SFJiECTTON OX THE YARTABTLTTY AND CORREI.ATTON OF ORCANS. 
55 
p = 208,425 - expt. - ^ ‘222050 (.r + 17-8404)2 + -320,900 (vy + I 5-8547)" 
- -480,450 (x + 17-8404) (?/+ 15-8547) ^ 
Now it is clear that if we wanted by a “ catastrophic ” selection to convert the 
French into something resembling the Aino, we should have to give the least deatli- 
rate to those French with femur corresponding to 7n^ -|- and humerus to m., + k.,, 
or to the dwarfs with femur = 27-382 centims. and humerus = 17-155 centims. I 
By no other means coidd we shift the modal value of the French population down as 
low as the Aino modal value. The physical meaning of this is that we have lieen 
compelled to put on an excessive death-rate for the bigger Frenchmen. 
An interesting point of our work is that 
l\= 1-2514 H, A 3-4971 FI., 
k. = - 1-0269 Fl^ + 5-8242 H., 
whence we see that while a selective reduction of humerus is far more effective in 
reducins: hotlr femur and humerus centres of survival than a reduction of femur, a 
selective reduction of femur occurring contemporaneously with that of the humerus 
actually tends to raise the centre of the humerus, i.e., the coefficient of H, is 
negative. 
Now let us consider the frequency of survivors per unit length, say centimetre of 
femur and humerus, at different points. The surface of survivors, i.e., the Aino 
population, is 
1 1 ( Cv - 2ri, (x - H,) (V - HO r.v - H..r ) 
„ __ ^ ~ “No 1 
~ 27rV2,v/(T-q,2) 
If we put X = 0, 7y = 0 we have the frequency after selectioi: of the original 
population type ; if we jDut x = y = H. we have the frequency after selection of 
the new population type ; and if we put x = k^, y ■= ly, we shall have the frequency 
after selection of those best fitted to survive. If these frequencies he Cg, n., Hj 
respectively, we find on substituting the numerical values that 
Hi : m : h, : : -11 7/1 (T^ : 1 ; -032289. 
Thus the most frequent type of the new population is iiow about tliirty times as 
frequent as the old most frequent type, while the type most fitted to survive has 
practically no existence at all. It probably lies outside the actual boundary of the 
French population. 
Here really arises the question as to how we are, in any actual problem, to fix the 
ratio of 7i to N, or, what amounts to the same thing, to fix a practical boundary to a 
given population. Such a boundary must be conventional, but I think that for 
