SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
1 i 
2 = constant X expt. — ^ ^ 
Ivv I qQ/ /Itw 
R a/J ^ R CT„< 7 , 
(xxix.). 
For brevity, we can also write this in the form 
2 = constant X expt. — i {S^ {cj,px/) + 28 ^ {cp^pX,^)] . . (xxix.)'>'^ 
Now consider for the time only </ + 1 organs—namely, the first q organs and the 
Hf' organ (m > q), and let ns write K {u), if u he > q, for the determinant : 
Fv [u) = 
r, 
21 ) 
n,, 
23 ) 
1, 
^ 72) ^ q 3 ^ 
v.li ^ u 2 ) ^ « 3 ) 
^ I7) ^ 1 1 ' 
r-zr. r.p. 
3 u 
1, 
f *„ 
r. 
VJp 
(xxx.). 
Then if F {u)p'p" 
7 . 1 '' (^ 0 /''?'' ^ 
be the minor corresponding to the constituent T^ipu, and if 
the distribution of the <7 + 1 organs will be given by the 
^ R {u) (j.p, (Xp 
frequency distribution 
2' = constant X expt. — {S, {hp'pXp?') + '2^.2{bp,pnXp,Xpr}j \ . . (xxxi.). 
S[ being a sum for every value of j) throughout the ^7 + 1 organs, and S,, for every 
pair of values. 
Now let the first q organs l)e given values /q, /q, ... Itrj, then the mean value of .t„ 
will l)e given by 
X „ — 
'i-th + i‘ h + ■ ■ ■ + f h,,, 
'-'HU '-'hH '-'HU 
R (?() 
Ft ^?t 
R {21).,, 
R {a),, 
f I 7 , 7, 
'^1 I T) / \~ \ I.y / \ 
l^R ('?()«,( (Ty R 
Now these coefficients can be found at once if q he known. 
For example : 
(xxxii.). 
< 1 = h 
q = 2, 
q = 3 , 
R {u\ 
qu 
R {u), 
R (w)i 
= r 
lU 5 
1 - r,f ’ 
R («)«» 
' 'III 
1 “ r, 
and 
R '12 \ JUH ^ ‘ 12 
Iq(y)i), _ (1 - r,i) - + r.^3 -f 
R {n)nu 1 — ri./ — r.^- — 
1^ 1 F ( 
— and — - , - can 
R (u). 
R {uh 
be written down by symmetry . (xxxiii.). 
