SELECTION ON THE A'ARIABILITy AND COPHiELATION OF ORGANS. 
we find at once 
crd(l-0/) • 
11 11 
¥ (1 - Fit) ~ (1 - Xj) “ ctG (1 - rj) ' 
1 Pu 
r,. 
13 
'13 
^D3 1 Pu 2]“3(t fis") ^l'^3(t~03") 
H, TLiV: 
§F (1 - Pu^) ^1^3 (1 - Fi 3^) (1 - r^G) (1 - iiGj • 
^"iFi3 
ct \ I ' TT r> 
JC: 
A 3 H 1 
H. 
^D3 a - Pi3“) ' 5,^1 - PiF) (1 - (1 - riG) 
(cuL). 
(civ.). 
(cv.). 
(cvi.). 
(cvii.). 
Let Si;Vi = X^, S^/'cTo = X^ measure the stringency of the selection, and 
/X = A/ ~ ^ measure the change in correlation."^ Then solving the above equations 
V X 
we find : 
p‘- = v'r->>^?vr^ . 
>r~5 
(cix.), 
(cx.), 
*•1 = 
N, \/l - iv,~ - (1 - qoO Xo'-* 
V 
— 
/I _ _ Xy - Xy + (1 - qy) Ayx/ + 2 qyioXiX. ' 
E.y/l - q y - (1 - q.^) V 
\/1 — /’jo" — Xy Xy Til — hs') ^i~X2" + ^qjqjXjX^, 
P} H-]^ 1 ^'13"^ ^3^ ~L ^*i 3 ^'i 3 XiX 2 I ^* 13 ^ 3^1 ^*13^1" 
13 
/3 
where 
Z’.T /q q.iXjXj — Zr, 1 — Xj" -j- h3^'i3AiA' 
O-o ~ 0-1 /3 CTj /3 • ■ ■ 
/3 = 1 — ?qy — Xy ■— Xy -fi (l — ) d” 
(cxii.), 
Similarly, if the original population and the curve of probability of surviving 
or of survival rates be given, xve have to find the selected population : 
l'i2 = 
.y/1 + V~K^~ y/I + ^“ 
(cxiii.), 
* If j'lo = cos d, ^12 = cos D, /j. = sill D / .sin d. The quantity D has been conveniently termed the 
“divergence" by Mr. Sheppard. Hence /a is the ratio of the sines of the selected and unselected 
divergences. The above formula for pu can be at once changed into one suitable for trigonometrical 
logarithmic calculation. Let sin xi = /xXj, sin 0.0 = yAo, and ^12 = cos 8 ; then, if A be the side of the 
spherical triangle, of ivhich ai, ao are the other sides and 8 the included angle : 
c-i.i 1 X _ 
sin (D - A) sin -J (D + A) 
