SELECTION OX THE VARIABILITY AND CORRELATION OF ORGANS. 
49 
If we now substitute from the first two equations for the a’s we find : 
(Gi — ^n) ^’l “h (Cr 2 — ^>1-2) ^‘2 + • • • H“ 
= — 6,iH^ — — ... — — ... — . . (xciv.). 
Now let A be the determinant 
^11 
^in 
Oe 
^12’ 
CO 
^13> 
■ 
— j 
^21’ 
&22’ 
Os 
^23) 
■ Co., 
- h,, 
^31 
<^32 
^32’ 
CO 
CO 
■ Co„ 
— 
C«i 
C«2 
^«2) 
('-nz 
0(.35 • 
■ ■ c„„ 
^ HJl 
and A„„ the minor of its constituent. 
Then we have at once : 
A X = A,.i + . . . + 
-f- A ,2 (^21^1 “h ^ 22^2 H“ • • • “h 
4* + 63214 ^ + ^33^3 • • • + ^ 3 «H„) 
Or : 
+ -^ivi + 0(2H2 H“ ■ • • “h 0»JI,/). 
A X /q = (Z^iiAfi + b^.2^,.2 + ?>i3Ai.3 + . . . + ?>i,;A„,) 
+ Ho (^21^!1 4" ^h2^<-2 4" 4“ • • • 4“ ^2>Ani) 
4“ Hg (^giAp-i + ?>3 oA,. 2 4“ 4“ • • • 4“ ?t;«A,.;,) 
+ . 
4“ H// ('^^«lA,i + ^/.oAr'j 4“ ^,r.-Ar;i 4“ ■ • • 4" ^:iiAni) 
(xcv.). 
Thus ho is determined in terms of Ho, . . . H,,, which define the maximum 
frequency of survival. 
In a similar manner by making the j^roper changes indicated above we have : 
a' X H,^. = I’l (aiiA^j-i fi- OioA^i-o + ttiA^Z 4" • • • 4“ ''hn^'r?) 
4* ho [aoA'i-x + n22^^-2 4~ C^2Z^'r3 4" • • • 4“ (^2/A'rii) 
4“ hs («3iA j-i A ^h2^'f3 4" ^hz^'vz 4" • • • 4“ (^hiA'n) 
I 
“T. 
+ h„ {a„A\.^ + a^oA'a 4- — ... 4- «»«A'r«) • • • (xcvi.), 
where A' is the determinant 
VOL. CC.—A. 
II 
