14 
PEOFESSOK K. PEARSON OX THE INFLUENCE OF NATUEAl. 
coefficient of the and organs after selection, then if u and v be selected organs, 
= yo„,.; if they be not both selected organs, then it has to be found. Let be 
the minor corresjoonding to the constituent c,,v in the above determinant, then by 
(x ) and (xiv.) 
.(xxxvni.), 
and 
S,S,IV, = ^.(xxxix.). 
Now let us write for brevity a,,„ = D„„/A and = L>,,„/A. Clearly as long as u and v 
are less than q a„„ and x,,,. will both be known, i.e., are equal to s} and s„Si.p,__. 
Now by a well-known property of detei'ininants 
~b “b ^3:?+l^l3 “b • • • “b ^q.'i+\^vi ~b ^?+i.y+i'^i,y+i “b • • • "b 0 
^1,9 + 2^11 "b ^2, ~b *^ 3 . 9 + 2®^13 ~b •••■!" ^q,q+Z^\q “b ^9+l,9+2'^l>9+2 ~b • • • “b ^/;,9+2^1« ^ 
' 1, //^ll 
+ 
^2, 
12 
+ 
+ 
+ 
^qu^lq 
“b ^q+l,it 
a 
1,9+2 
+ 
+ 
= 0 
(xl.). 
Comparing these equations for the n — q unknowns <^i,q+i, “1,9+2 • • • “i« with (xxxiv.) 
for finding . . . Xp, we see that they are absolutely identical if we change 
Aj, ho . . . hq in the latter into a^-^, . ■ . cl^i- Accordingly the solution is given by 
(xxxvi.), or we have 
a 
1.9+1 ~ 
“1,9+2 
I fi(g+l)l. 9 -H “ 9+1 
1 h (2 "t 1)2+1,9+1 “1 
(2 ~t 1)3,2+] “2+1 gj _j_ 1^ (2 ~t 1)2,2+1 “2+1 
h (2 U 1 )y+l,2+l O’;, ~ h (2 ”t 1)9+1,9+1 <yq 
E( 5 ''P -^)i,9+2 “ 9+2 
h (2 "t 2)9+3,9+2 O’! 
a 
11 
+ 
11 (2 ~t ~)2.2+2 “ 9+2 I I h (2 ~t -\,q+i 0'2+2 
2+2 “2 ’ ’ ’ h(2 + -)2+2.2+2 “2 
E {q + 2 j^+3_ 
^1, n 
Cn It I 
R o-o 
" 4 "- - — — OL 
h “2 
19 
Provided v be < q -b 1 we might equally well have used a,.,, a^.o, 
we conclude that if r he <5+1 and u be > q, 
Hence 
Fv (2O1,, o-„ Fi qiC) o„ aq 
I1(«)»hO-^ E(2l)„„cr3 
+ 
E {U)g 
K(«), 
a,, 
«» q 
. (xli.). 
Or, substituting the known values of a^.^, a,..,, . . . we have for r < -|- 1 and 
u> q 
