32 
PROFESSOR K. PExVRSON ON THE INFLUENCE OF NATURAL 
dilFers from zero by terms of the first order in sjcr. Hence, when selection is intense 
( 5 / 0 - small), we may neglect the former as com23ared with the latter, and we have 
thus the basis of a method of approximation very useful in some cases. 
I have not yet succeeded in giving a geometrical interpretation to the above 
formulae, but have little doubt that it would be quite easy if the “ spherical ” 
geometry of four dimensioned space were more familiar to me. It will suffice to 
observe that it is easy to find cases in which the correlation of a non-directly 
selected organ with a directly selected organ, or with another of its ovm class, can 
be reduced, destroyed, increased, or reversed. In fact, all our previous warnings as 
to the caution necessary in avoiding unintentional selection in collecting material for 
testing correlation remain in force, and, indeed, are emj^hasised. 
The following illustrations will indicate the kind of jDroblems which may be 
attacked by such formulm as the above :— 
(8). Illustration I. — Influence of a Selection of the Long Bones of the Leg o)i the 
Long Bones of the Arm, and on the Relation of the Leg to the Arm. 
A numerical example will throw light on the apjDlication of the above formulm, and 
effectively illustrate the manner in which a selection influences size, variation, and 
correlation. 
Consider the long leones femur, tibia, humerus, and radius, indicated by the 
subscrqits I, 2, 3, 4 resjrectively, and let m^, rn^, nig, 7/q be the mean values in 
centimetres. Then the following numerical values are given in a memoir by Miss 
Alice Lee and myself:—* 
French 
Aino (J. 
TOi 
45-23 
40-77 
llhi 
36-81 
33-89 
m 3 
33-01 
29-50 
Mi 
24-39 
21 -55 
0-1 
2-37 
1-90 
(To 
1-80 
1-67 
0-3 
1-54 
1-34 
0‘4 
1-17 
1-06 
>12 
-806 
-827 
>'n 
-842 
-858 
>'ii 
-744 
-789 
In 
-860 
-745 
'>' 2 i 
-780 
-865 
I'Si 
-845 
-776 
* ‘ Roy. Soc. Proc.,’ vol. 61, p. 343 et se(i. The correlations are not worked ont for exactly the same 
lengths in the case of the two races, but the numbers will serve quite well for the purposes of illustration. 
