22 
PROFESSOR Iv. PEARSOX ON THE INFLUENCE OF NATURAL 
or group of constants, which is tlie same for all local races, then these constants must 
not be sought in the values of mean characters, degrees of variability, or of correlation, 
but in a system of partial regression coefficients, and the discovery of these is therefore 
of first class biological importance ; it is the classification of the characters into directly 
and non-directly selected groups, be., it is the discovery of the modus operaudi of the 
factors by v^hich the differentiation has taken juace. We are a long way from 
solution yet, but we may venture, perhaps, to admit a faint giimmer of light in the 
direction of what might seem the culminating jjroblem of the mathematical method 
as applied to evolution—the piecing together by quantitative analysis of the stages of 
descent. 
( 5 .) I will take now the application of the above results to simple cases ; but for the 
l^enefit of those who cannot easily follow the main principles of our investigation 
through the stages of determinant analysis, I Avill prove directly the proj^osition that ; 
the selection of an organ A alters the mean and variability of a correlated oi'gan B, 
a.nd also the correlation between A and B. 
Let the correlation surface for the tAvo organs be 
N 
iircT 
lO-o Al — rf 
-_A— - 
o-iO-.,(I-/-,o-) a-.i 
AA^iere N is the number of individuals in the general population before selection, and 
the subscripts 1 and 2 refer to the organs A and B respectiA^ely. 
liOt the distribution of the population after selection of the A oi-gan be 
.u,-/<,)- 
iir s, 
AA'here N — )i is the total destructi(m, /q the mean and 6’j the A'-ariahility of the 
})opulation AAuth regard to A after selection. Before selection this distribution AA’as 
= 
\/2 
N -iil 
e . 
TTO', 
Hence, the selection being random AAuth regard to the array of B’s corresponding to 
any A, ^ve have for the surface after selection 
Z = . X 
lor each array must be altered in tlie lutio of the corresponding z' to z^ 
This uiA'Cs for the surface in full 
Z=r 
n 
27rcr.-,.s 
o/l 
expt. + 
h‘'T‘'T 
o-q (1 — rf)) (1 — •ri 2 '-) 
1 
“k >^’2” .1 
-w) 
. (xlviii.). 
