DATA FOR THE PROBLEM OF EVOLUTION IN MAN. 
227 
correlation are not constant for all the local races of a species ; some of the limits of 
this legitimacy will be considered in this paper. A very full discussion of the matter 
for the regression equations of the long bones in the case of twenty local races in 
man by Mr. Leslie Bramley-Moore is nearly completed. 
(iii.) The reconstruction of an organ in the living individual not measurable during 
life, from a determination of the size of accessible organs, and a knowledge of the 
correlation between these organs and the inaccessible organ obtained from measure¬ 
ments made on individuals of the same race after death. 
As an illustration, we may take the determination of the skull capacity from 
measurements made on the head of living individuals. 
In all the three problems cited above, we can only obtain 'probable results, i.e., 
we obtain the average value—generally not very far from the modal value of the 
second organ in a group of individuals with their first organ equal to that of the 
particular individual measured. The closeness of the result obtained is determined 
fairly accurately by the probable error of the array or group of individuals above 
referred to. If, instead of reconstructing an individual, we reconstruct a local race 
from a fairly large number of organs, this pi’obable error will l)e at once largely 
reduced ; but in doing this we assume tlie legitimacy of applying results obtained 
from one local race to a second local race. 
(2.) The whole theory of reconstruction is summed uji in the determination of the 
regression equations. It has been shown"^ that the most probable value of an organ. 
B, reconstructed from n oi’gans A^, Ao . . . . A,„ is given by the expression 
I ) I Lni ^0 
5 — Win = — ‘ 
(^1 ~ + p'”" ” (^3 + • • ■ + p^ 
J-Ioo *^1 -*-‘00 -*■'■00 
with a probable error 
= •67449o-ov/E/R, 
/ -^‘'00 
wher 
'•e 
= correlation coefficient of B and A^, 
A A 
59 59 95 
ctq = standard deviation of B, 
,, ,, 
niQ = mean of B, 
nir^ 
L^ CTfi 
Boo 
A„ 
= partial regression coefficient of B from A, 
and Pi is the following determinant, B.^^ the miiior corresponding to 7},^ : 
1, 
'^’oo 
A|-2» 
. . . 
Ad’ 
L 
1'],/ 
^ ?i0) 
1 //i) 
r,o . . . 
. . 1 
* ‘ Phil. Trans.,’ A, vol. 192, jr. 172. 
2 G 2 
(ii-), 
