SELECTTOX OX THE VARTABILITY AND CORRELATIOX OF ORGANS. 
2 3 
Integrate this for every possible value of and we shall have the distriliution Ao and 
6 “o of X.2 or B after the selection of A. After some reductions we find for the frequency 
wliere 
n 
\' 'lir'l:, 
(xlix.), 
which gives the standard deviation of the indirectly selected organ, and tlie 
of this organ is given hy 
“ centre ” 
(U 
These are special cases of our results (xlv.) and (xxxvi.) above respectively. 
Further, returning to the correlation surface (xlviii.), the coefficient of correlation 
Tjo is the coefficient of x^x,^ divided by the product of the coefficients of x^ and xj. 
Hence we find 
r 
1-2 — 
(li.). 
Let r^.2 = sin = sin fi^en we have 
tan (f)^2 
- tan 0 ^., 
(lii.) 
This shows us that decreases with s^, or that iq.j decreases with s^, that is to say, 
the more intense the selection the less is the correlation. This in broad terms 
demonstrates the general principle that intensity of selection connotes a lessening of 
correlation. It is this principle which very possibly accounts for the fact that the 
more civilized races of man appear to be not only more variable but more higldv 
correlated than the less civilized, among whom the struggle for existence is more 
intense. It may, perhaps, also account for the skeletons of women of the civilized 
races having their parts more highly correlated than the parts of those of men."^ 
Lastly, it may well throw some light on the markedly plastic character of races 
which have been stringently selected with regard to one or a few organs only. 
As an illustration, suppose that the correlation between femur and tibia were 7, 
and let us investigate what would be the effect of reducing the variability of the til)ia 
by direct selection 50 per cent. Vbe find at once on substituting sjcr^ = ‘5 and 
?q,T = 7 in (li.) above that iq.j = ‘ 44 , or a reduction of about 37 per cent. This will, 
perhaps, be sufficient to indicate what immense changes must be made in the 
correlation of highly correlated organs whenever selection, artificial or natural, is 
stringent. It is important to notice that the change in the .size of the organ in no 
* See Lee and Peaesox, ‘ Roy. Soc. Proc.,’ vol. 61, p. .354; and Lee, ‘Phii. Trans.,’ A, vol. 196, p. 231. 
