58 
PROFESSOR K. 1‘EARSOX OX THE IXFLUEXCE OF NATURAL 
from which we could produce 1000 Frenchmen by a catastroj^liic selection. In this 
case the surface of survivals is simply oldained by inverting p, and, if N' he the 
number of Aino, n = 1000 = recpiired number of Frenchmen, we liaA’e ; 
p = 
n 
y‘ 
208,425 X 
e'‘ I (4-4115)2 (-9775)2) 
Here p' gets larger as we go away from the centre of the surface of survivals, 
and we must therefore make the French limiting ellipse just touched internally by 
the contour line of the surface of survivors for which p' = 1. The major axis of this 
contour line for p' == 1 was found liy a graphical process to Ire about 33‘91. This 
gives for k.^ 
K, X (4-4]]r)) = 33-91, or ko = 7-6867. 
Thus : 
= 1 = 
1000 1 
208,425 X 
- (7-6807)- 
/ 5 
leads to N' = 32,460,000,000 about, or we should want upwards of 32,460,000,000 of 
Aino to produce the 1000 Frenchmen. The bounding contour line of this number of 
Aino has a major axis of 15-890 centims. about, and touches the French limiting- 
contour in the point in which it is touched liy the j)' = 1 contour of the surfiice of 
survivals. 
Now the difterence between these two unselected po])ulations is very great. We 
see that to get the Aino a very great number of Frenchmen woidd have to be 
exterminated, about 7000 for each Aino selected; but to get the Frenchmen from 
the Aino an appalling number of Aino w'ould have to be destroyed, ujiwards of 
32,000,000 for eacli Frenchman selected. Even if tlie selection were not catastrophic 
hut s})read over centuries and centuries, we must recognise what a large consumption 
of life there must lie—individuals destroyed without progeny'^—if we are to suppose 
any highly civilized race like the French produced liy selection from an apparently 
primitive ty})e like the Aino. Indeed, the return journey in this case seems much 
easier than the upv-ard ascent. Beyond all this we have only made French and 
Aino alike for two organs, and only for one character of each of them ! Allowing for 
our conventional limit to the population, allowing for the fact that our Aino data are 
drawn from a very limited })opulation of remarkably small varial)illty, it seems very 
improbable that the Frencli have ever been produced l)y selection from a primitive 
race at all resembling the Aino. Tlie fact that the Aino could be so much more 
easily obtained by selection from the French seems to indicate that they are rathei- 
* Of course, with a secular selection spread over many generations, it is hu’gely the potentiality and not 
the actuality of life Avhich is destroyed. Still, while the gross numl)cr killed among a small ja'iniitive 
community may not he large, the death-rate must still be immense. I hope to return to these points 
when dealing with secular selection as distinguished from catastrophic selection. 
