10 
PKOFESSOK K. PEAKSOX OX THE IXELUEXCE OF XATUKAL 
Retiuiiiiig to (xxv.), we remark that tlie terms of tlie second order in and x.., on 
Avliicli the correlation and variations depend, are not altered by a transfer to the 
centre and x.^ of the array. 
Hence l)y (ix.) and (xvii.) we have 
10 = — /--H— = — Kio/vHljiIloo 
(xxvii.). 
This is the partial correlation of the 1st and 2nd organs for the remaining n — 2 
Tans w 
Again, 
organs with constant values. 
> C.io — 
—"2/1 2\ 
2 ^12 ) 
Whence we easily lind from (xviii.) and (xxvii.) 
p p 
CT p = CTi 
1 EiiE,, - EiP 
—// o 0 h h 
> O' 0^ — O'.-" 
U 
2 P P P 2 ’ 
or, 
cr''i = o-j \/ltoo/lV, o-A = o-o \/lti]/R' 
(xxviii.). 
where IT'' is, as before, the determinant li without its first two rows and columns. 
These by (xxiv.), are what we should have reached by ignoring x.^ in finding (t\, and 
x^ in finding o-h. 
(3.) General llieoreni in Selection. 
To find the selected means, the selected variations and selected correlations, ivhen 
q organs are selected, naturcdly or artificicdli/, out of a complex of n organs. 
Let the selected group of q organs have their means raised /p, A, //g, . . . (some 
of tliese quantities may be negative) ; their .standard deviations changed from 
O'], o-o, . . . cTri to S], ig, . . . Sq, aiid their mutual correlations from ^\. 2 , 
• • • '^b?’ • • • Pa-’ • • • Piv Pvi‘> Piv • • • Piq^ ■ • • Pq-Ur 
The whole .system of n organs before selection will be defined by the means as 
origin of measurement for each organ, by the standard deviations o'], o',,, o'g, . . . o',,, 
aiid l:)y the coefficients of correlation Tv.^^ • ■ • • • • Gn-, ■ • • I'n-m- Let 
It l)e tlie determinant 
L ^12? • • • ^1// 
r.,], 1, 7'.,3, . . . 
^ n\'> ^ n'l’i ^ u'M ... 1 
and the minor corresponding to the constituent /',/t. Then the unselected 
population is given by the frequency surface of ecpiation (xix.). 
