44 
PROFESSOR K. PEARSON ON THE INFLUENCE OF NATURAL 
so that = roj, = r’ l:)efore any selection takes place. Let r, the correlation of the 
organs in tlie parent and offspring he supposed to be the same for both organs ; then 
V = Finally we have the coefficients of cross-heredity, and These 
must vanish if there be no heredity and no organic correlation, and should be perfect 
if both these are perfect. Hence we will take = rr' as a probable hypothesis.* 
With these values of the correlation coefficients we easily find 
/^13 — 
Hence from (Ixvlil.) and (Ixix.) we have : 
^ o r -1 .n I .'I n ■) <'1 n j 0 ^ 
-3“ = o-s' 11 “ + ^"prl = -u = H ^ H ) 
r' (1 — ?■-) + 
'34 _ ,,3 + ■ 
. (Ixxxiii.), 
. (Ixxxiv.). 
For simplicity, suppose the stringency of the selection to be the same for both 
organs, then : 
I ^ ^ 
1 - 
1 +/^f 
1 - 1 - 
If r = ‘4, and = yr', 
= r X 
1 + FtTPi ' 
1 4- fVpi’ 
(Ixxxv.). 
The following table Indicates the value of •—" 
Pi = L 
pi = • 8. 
pi = • 6. 
pi= -4. 
Pi= -2. 
0 
II 
y = l 
1 
1 
1 
1 
1 
1 
7 = 0-8 
-9680 
•9783 
•9872 
•9941 
• 9985 
1 
7 = 0-6 
- 9360 
•9565 
•9743 
•9882 
•9970 
1 
' 7 = 0-4 
- 9040 
•9348 
•9615 
•9823 
• 9955 
1 
7 = 0-2 
-8720 
•9131 
•9487 
•9763 
•9940 
1 
7 = 0-0 
-8400 
•8913 
•9358 
•9704 
•9924 
1 
It will be clear from this table .that if the selection be at all stringent, no reductioR 
of organic correlation in the parents will affect substantially the organic correlation in 
the offspring. 
On the other hand, if y be >1, we can have considerable modifications in the 
value of the correlation, even if the selection be stringent. 
* See * Roy. Soc. Proc.,’vol. 62, p. 411. I have cV good deal of daLa on the value of these cross^eredity 
correlationB now reduced and soon to be published. 
