there can be little 
doubt that the general health of boys is a character which closely follows the 
normal law of distribution, and has a true line of regression. The slope of that 
line is '52, or we may safely say that general health in the community is inherited 
in precisely the same manner as head-measurements or body-lengths. 
I now come to the fundamental idea of my comparison of the psychical and 
physical resemblance of brothers. Suppose we assume that moral and mental 
qualities in man, like the phy.sical, follow a normal law of distribution, and that 
* Mathematical Contributions to the Theory of Evolution. VII. " On the Correlation of Characters 
not Quantitatively Measurable," Phil. Trans. Vol. 195, A, pp. 1 — 47. 
t For the benefit of the mathematical statistician, I may say that I used the modal group of each 
sub-array to determine its mean and standard deviation in terms of those of the scale for the whole 
population. 
Biometrika iii 19 
