SELECTION ON THE VAEIABILITY AND COERELATION OF ORGANS. 
57 
This will enable us to determine our conventional boundary to eftective population. 
Now let us refer our non-selected and selected populations to their centres and 
princijDal axes. 
We find for the contour curves :— 
Hnselectecl Population 
(/.o, French). 
Selected Population 
{i.c., Aino). 
Surface of Survival 
(f.c., Rate of Survival). 
;c centre (femur) .... 
ij centre (humerus) . 
tan 0 (slope to a’). 
Principal axes g 
1 in 1000 limit/* ’ 
(_ kL . 
45■228 
.3.3-010 
•601,3775 
2-7338 
•7197 
10-1615 
2-6750 
40 - 770 
29-502 
•670,1454 
2-2514 
•5808 
8-3682 
2-1588 
27•382 
17-155 
•807,3371 
4-4115 
•9775 
Referred to its principal axes, the rate of survival is now 
p = 208,425 ^ e 
' 
04-41 (-O??')) 
2 \ 
Suppose we require to get at least 1000 Aino out of the French popidation, N, then 
n = 1000. Now suppose the Aino limiting ellipse drawn, then the French population 
must be sufficiently large to give the individuals Inside this ellipse. Now y> gets 
smaller as we e:o further from the centre of the survival surface. Hence the contour 
line of the survival surface corresponding to y) = 1 must l:)e touched externally by tlie 
limiting contour of the Aino population, in order that we may get at least 1000 Aino 
out of N Frenchmen. Now, hj a graphical construction, I find the major axis of tlie 
ellqAic contour line of the .survival surface which touches tlie Aino limiting ellipse, is 
about 11'44. This gives for the parameter Ky of this ellipse, /c, X 4'1 149 = 11*44, or 
Ky = 2*5932. Whence ; 
p., = I = 208,4-25 ~ e-se-snw 
gives the greatest po.ssible value p and the least possible value of N. Numerically 
this gives us N = 7,200,000 about, or we should want more than 7,000,000 of 
Fi'enchmen to obtain our 1000 Aino by a catastrophic selection. The actual bounding 
contour line of this least possible number of Frenchmen'^ has for its major axis 
15*285 centims., and it touches the Aino limiting ellipse at the point where it is 
touched by the .survival contour p = 1. 
Now let us turn the problem round and ask what is the least population of Aino 
* Tlie least possible to reproduce the jViiio, as far as femur and humerus are concerned, to 1 in a 1000 
of the population. 
VOL. CO.—A. 
r 
