302 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
A^ _1 = 
An, 
A ia , 
A 13 .... 
A. n , 
Ao 2 , 
a, 3 .... 
co 
Ag.i, 
Aoo .... 
1, 
P 12 j 
P 13 
Pzv 
1, 
P23 
Pa n 
Pi-2’ 
1 
Hence 1/A = sffiis 3 2 . . . R, where R is the determinant formed by the correlation 
coefficients with a diagonal of units. 
Further, if B n , B 22 . . . B 13 . . . be the minors of the A-determinant, and R n , 
Ro 2 , . . . R 12 , • • - of the R-determinant, we have (Salmon, loc. at.) : 
« n — B 11 /A / ' • — ^R 11 s FA 2 ' s Y' 
U'22 = B 22 /A^- 3 = AR.oSiVv 
a 12 = B 12 /A? J ~ 3 = AR 1 oS 1 2 ,s‘ 3 3 .s‘ 3 2 
. . Is* = R n /(R 5l 2 ) 5 
. . /si = R 22 /(R.v), 
. • / *Sp9o R^ 2 j (R<9 3 <9.d 
Thus, the correlation surface may be written 
. + 2R 12 M?+ . .. 
where n is the total number of sets of p organs and /x is a numerical factor denoting 
the number of {p -j- l) th organs corresponding to each set—in inheritance what may 
be termed a factor of reproductivity # —which is assumed to be practically constant, 
if not over the whole unselected correlation surface, at least over the selected 
portion of it. 
(c.) Selection of Parentages. Correlation Coefficients for Ancestry .—The results on 
p. 300 and p. 301 for the regression £ and the standard-deviation % when p correlated 
organs are arbitrarily selected about p means will, I think, be found to express the 
chief features of natural selection. A few special corollaries may follow here. 
Cor. 1.—If a single parentage be selected with mean h x above the mean of the 
general population and standard deviation s L , then > 8 1 = r 01 —, where r 01 is the 
°"i 
* The variation of this factor is, however, the essential feature of reproductive selection, as I shall 
show on another occasion. 
/jbii 
(27r)^s r s 3 s 3 . . . \/R 
-A (k u A + B 2 .,‘nf+ 
o 2U \ sf 
