18 
PROFESSOR K. PEARSOX OX THE IXFEUEXCE OF XATURAL 
Here in 8^ : p takes every value from 1 to rp and in 8^ : p' and p' every possible pair 
of values from 1 to q. Ecjuations (xlv.)-(xlvii.) fuJly determine all the recpiired 
quantities and form the fidl solution of the problem of selection. Before we see the 
remarkably simple forms they take for simpler cases, we mav draw some general 
conclusions of a most important character. 
In the first place we must distinguish l)etween directly selected and what we 
have termed non-selected organs. It would he better to term the latter indireetlij 
selected organs. SujDpose the recruiting sergeant were to pay attention only to 
stature and seek to form a regiment of men of ahout 5 feet 10 inches. He might 
have a real range of stature ahout G or 7 inches, hut he woidd strive to get men 
of ahout this height from the population. We will suppose that he did not consider 
chest-lmeadth, head-length, foot-length, hmgs or any other character. The distribu¬ 
tion of these “ non-selected” characters in the regiment would not he the .same as in 
tlie general population. Their means would liave changed by (xxxvi.) and their 
variabilities and correlations he given by (xlv.)-(xlvii.). In other words, an indirect 
selection would have taken place. A selection by stature would change foot-length 
and head-length and indeed every other correlated organ. Much the same result must 
occur in natural selection. If it l)e advantageous for a .species to have a certain group 
of its organs of definite size, falling within a definite range, and related to each other 
in a definite manner, then these clianges cannot take place without modifying not onlv 
the size, hut the varial^ility and correlation of all the other organs correlated with these, 
although these organs themselves be not directly selected. Practically this means 
all the other organs, for so far one can hardly say with certainty that we have come 
across any two characters in an organism which are uncorrelated. Many of those 
investigated are highly correlated, all appear to liave some correlation, even if it he 
very small or negative. 
M^e may therefore conclude as follows:— 
(«) The selection of any complex of characters or organs in an organism changes 
all the other characters and organs not directly selected. 
(G) If the change in the complex l)e continuous and progressive, the other 
characters will continue to he modified until the change in them is so considerable 
that selection begins to act directly upon them also. 
(c) The changes noted here are not confined to the average value of a non- 
directly selected character and to its variability ; the correlations between non-directly 
selected characters and the correlations l)etween directly and non-directly selected 
characters are also both changed. 
(f/.) If local races have been produced by selection from a common stock, it will 
be impossible to look upon correlation as a criterion for species. Every selection will 
modify such correlation, and it has no greater fixity than either tyjDe value (mean) 
or variability (standard devdation). 
The whole of these statements will I)ecome more manifest as we apply our geneivd 
