PROFESSOR K. PEARSON ON THE INFLUENCE OF NATURAL 
which ai'e linear and for which the survival-rate is the same, they may be termed the 
“ critical lines/’ For one pair of angles the centre is now a “ centre of fitness,” for 
the other pair of angles a “ centre of nnhtiiess.” It seems to me that these critical 
organic relations may possess considerable biological importance. 
If the contour lines of tlie surface of survival-rates are parabolas, we have really 
only a limiting case of the centre at a very great distance. It is one in which the 
fittest (or most unfit) has no practical existence, but there is a direction towards 
which the rate of survival will be found to be always increasing or decreasing. 
If the contour lines of the surface of survival-rates are parallel straight lines, then 
so long as the deviation in one organ lias a certain definite relation to that in the 
other, the survival-rate will remain constant. In this case the survival-rate will 
fall uniformly in one direction and remain constant in the direction at right angles 
to it. 
All the cases I have given here can occur just as easily as the elliptic contour 
system of our illustration and diagram. Each is marked by quite definite biological 
characteristics, and Ave may, perhaps, class them as elliptic, hyjDerbolic, parabolic, 
and linear selection. Even if the surface of surviA'al-rates be not of the exponential 
quadric type discussed in this pa|)er, yet to the neighbourhood of each part of it 
this classification of selection types Avill apply. 
If Ave pass to more than two oi'gans, then similar considerations Avill apply ; Ave 
shall only be reproducing the geometry of quadric surfaces in space of three and 
higher dimensions. But before Ave alloAv oursehes excursions into the higher 
geometry of the surface of surviAud-rates, it seems desirable that Ave should obtain 
quantitative determinations of this surface by experiments in artificial selection. 
We shall then be better able to see Avhat part of our geometry Avill really be of 
service for the |)roblenis of natural selection. The field is too large to be cultiA'ated 
for merely theoretical intei'ests. We must fii’st determine Avhat parts of it are likely 
to have practical application to life as Ave find it, but of death-rates in the case of 
any living f(Arni but man, A\’e are at present sadly ignorant. 
