50 
PROFESSOR K. PEARSON ON TFTE TNEI^TteNCE OF NATT'RAL 
(c'n + 
(r,.^ -j- af, 
“b • ■ 
■ . (Cu 
+ t'o/) 1 
(Ai + '"til). 
{Coo + 0.0.,), 
{r-.,3 + ft.,,.) . . 
■ {c>n 
+ of 
(t;n + ap.l). 
+ tt. 2 ). 
(f:« + of . . 
1 
(t«i + 
f‘/i2 + 
• mi 
+ 0 , 1 , h) 
and A',„. the minor of its constituent. 
Now it will he clear from these results that as a general rule it is impossible for to 
he equal to H,.. In other words : The incjivldiial most frequently met with in any given 
selected community, i.e., the mediocre individucd, is not the individual fittest to survive. 
It is only in the limiting case of natural selection heing so stringent that one type 
of individual alone is able to survive, that the fittest class has a numerical majority 
over any other class of the community. This seems to me an important, algebraically 
almost self-obvious truth, and yet one which is very much obscured by the use of such 
a phrase as the “ survival of the fittest.” 
Of course, if there be continuous selection, or an environment so stable that the 
])rol3alnlity of survival remains constant for a long period, there will be a gradual 
ap})roach, never theoretically an actual identification of the mediocre and the fittest. 
But in actual nature the environment, at any rate so far as it depends on climato¬ 
logical conditions, must have a long period as compared with the vital and reproductive 
2 :)ei'iods of innumerable forms of life. A hard winter, a drought, a flood, a famine, 
a plague oi‘ epidemic of any kind, even if fairly stringent, will rarely, if ever, render 
the most frequently surviving individual identical with the individual who is fittest 
to survive."^ Still less will this identity take place in the many processes of artificial 
selection, which are loecoming and will more and more become valuable laboratory 
aids in our appreciation of the action of natural selection. The divergence between 
the most frequently surviving and the fittest individual is measured by the above 
fornndpe for the /:’s in terms of the H’s.t 
Tr» complete the solution, the «’s must be found from the e(iuations of type 
a,„. = l),,^ — and then from the n’s the s’s and p’s follow'- by the well-known 
determinants for multiple correlation : see our Equations (xi.) and (xii.). 
Throughout the earlier part of this memoir I liave used only the surface of selection, 
hut the above investigation wfill enable us Avhenever desired to replace it by the 
ju'obability of survival. I will illustrate this 1)V obtaining the fornudm suitable to the 
simpler cases. 
* We badly want a name for the selection which acts for a short time and rapidly modifies the adnlt 
population. It is practically the type of selection considered in this paper. It is epidemic or catastrophic 
in character. 
t The point is of considerable importance, for more than one influential writer has spoken of the result 
of natural selection as the preservation of the type the mortality of which is least under the given 
conditions. 
