156 
Biometric Constants of English Brain-weights 
characters several years' interval between the two primes. If we change the 
problem and ask, what is the brain-weight of a man of male mean age equal to 
the mean woman in physical characters, we find it is 1230 grs. or only 5 grs. 
more than the brain-weight of the mean woman. On the other hand the brain- 
weight of a woman of female mean age equal to the mean man in physical characters 
is 1319 grs. or only 9 grs. less than the brain-weight of the mean man. 
These differences are extremely slight, and would probably disappear entirely 
if we took another important cranial character like frontal breadth into con- 
sideration and gave the woman equal frontal breadth with the mean man and 
vice versa. On the wliole as far as present evidence goes, we can safely conclude 
that there is no sensible relative difference in the brain-weights of man and 
woman, the absolute differences observed are quite compatible with the differences 
which result from the relative sizes of tlie two sexes. In other words any 
argument as to the relative intellectual capacity of men and women based upon 
their absolute brain-weights applies equally to the thesis that the average big 
man has more intellectual capacity than the average small man, because he has 
on the average gi'eater absolute brain-weight. 
While our results thus apparently contradict those of Pearl on p. 51 of this 
Journal, the contradiction is only on the surface, for we liave been able to use 
a far more complete s\stem of physical measurements; and it is clear that the 
more measurements taken the closer is the approach to relative equality in the 
brain-weights of man and woman. 
(11) On tlie Gapitulo-Statural Index. 
Gladstone has introduced a quantity equal to 100 x \^Diametral Product/Stature 
or to 100P^/>S' in our notation and termed it the capitulo-statural index*. He 
shows that it decreases with stature — an almost necessary result of its algebraic 
form. As he has not discussed it with special relation to the Middlesex Hospital 
measurements, it appears worth while to discuss some of its properties and 
correlations. We will represent it by the letter and take 
Clearly, since it involves no new measurement, all its properties can be deduced 
from the biometric constants already tabled. 
W^e have at once 8^ = iP~''8P/S - PiSS/S"; 
whence squaring, summing and dividing by the number of individuals, we find : 
a/ = {i^S V/ -t- PV/ - lPScrj.cr,rj.s}/S^PK 
or V^^ = {WOaJ^/r^iV/+Vs^-^rpsVsVp (i). 
Again, multiply the value of above by SS, sum and divide by number of 
individuals, and we have : 
r^s-iir^sVp-VsW^ (ii). 
* Biometrika, Vol. iv. p. 115. 
