K. Pearson 
137 
I have not yet investigated my own school data from this stand- 
point, but I have every confidence in the care taken by the late 
Dr W. Pfitzner in his elaborate system of measurements, and the 
above is the conclusion he reaches*. 
(6) Several great authorities have recently stated that they do not " believe " 
in the cephalic index, i.e., consider it of small value for anthropometric 
purposes. 
In Table E (i), Appendix III., we have the cephalic index given for 1982 pairs 
of brothers. This table is, I hope, perfectly intelligible. Taking the boys, for 
example, with cephalic indices between 74 and 75, these boys had 78 brothers 
who were distributed according to the arrangement in the column headed 74 to 75. 
Brothers are not alike in cephalic index, but distributed with a considerable range 
of variation. We now take in the usual way the arithmetic mean of this array 
of brothers, and find it to be 77-45. The average brother of a boy with cephalic 
index = 74"5 has an index of 77-45. This is the phenomenon of regression towards 
the general population mean (78'9) as discovered by Francis Galton. Now turning 
to Diagram I. we plot to 74 5, the mean brother 77-45, and doing this for all arrays 
Diagram I. Resemblance of Brothers in Cephalic Index. 
67 68 6 9 70 71 72 73 74 75 76 77 78 79 80 81 82 83 8 4 85 86 87 88 89 90 91 92 93 
OBSERVED INDtX, FIRST BROTHER 
SLOPE of REGRESSION LINE =-49 
we get the series of points there exhibited. You will see at once that they lie 
almost exactly on a straight line. This is the well-known regression line. If 
* Zeitschrift fiir Morphologie u. Anthropologic, Vol. i. 1899, p. 372. My schoolboys from all districts 
give 78'9; 3000 criminals of adult age from all districts give 78'5 — there is not much room for sensible 
growth change in these juvenile and adult results. Observations of my own on actually the same 
growing children, show very small, if any change. 
Biometrika iii 
18 
