SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
47 
Let the unselected population be given by 
Z = Zq expt. — . . . + 
+ 2 ci.,x^x. 2 -\- . . . + ‘2,Cu_i^„x„_-^x„} . . . (Ixxxvi.). 
Let the j^rol^ability of survival be given by 
P —— ^3 ~ . . (Ixxxvii.), 
where f is at present an unknown function, which is to l)e a maximum for 
a j — ^"3 ^-'>5 ^^3? • • * 
and, if the selection be at all stringent, to take rapidly decreasing values as 
x^ ““ a .1 Lt, ““ ^ 3 ? • ' * X ““ I^n 
take increasing large negative or 2 )ositive values. It will be clear then that the 
individuals who are “ fittest to survive,” i.e., have the smallest death-rate, are those 
whose organs are defined by : 
./■ I — /i^i, a.'^ — . . . X/i — 
and fitness generally will be measured by the closeness of the individual to these 
“ fittest ” individuals. 
In order to find the surface of survivors, immediately after the selection if growth 
be taking jjlace,"^^ or at any later stage if growth have ceased, we liave only to multiply 
Z by 2\ or : 
z = Z X p .(Ixxxviii.), 
is what in the earlier part of this memoir I have termed the selection surface. Now 
if this selection surface be itself normal, it will be of the form : 
z = Zq expt. — ^ -j- 633 (xo — + • • • 
+ {Xn — h„f + 26^3 (.Xi — by) (Xo — f> 3 ) 
— . . . + 26 „_i,„(x„_i — h„_y) (x„ — h,) . . (Ixxxix.). 
Here, as in the value of Z, all the constants hyy, 633 , . . . b„„, by^ . . . b„_y u are known 
in terms of the variations and correlations. If there be selection of q organs only 
out of the n, then b^^y ^^y . . . *^ 3 ,^+ 1 , • • • b„_y ,i, will all be zero. Since by 
Equation (Ixxxviii.) = s'/Z, it follows that the function f which defines the prob¬ 
ability of survival must be of the normal exponential type, or 
* I propose to deal in another memoir with the important problem's of slow selection during rapid 
growth, and of secular selection during several generations. 
