K. Pearson 
121 
paper* that no sensible modification is made in this result if allowance be made 
for either weight or stature. I shall now proceed to consider the data more in 
detail. 
I shall first inquire what amounts of intelligence can on the average be 
accounted for by differences in head measurement. The average correlation 
between head length or head breadth and intelligence is '11 ; that for auricular 
height is distinctly lower, and we may leave it out of consideration. The varia- 
bility cT; in intelligence for all three classes is somewhat under 100 raentaces. 
The variability cr in a head measurement is roundly 5 to 6 mms. Hence the 
regression coefficient = Vijj a^/ a = 2 mentaces per millimetre. Now the intel- 
lectual range from the average slow man to the average specially intelligent is 
(see Fig. 1) at least 200 mentaces, or we should require a difference in head 
measurement of at least 100 mm. to account for this intellectual difference. Now 
in adidts there is at most huo millimetres difference between the head measure- 
ments of the average slow and the average especially able classes. In children, for 
some measurements, the average difference between the Quick Intelligent and the 
Very Dull may amount to 5, but is more usually 2 to 4. Even if we add together 
the result of two or three separate measurements, supposed independent, we shall 
not obtain a difference of more effect than 6 to 10 mm., and this depends upon our 
neglecting the sensible correlation of head measurements. Thus, at a maximum, 
size of head might account for 12 to 20 mentaces out of the 350 which separate 
the mean of the specially able group from the mean of the very dull group. The 
millimetre which separates the head measurements of the slow boy from that of 
the intelligent corresponding to 2 mentaces, — or if supposed additive for several 
measurements, to 6 or 10 at most, — is of no effectiveness or value for purposes of 
prediction compared with the other causes which lead to an average difference of 
120 mentaces. Differences in size of head will not account for at most j\, and 
probably not as much as J^y, of the observed differences of capacity whether between 
adults or between children. 
These results are to some extent exhibited graphically in Figs. 5 and 0. In 
Fig. 5 we see a drop of about 2 mm. in head length and one of about 1 mm. in 
head breadth in the Cambridge graduates as we pass from one end of the scale to 
the other. But the mean head measurement of first class honours men has for 
length a variability of 5"89 mm., or a quartile of about 4 mm. In other words, 
while 25 per cent, of able men have head lengths under 191 mm., 25 per cent, of 
slow men have head lengths over 197 mm. The average specially able man is 
195 mm. and the average slow man 193 mm. Or again, some 44 per cent, of very 
able men have heads smaller than the average slow man and some 44 per cent, of 
slow men heads larger than the average specially able man. This order of 
numerical relationship holds for the whole range of the characters dealt with, and 
in view of it we see how idle it is to assert that head measurements can be of any 
service in the prediction of intelligence. In the case of Fig. G, we see that for 
* li. S. I'lvc. Vol. 71, pp. 100—114. 
Biometrika v 16 
