SELECTION ON THE VARIABILITY AND CORRELATION OE ORGANS. 
25 
Further, taking AP as our unit, AN' = I — and QN^ 
from (Ixix.) : 
s/ = ct/ (AN^ + QN^) = cr/AQ‘1 
/’j.P X Hence, 
Therefore if Acr^ in the diagram be taken equal to and QNj be drawn parallel 
to PcTj, we shall have AS^ = Ng, or we can scale off the reduced variability. 
Thus the diagram enables us to see at a glance the reduction in correlation and 
variability. 
(6.) Let us now write down the results when an organ A is selected out of a group 
of three organs. A, B, C, whose constants are marked by the subscripts 1. 2, 3 , 
respectively. Let = s^/a-i, and be represented, when required, by cos Xi- Then 
we find from (xlv.) (xlvii.) : 
V 
II 
^2 
- (1 - 
\ 
— ( 1 — 
/^i 
\ ^ 
\ 
0-.J 
rig'^ \ = 0-3 {1 — siiF xi 
13 i 
cos Xi cos $^2 
^13 {!_(!_ _ silP cos^ 0 ,, 
COS Xl cos ^^3 
La — 
{1 - (1 - _ gpp cos2 
]3 
1*23 — 
('’23 Ls"'’i 2 ) (1 o ) + 2 q 
cr. 
_ cos 6^23 4 - siid Xi cos 0 ^.;^ cos 
\/(l — siid Xi COS' ^12) (1 ~ ^hd Xi cos^ 0 ^^) 
where, as before, we write = cos 0 j,j. Let us also write = cos and 
sin Xi cos 0^.2 = cos cqo’ Xi ^13 = ^^i3- 
Then we can replace the above results by 
= cTg sin a^o, 
cos 0^3 = cot Xi cot cqo, 
cos ^23 — cos fl ,2 COS 
S3 = 0-3 sin cqg, 
cos 0^3 = cot Xi cot fqg. 
cos 0.,.. = 
VOL. CC.—A. 
Sin sin «i3 
E 
(liii.). 
(hv.). 
(Iv.). 
(Ivi.), 
(Ivii.). 
