J. Blakeman 
141 
that in the criminal population there is no shrinkage of head breadth, perhaps a 
slight increase, with age, and a sensible inci'ease, not a shrinkage, of head length 
with age. Unfortunately we could not test the auricular height change. It 
follows from this that the shrinkage of head size with age appears to differentiate 
the General Hospital from the criminal and very possibly from the normally 
healthy general population. Hence in determining the probable bi'ain-weight 
from size of the head in a normal population probably little stress ought to be 
laid on any change of the diameters and therefore their product with age. It is 
possibly in our case a result of the increasing amount of chronic illness in the 
older members of the General Hospital Population. The possible shrinkage oi 
the head with age in the general population would form an interesting subject for 
investigation. 
Of course when the three diameters have negative correlation with age, we 
should expect to find, as we do find, that the product would shrink with age. 
We have no data to compare with the observed shrinkage of the horizontal 
circumference with age. 
(d) The correlation of the horizontal circumference with stature, "33, is we 
believe new, but is very much what we might have anticipated. So also is the 
correlation, SI, of stature with the diametral product. Thus Macdonell found for 
3000 criminals the correlation of stature and maximum head length, '34, of stature 
and maximum head breadth, "18, and of stature and face breadth, -35*. 
With regard to the correlation between the horizontal circumference U and 
the product F of the three diameters L, B, H, we note that if F be a coefficient 
of variation we must have : 
rpu = ( ruL + Vb ruB + Vh run)/ Vp 
= (2'957v^ + 3-62rj,5 + 3-39/v^)/7-68 
for English males from Table II. Now we are unacquainted at present with any 
determinations of Vij^, Tuj^ and rujj, but in round numbers rm and Vfj^ cannot 
differ much from •? and rjjjj from 'o. Substituting we find Vpu = "82 ; so that the 
observed value '83 for males appears quite probable. A similar investigation gives 
•79 as against the observed "80 for females. 
(e) We turn lastly to the correlations between brain-weight and the other 
characters. 
We see in the first place that cephalic index is the least important of these 
correlated characters, and further that its correlation with brain-weight varies 
markedly from male to female. It is within the limits of random sampling zero 
for men, and has the quite sensible value '2 for women. We have no similar data 
to compare our results with. AH we can do is to consider the correlation of skull 
capacity with cephalic index, which has been determined in a number of cases. 
The irregular and divergent values of this correlation were first pointed out by 
* Biometrika, Vol. i. p. 202. 
