260 
DR, A. LEE AND PROFESSOR K. PEARSOX OX 
easily l^e demonstrated. Or again because English women have a mean brain weight 
of 1235 grs. and French women of 1142 grs., are we to argue that Engli.sli women 
are intellectually abler than French women? The fact is that to solve a problem ot 
this kind we ought to keep within one fairly ecpially nourished class, and within one 
local race and actuallv correlate brain size and alnlitv. I do not see how this can he 
done for brain weight, hut it seems to me quite possible for the capacity of the brain 
chamber estimated from external measurements. 
(15.) Conclusions. I liave now completed the discussion of the three problems I 
nroposed to investigate. It will he seen that the accuracy of predictions depends 
sensibly on two factors: (i) the existence of suitable data upon which the regression 
formulae can he based and (ii) the number of measurements used to form an estimate. 
Thus in the third fundamental problem we do not get as good absolute results as we 
miglit hope to do, because we have not really at present available the best data 
jcossible. Again in the first fundamental problem we cannot expect to reconstruct 
the capacity of the individual skull without a fairly large average error. For it is of 
the very essence of the principle of variation, on which evolution itself depends, that 
in any population we should have an array of skulls with the same length, breadth, 
and height, and yet having within certain limits a variety of capacities. All we can 
hope to say is, that with such a length, breadtli and height such a capacity is most 
frequent. When we come to averaging a series, then we shall determine with far 
greater accuracy the mean of an array. Here the nature of the problem is, however, 
modified. Tlie question is now how far can we a])ply results deduced from one local 
race to a second. We want in fact a “ panracial ” regression formula to replace our 
intraracial regression formula. As it is imj^ossible to find such a regression formula for 
the primitive stock from which man may be siq^posed to be derived, we are compelled 
to take the regression formulae which are least changed as pass from race to race. 
The mean formula thence derived appears to give excellent results, when applied to 
detei inine tlie capacity of very diverse races. While I do not profess to have solved 
the problems proposed to the degree of accuracy which might be obtained with wider 
data and measurements made ad hoc in the anatomical school, I yet consider that 
1 have given practical solutions to the following prolfiems :— 
(i.) The reconstruction of the capacity of the individual skull, when this cannot be 
measured directly. This is done with a mean error of 3 to 4 per cent. 
(ii ) I'he determination of the mean skull caj)acity of a race vhthout the use of 
sand, seed, or shot, to a degree of accuracy comparable with that of the direct 
method owing to the personal equation of the measurers even when using the 
same method of direct determination. 
(iii.) The determination of the skull capacity of living individuals with a degree of 
accuracy sufficient to determine wlietlier skull capacity is or is not closely 
correlated with intellectual powei'. 
