SELECTION ON THE VARIABILITY AND CORRELATION OE ORGANS. 
5 
V V 
— n> 
— 'S.cr, 
R (?()„ 
P\t< 
+ 
E ( zpa 
R (u)„ 
P-lr — + • 
(To 
+ 
E {u \ 
E {u)„. 
+ 
+ 
ll pllpqu ^ 1 / 1 
E 00 - 
(xli.)'”®. 
The next stage in our work is to find a^,„ when both v and u are > q, and also 
when V = u and both are > q. This is done at once by substituting the minors a„i, 
a„.2, . . . »^i,q ■ • • in the equations formed from the last p— q lines of the determinant 
(xxxvii.). 
We obtain the following system ; 
^'1, y + “T ^' 2 , q+\^ii 2 
^\,q + 2^u\ H“ ^‘l,q+2'^ii2 
“h + ~t~ • • • “1“ ^ q,q + \^i>q “h (^q+2 + i^ir,q-\-\ 
“h “h • • • “h ^q,q+2'^itq ~l~ ^'q + \^q + 2^ii,<i + \ 
• 1 ^n,q-\-\^Uit 
+. • 
' • “ 1 “ 
= 0 
= 0 
' 1. u^ul 
+ 
wl + 
C;5_„a 
//3 
+ . . . + c 
H^ltq 
~h ^q + \,i'^ii^q+\ "h 
I I O';j„0C„y I • • • I ^q^n'^nq 
Cl //Ct,, 
uCt,, 
+ 
q+ 1, n^n, q + 
1 I • • ■ “h - 0. 
These are identical with equations (xL), exce})t that the equation wilh tlie 
coefficients Ci,,, c.,,,, . . . has unity instead of zero on the right-hand side. Hence 
we see that > q) will be the same function of a„i, . . . oi-uq that x\, is of /q, 
/q, . . . /oy in equation (xxxvi.), hut it will add to this a function of the last p —q 
system of r’s, the c’s 
^’'A'/+n + 
R/+ia/+2) 
c 
«, 7+3 
^q HI + 
Whatever this function may he we will represent it for the time l)y y„„; we notice 
tliat it is independent of the selected variations ^q, .q, . . . .sVy, the selected means /q, 
A.i, . . . /q, and the selected correlatioii coefficients Piz-> ■ ■ ■ Pq-i.r If depends 
only on the characters before selection. 
We thus have 
E ((;)n. o-,. 
E (rgj. 0-,, 
\'"/ll' I ''V . 1 
^^,n- — Jh,: ~ 1 p y . ^ ««1 + p , . ' -j- . . . + 
LE(c)„: o-j R(r)„o-o E 
uq 
Now the system . . . a,„^ can he fmnd from (xli.), since a,,,,,,, = wliatever 
v! and n." be. 
