136 
Biometric Constants of English Brain-weights 
great labour involved (each coefficient being found without grouping), and partly 
because we realized at once that the product of the diameters and the horizontal 
circumference had the highest correlations with brain-weight, and that accordingly 
these, and not the individual diameters or cephalic index, were the appropriate 
characters to use in the multiple regression equations, if the latter were not to be 
too unmanageable. The relationship of the head diameters to each other and to 
stature has already been determined for more copious and better material, and was 
accordingly hardly worth repeating here*. 
(a) We will consider first the influence of sex on the observed characters. 
We note that with two exceptions, the correlations of length of head with brain- 
weight and the product of the diameters with the horizontal circumference, the 
female has higher correlations than the male. Even in these cases the difference 
is within the probable error of the difference. This confirms the result already 
reached by Pearson and Lee that in civilised races the organs of the women are 
more highly correlated than those of the men-f. It will be remembered that this 
was attributed to more intense selection in the case of the male. 
(b) We turn next to the consideration of the influence of age on the other 
characters. We note at once that all twelve coefficients of correlation are negative, 
or the average value of each physical character dealt with decreases with age. 
We conclude that at any rate for a general hospital population, the physical 
characters all shrink with age. While the brain-weight shrinkage is most marked 
the auricular height is also very significant, then follows the product of the 
diameters, while the shrinkage of stature only comes fourth on the list. 
If age be measured in years the following are the regression lines for 
Gladstone's data for stature, together with those for Swedes deduced from the 
reduction of Retzius' data by Pearl j. 
Shrinkage of Stature luith Age. 
Males : English : 
Females : English 
,S'= - -0378 .4 -I- 69-02 (unit of stature = inch) 
,S'= - -0960 A + 175-31 (unit of stature= cm. ) 
Swedes: ;S'= - -0807 .1 -I- 173-42 ( „ „ „ ) 
S=--0G55A+ 66-05 (unit of stature = inch) 
,S'= - -1662 167-78 (unit of stature= cm.) 
Swedes: »S'= - -1008 .1 -H 163-51 ( „ „ „ ). 
From these we conclude that the English shrink in stature more than the 
Swedes with age, and that women of the General Hospital Population in both 
races shrink more than the men. The lines are represented in Fig. 1 below, 
which gives a fair idea of the etfect of age on stature. We now inquire whether 
* See for example Macdonell's results for 3000 criminals, Biomctrika, Vol. i. p. 202, and Fawcett 
and Pearson's results for 1000 Cambridge graduates, R. S. Proc, Vol. 66, p. 23. 
t R. S. Proc, Vol. 61, pp. 36.5. 
X Biometrika, Vol. iv. pp. 53, 54. 
