SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
51 
(12.) Case (i.).— Selection of a Single Ovgan only. 
The original population is given by 
and the curve of survivors bv 
-- 0 ^ 
The jDrobability of survival is 
where we easily find, if S/cr == X, 
k = H/(l — X“).(xcvii.), 
s = N/\/l — X~.(xcviii.), 
^ _H2_ 
and Pjj = ^ .(xcx.). 
As an illustration consider a selection from modern French peasants, which should 
reduce the mean and variability of their cephalic index to those of the Libyan race. 
French peasants :— 
ni = 79'786, cr = 3'84I. 
Libyans;— 
m + H = 72-938, S = 2-885. 
Hence : H = — 6-848, X = -751 L. 
These give : h = — 15-712, s = 4-370. 
Thus for such a change as 7 points in the cephalic index to take place by selectioif''" 
we should have to make the “fittest to survive” of such a ridiculously low cephalic 
index as 64-074, and such a high variation as 4-370. 
We find = 51 -0474 njSi, 
and accordingly the probability of survival given by 
p = 51-0474 4 + 
N 
where N are the number of Frenchmen converted into n Libyans so far as cephalic 
index is concerned. 
I have purposely taken a somewhat extreme case of selection in order to illustrate 
how wfidely the most frequently surviving individual can diverge from the fittest. 
In this case, if the chances of survival (i.) of the fittest, (ii.) of the individuals most 
frequent after selection, and (iii.) of the individuals most frequent before selection, be 
Cj, C 2 , and Cg respectively, we have ; 
* This is, of course, supposing the change to occur by catastrophic selection and not by a continuous 
secular selection, see footnote preceding page. 
